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http://rosettacode.org/wiki/Barnsley_fern | Barnsley fern |
A Barnsley fern is a fractal named after British mathematician Michael Barnsley and can be created using an iterated function system (IFS).
Task
Create this fractal fern, using the following transformations:
ƒ1 (chosen 1% of the time)
xn + 1 = 0
yn + 1 = 0.16 yn
ƒ2 (chosen 85% of the time)
xn + 1 = 0.85 xn + 0.04 yn
yn + 1 = −0.04 xn + 0.85 yn + 1.6
ƒ3 (chosen 7% of the time)
xn + 1 = 0.2 xn − 0.26 yn
yn + 1 = 0.23 xn + 0.22 yn + 1.6
ƒ4 (chosen 7% of the time)
xn + 1 = −0.15 xn + 0.28 yn
yn + 1 = 0.26 xn + 0.24 yn + 0.44.
Starting position: x = 0, y = 0
| #Yabasic | Yabasic | 10 REM Fractal Fern
20 LET wid = 800 : LET hei = 600 : open window wid, hei : window origin "cb"
25 backcolor 0, 0, 0 : color 0, 255, 0 : clear window
30 LET maxpoints=wid*hei/2: LET x=0: LET y=0
40 FOR n=1 TO maxpoints
50 LET p=RAN(100)
60 IF p<=1 LET nx=0: LET ny=0.16*y: GOTO 100
70 IF p<=8 LET nx=0.2*x-0.26*y: LET ny=0.23*x+0.22*y+1.6: GOTO 100
80 IF p<=15 LET nx=-0.15*x+0.28*y: LET ny=0.26*x+0.24*y+0.44: GOTO 100
90 LET nx=0.85*x+0.04*y: LET ny=-0.04*x+0.85*y+1.6
100 LET x=nx: LET y=ny
110 DOT x*wid/12,y*hei/12
120 NEXT n |
http://rosettacode.org/wiki/Babbage_problem | Babbage problem |
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.
For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].
Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.
| #Gambas | Gambas | Public Sub Main()
Dim iNum As Long
For iNum = 1 To 100000
If Str(iNum * iNum) Ends "269696" Then Break
Next
Print "The lowest number squared that ends in '269696' is " & Str(iNum)
End |
http://rosettacode.org/wiki/Balanced_brackets | Balanced brackets | Task:
Generate a string with N opening brackets [ and with N closing brackets ], in some arbitrary order.
Determine whether the generated string is balanced; that is, whether it consists entirely of pairs of opening/closing brackets (in that order), none of which mis-nest.
Examples
(empty) OK
[] OK
[][] OK
[[][]] OK
][ NOT OK
][][ NOT OK
[]][[] NOT OK
| #360_Assembly | 360 Assembly | * Balanced brackets 28/04/2016
BALANCE CSECT
USING BALANCE,R13 base register and savearea pointer
SAVEAREA B STM-SAVEAREA(R15)
DC 17F'0'
STM STM R14,R12,12(R13)
ST R13,4(R15)
ST R15,8(R13)
LR R13,R15 establish addressability
LA R8,1 i=1
LOOPI C R8,=F'20' do i=1 to 20
BH ELOOPI
MVC C(20),=CL20' ' c=' '
LA R1,1
LA R2,10
BAL R14,RANDOMX
LR R11,R0 l=randomx(1,10)
SLA R11,1 l=l*2
LA R10,1 j=1
LOOPJ CR R10,R11 do j=1 to 2*l
BH ELOOPJ
LA R1,0
LA R2,1
BAL R14,RANDOMX
LR R12,R0 m=randomx(0,1)
LTR R12,R12 if m=0
BNZ ELSEM
MVI Q,C'[' q='['
B EIFM
ELSEM MVI Q,C']' q=']'
EIFM LA R14,C-1(R10) @c(j)
MVC 0(1,R14),Q c(j)=q
LA R10,1(R10) j=j+1
B LOOPJ
ELOOPJ BAL R14,CHECKBAL
LR R2,R0
C R2,=F'1' if checkbal=1
BNE ELSEC
MVC PG+24(2),=C'ok' rep='ok'
B EIFC
ELSEC MVC PG+24(2),=C'? ' rep='? '
EIFC XDECO R8,XDEC i
MVC PG+0(2),XDEC+10
MVC PG+3(20),C
XPRNT PG,26
LA R8,1(R8) i=i+1
B LOOPI
ELOOPI L R13,4(0,R13)
LM R14,R12,12(R13)
XR R15,R15 set return code to 0
BR R14 -------------- end
CHECKBAL CNOP 0,4 -------------- checkbal
SR R6,R6 n=0
LA R7,1 k=1
LOOPK C R7,=F'20' do k=1 to 20
BH ELOOPK
LR R1,R7 k
LA R4,C-1(R1) @c(k)
MVC CI(1),0(R4) ci=c(k)
CLI CI,C'[' if ci='['
BNE NOT1
LA R6,1(R6) n=n+1
NOT1 CLI CI,C']' if ci=']'
BNE NOT2
BCTR R6,0 n=n-1
NOT2 LTR R6,R6 if n<0
BNM NSUP0
SR R0,R0 return(0)
B RETCHECK
NSUP0 LA R7,1(R7) k=k+1
B LOOPK
ELOOPK LTR R6,R6 if n=0
BNZ ELSEN
LA R0,1 return(1)
B RETCHECK
ELSEN SR R0,R0 return(0)
RETCHECK BR R14 -------------- end checkbal
RANDOMX CNOP 0,4 -------------- randomx
LR R3,R2 i2
SR R3,R1 ii=i2-i1
L R5,SEED
M R4,=F'1103515245'
A R5,=F'12345'
SRDL R4,1 shift to improve the algorithm
ST R5,SEED seed=(seed*1103515245+12345)>>1
LR R6,R3 ii
LA R6,1(R6) ii+1
L R5,SEED seed
LA R4,0 clear
DR R4,R6 seed//(ii+1)
AR R4,R1 +i1
LR R0,R4 return(seed//(ii+1)+i1)
BR R14 -------------- end randomx
SEED DC F'903313037'
C DS 20CL1
Q DS CL1
CI DS CL1
PG DC CL80' '
XDEC DS CL12
REGS
END BALANCE |
http://rosettacode.org/wiki/Averages/Mode | Averages/Mode | Task[edit]
Write a program to find the mode value of a collection.
The case where the collection is empty may be ignored. Care must be taken to handle the case where the mode is non-unique.
If it is not appropriate or possible to support a general collection, use a vector (array), if possible. If it is not appropriate or possible to support an unspecified value type, use integers.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #AWK | AWK | #!/usr/bin/gawk -f
{
# compute histogram
histo[$1] += 1;
};
function mode(HIS) {
# Computes the mode from Histogram A
max = 0;
n = 0;
for (k in HIS) {
val = HIS[k];
if (HIS[k] > max) {
max = HIS[k];
n = 1;
List[n] = k;
} else if (HIS[k] == max) {
List[++n] = k;
}
}
for (k=1; k<=n; k++) {
o = o""OFS""List[k];
}
return o;
}
END {
print mode(histo);
}; |
http://rosettacode.org/wiki/Averages/Simple_moving_average | Averages/Simple moving average | Computing the simple moving average of a series of numbers.
Task[edit]
Create a stateful function/class/instance that takes a period and returns a routine that takes a number as argument and returns a simple moving average of its arguments so far.
Description
A simple moving average is a method for computing an average of a stream of numbers by only averaging the last P numbers from the stream, where P is known as the period.
It can be implemented by calling an initialing routine with P as its argument, I(P), which should then return a routine that when called with individual, successive members of a stream of numbers, computes the mean of (up to), the last P of them, lets call this SMA().
The word stateful in the task description refers to the need for SMA() to remember certain information between calls to it:
The period, P
An ordered container of at least the last P numbers from each of its individual calls.
Stateful also means that successive calls to I(), the initializer, should return separate routines that do not share saved state so they could be used on two independent streams of data.
Pseudo-code for an implementation of SMA is:
function SMA(number: N):
stateful integer: P
stateful list: stream
number: average
stream.append_last(N)
if stream.length() > P:
# Only average the last P elements of the stream
stream.delete_first()
if stream.length() == 0:
average = 0
else:
average = sum( stream.values() ) / stream.length()
return average
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Lua | Lua | function sma(period)
local t = {}
function sum(a, ...)
if a then return a+sum(...) else return 0 end
end
function average(n)
if #t == period then table.remove(t, 1) end
t[#t + 1] = n
return sum(unpack(t)) / #t
end
return average
end
sma5 = sma(5)
sma10 = sma(10)
print("SMA 5")
for v=1,15 do print(sma5(v)) end
print("\nSMA 10")
for v=1,15 do print(sma10(v)) end
|
http://rosettacode.org/wiki/Averages/Pythagorean_means | Averages/Pythagorean means | Task[edit]
Compute all three of the Pythagorean means of the set of integers 1 through 10 (inclusive).
Show that
A
(
x
1
,
…
,
x
n
)
≥
G
(
x
1
,
…
,
x
n
)
≥
H
(
x
1
,
…
,
x
n
)
{\displaystyle A(x_{1},\ldots ,x_{n})\geq G(x_{1},\ldots ,x_{n})\geq H(x_{1},\ldots ,x_{n})}
for this set of positive integers.
The most common of the three means, the arithmetic mean, is the sum of the list divided by its length:
A
(
x
1
,
…
,
x
n
)
=
x
1
+
⋯
+
x
n
n
{\displaystyle A(x_{1},\ldots ,x_{n})={\frac {x_{1}+\cdots +x_{n}}{n}}}
The geometric mean is the
n
{\displaystyle n}
th root of the product of the list:
G
(
x
1
,
…
,
x
n
)
=
x
1
⋯
x
n
n
{\displaystyle G(x_{1},\ldots ,x_{n})={\sqrt[{n}]{x_{1}\cdots x_{n}}}}
The harmonic mean is
n
{\displaystyle n}
divided by the sum of the reciprocal of each item in the list:
H
(
x
1
,
…
,
x
n
)
=
n
1
x
1
+
⋯
+
1
x
n
{\displaystyle H(x_{1},\ldots ,x_{n})={\frac {n}{{\frac {1}{x_{1}}}+\cdots +{\frac {1}{x_{n}}}}}}
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #C | C | #include <stdio.h>
#include <stdlib.h> // atoi()
#include <math.h> // pow()
int main(int argc, char* argv[])
{
int i, count=0;
double f, sum=0.0, prod=1.0, resum=0.0;
for (i=1; i<argc; ++i) {
f = atof(argv[i]);
count++;
sum += f;
prod *= f;
resum += (1.0/f);
}
//printf(" c:%d\n s:%f\n p:%f\n r:%f\n",count,sum,prod,resum);
printf("Arithmetic mean = %f\n",sum/count);
printf("Geometric mean = %f\n",pow(prod,(1.0/count)));
printf("Harmonic mean = %f\n",count/resum);
return 0;
} |
http://rosettacode.org/wiki/Barnsley_fern | Barnsley fern |
A Barnsley fern is a fractal named after British mathematician Michael Barnsley and can be created using an iterated function system (IFS).
Task
Create this fractal fern, using the following transformations:
ƒ1 (chosen 1% of the time)
xn + 1 = 0
yn + 1 = 0.16 yn
ƒ2 (chosen 85% of the time)
xn + 1 = 0.85 xn + 0.04 yn
yn + 1 = −0.04 xn + 0.85 yn + 1.6
ƒ3 (chosen 7% of the time)
xn + 1 = 0.2 xn − 0.26 yn
yn + 1 = 0.23 xn + 0.22 yn + 1.6
ƒ4 (chosen 7% of the time)
xn + 1 = −0.15 xn + 0.28 yn
yn + 1 = 0.26 xn + 0.24 yn + 0.44.
Starting position: x = 0, y = 0
| #zkl | zkl | fcn barnsleyFern(){
w,h:=640,640;
bitmap:=PPM(w+1,h+1,0xFF|FF|FF); // White background
x,y, nx,ny:=0.0, 0.0, 0.0, 0.0;
do(0d100_000){
r:=(0).random(100); // [0..100)%
if (r<= 1) nx,ny= 0, 0.16*y;
else if(r<= 8) nx,ny= 0.2*x - 0.26*y, 0.23*x + 0.22*y + 1.6;
else if(r<=15) nx,ny=-0.15*x + 0.28*y, 0.26*x + 0.24*y + 0.44;
else nx,ny= 0.85*x + 0.04*y, -0.04*x + 0.85*y + 1.6;
x,y=nx,ny;
bitmap[w/2 + x*60, y*60] = 0x00|FF|00; // Green dot
}
bitmap.writeJPGFile("barnsleyFern.jpg");
}(); |
http://rosettacode.org/wiki/Barnsley_fern | Barnsley fern |
A Barnsley fern is a fractal named after British mathematician Michael Barnsley and can be created using an iterated function system (IFS).
Task
Create this fractal fern, using the following transformations:
ƒ1 (chosen 1% of the time)
xn + 1 = 0
yn + 1 = 0.16 yn
ƒ2 (chosen 85% of the time)
xn + 1 = 0.85 xn + 0.04 yn
yn + 1 = −0.04 xn + 0.85 yn + 1.6
ƒ3 (chosen 7% of the time)
xn + 1 = 0.2 xn − 0.26 yn
yn + 1 = 0.23 xn + 0.22 yn + 1.6
ƒ4 (chosen 7% of the time)
xn + 1 = −0.15 xn + 0.28 yn
yn + 1 = 0.26 xn + 0.24 yn + 0.44.
Starting position: x = 0, y = 0
| #ZX_Spectrum_Basic | ZX Spectrum Basic | 10 REM Fractal Fern
20 PAPER 7: BORDER 7: BRIGHT 1: INK 4: CLS
30 LET maxpoints=20000: LET x=0: LET y=0
40 FOR n=1 TO maxpoints
50 LET p=RND*100
60 IF p<=1 THEN LET nx=0: LET ny=0.16*y: GO TO 100
70 IF p<=8 THEN LET nx=0.2*x-0.26*y: LET ny=0.23*x+0.22*y+1.6: GO TO 100
80 IF p<=15 THEN LET nx=-0.15*x+0.28*y: LET ny=0.26*x+0.24*y+0.44: GO TO 100
90 LET nx=0.85*x+0.04*y: LET ny=-0.04*x+0.85*y+1.6
100 LET x=nx: LET y=ny
110 PLOT x*17+127,y*17
120 NEXT n
|
http://rosettacode.org/wiki/Balanced_ternary | Balanced ternary | Balanced ternary is a way of representing numbers. Unlike the prevailing binary representation, a balanced ternary integer is in base 3, and each digit can have the values 1, 0, or −1.
Examples
Decimal 11 = 32 + 31 − 30, thus it can be written as "++−"
Decimal 6 = 32 − 31 + 0 × 30, thus it can be written as "+−0"
Task
Implement balanced ternary representation of integers with the following:
Support arbitrarily large integers, both positive and negative;
Provide ways to convert to and from text strings, using digits '+', '-' and '0' (unless you are already using strings to represent balanced ternary; but see requirement 5).
Provide ways to convert to and from native integer type (unless, improbably, your platform's native integer type is balanced ternary). If your native integers can't support arbitrary length, overflows during conversion must be indicated.
Provide ways to perform addition, negation and multiplication directly on balanced ternary integers; do not convert to native integers first.
Make your implementation efficient, with a reasonable definition of "efficient" (and with a reasonable definition of "reasonable").
Test case With balanced ternaries a from string "+-0++0+", b from native integer -436, c "+-++-":
write out a, b and c in decimal notation;
calculate a × (b − c), write out the result in both ternary and decimal notations.
Note: The pages generalised floating point addition and generalised floating point multiplication have code implementing arbitrary precision floating point balanced ternary.
| #11l | 11l | F py_idiv(a, b)
I a >= 0
R a I/ b
R (a - b + 1) I/ b
F BalancedTernary_int2ternary(n)
I n == 0
R [Int]()
V n3 = ((n % 3) + 3) % 3
I n3 == 0 {R [0] [+] BalancedTernary_int2ternary(py_idiv(n, 3))}
I n3 == 1 {R [1] [+] BalancedTernary_int2ternary(py_idiv(n, 3))}
I n3 == 2 {R [-1] [+] BalancedTernary_int2ternary(py_idiv((n + 1), 3))}
X RuntimeError(‘’)
F BalancedTernary_neg(digs)
R digs.map(d -> -d)
V table = [(0, -1), (1, -1), (-1, 0), (0, 0), (1, 0), (-1, 1), (0, 1)]
F BalancedTernary_add(a, b, =c = 0)
I !(!a.empty & !b.empty)
I c == 0
R I !a.empty {a} E b
E
R BalancedTernary_add([c], I !a.empty {a} E b)
E
(V d, c) = :table[3 + (I !a.empty {a[0]} E 0) + (I !b.empty {b[0]} E 0) + c]
V res = BalancedTernary_add(a[1..], b[1..], c)
I !res.empty | d != 0
R [d] [+] res
E
R res
V BalancedTernary_str2dig = [‘+’ = 1, ‘-’ = -1, ‘0’ = 0]
V BalancedTernary_dig2str = [1 = ‘+’, -1 = ‘-’, 0 = ‘0’]
T BalancedTernary
[Int] digits
F (inp)
I all(inp.map(d -> d C (0, 1, -1)))
.digits = copy(inp)
E
X ValueError(‘BalancedTernary: Wrong input digits.’)
F to_int()
R reversed(.digits).reduce(0, (y, x) -> x + 3 * y)
F String()
I .digits.empty
R ‘0’
R reversed(.digits).map(d -> BalancedTernary_dig2str[d]).join(‘’)
F +(b)
R BalancedTernary(BalancedTernary_add(.digits, b.digits))
F -(b)
R (.) + BalancedTernary(BalancedTernary_neg(b.digits))
F *(b)
F _mul([Int] a, b) -> [Int]
I !(!a.empty & !b.empty)
R [Int]()
E
[Int] x
I a[0] == -1 {x = BalancedTernary_neg(b)}
E I a[0] == 0 {}
E I a[0] == 1 {x = b}
E
assert(0B)
V y = [0] [+] @_mul(a[1..], b)
R BalancedTernary_add(x, y)
R BalancedTernary(_mul(.digits, b.digits))
F createBalancedTernaryFromStr(inp)
R BalancedTernary(reversed(inp).map(c -> BalancedTernary_str2dig[c]))
F createBalancedTernaryFromInt(inp)
R BalancedTernary(BalancedTernary_int2ternary(inp))
V a = createBalancedTernaryFromStr(‘+-0++0+’)
print(‘a: ’a.to_int()‘ ’a)
V b = createBalancedTernaryFromInt(-436)
print(‘b: ’b.to_int()‘ ’b)
V c = createBalancedTernaryFromStr(‘+-++-’)
print(‘c: ’c.to_int()‘ ’c)
V r = a * (b - c)
print(‘a * (b - c): ’r.to_int()‘ ’r) |
http://rosettacode.org/wiki/Babbage_problem | Babbage problem |
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.
For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].
Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.
| #Go | Go | package main
import "fmt"
func main() {
const (
target = 269696
modulus = 1000000
)
for n := 1; ; n++ { // Repeat with n=1, n=2, n=3, ...
square := n * n
ending := square % modulus
if ending == target {
fmt.Println("The smallest number whose square ends with",
target, "is", n,
)
return
}
}
} |
http://rosettacode.org/wiki/Balanced_brackets | Balanced brackets | Task:
Generate a string with N opening brackets [ and with N closing brackets ], in some arbitrary order.
Determine whether the generated string is balanced; that is, whether it consists entirely of pairs of opening/closing brackets (in that order), none of which mis-nest.
Examples
(empty) OK
[] OK
[][] OK
[[][]] OK
][ NOT OK
][][ NOT OK
[]][[] NOT OK
| #ABAP | ABAP |
CLASS lcl_balanced_brackets DEFINITION.
PUBLIC SECTION.
CLASS-METHODS:
class_constructor,
are_brackets_balanced
IMPORTING
seq TYPE string
RETURNING
VALUE(r_are_brackets_balanced) TYPE abap_bool,
get_random_brackets_seq
IMPORTING
n TYPE i
RETURNING
VALUE(r_bracket_seq) TYPE string.
PRIVATE SECTION.
CLASS-DATA: random_int TYPE REF TO cl_abap_random_int.
CLASS-METHODS:
_split_string
IMPORTING
i_text TYPE string
RETURNING
VALUE(r_chars) TYPE stringtab,
_rand_bool
RETURNING
VALUE(r_bool) TYPE i.
ENDCLASS.
CLASS lcl_balanced_brackets IMPLEMENTATION.
METHOD class_constructor.
random_int = cl_abap_random_int=>create( seed = CONV #( sy-uzeit )
min = 0
max = 1 ).
ENDMETHOD.
METHOD are_brackets_balanced.
DATA: open_bracket_count TYPE i.
DATA(chars) = _split_string( seq ).
r_are_brackets_balanced = abap_false.
LOOP AT chars ASSIGNING FIELD-SYMBOL(<c>).
IF <c> = ']' AND open_bracket_count = 0.
RETURN.
ENDIF.
IF <c> = ']'.
open_bracket_count = open_bracket_count - 1.
ENDIF.
IF <c> = '['.
open_bracket_count = open_bracket_count + 1.
ENDIF.
ENDLOOP.
IF open_bracket_count > 0.
RETURN.
ENDIF.
r_are_brackets_balanced = abap_true.
ENDMETHOD.
METHOD get_random_brackets_seq.
DATA(itab) = VALUE stringtab( FOR i = 1 THEN i + 1 WHILE i <= n
( COND #( WHEN _rand_bool( ) = 0 THEN '['
ELSE ']' ) ) ).
r_bracket_seq = concat_lines_of( itab ).
ENDMETHOD.
METHOD _rand_bool.
r_bool = random_int->get_next( ).
ENDMETHOD.
METHOD _split_string.
DATA: off TYPE i VALUE 0.
DO strlen( i_text ) TIMES.
INSERT i_text+off(1) INTO TABLE r_chars.
off = off + 1.
ENDDO.
ENDMETHOD.
ENDCLASS.
START-OF-SELECTION.
DO 10 TIMES.
DATA(seq) = lcl_balanced_brackets=>get_random_brackets_seq( 10 ).
cl_demo_output=>write( |{ seq } => { COND string( WHEN lcl_balanced_brackets=>are_brackets_balanced( seq ) = abap_true THEN 'OK'
ELSE 'NOT OK' ) }| ).
ENDDO.
cl_demo_output=>display( ).
|
http://rosettacode.org/wiki/Averages/Mode | Averages/Mode | Task[edit]
Write a program to find the mode value of a collection.
The case where the collection is empty may be ignored. Care must be taken to handle the case where the mode is non-unique.
If it is not appropriate or possible to support a general collection, use a vector (array), if possible. If it is not appropriate or possible to support an unspecified value type, use integers.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #BBC_BASIC | BBC BASIC | DIM a(10), b(4)
a() = 1, 3, 6, 6, 6, 6, 7, 7, 12, 12, 17
b() = 1, 2, 4, 4, 1
DIM modes(10)
PRINT "Mode(s) of a() = " ;
FOR i% = 1 TO FNmodes(a(), modes())
PRINT ; modes(i%) " " ;
NEXT
PRINT
PRINT "Mode(s) of b() = " ;
FOR i% = 1 TO FNmodes(b(), modes())
PRINT ; modes(i%) " " ;
NEXT
PRINT
END
DEF FNmodes(a(), m())
LOCAL I%, J%, N%, c%(), max%
N% = DIM(a(),1)
IF N% = 0 THEN m(1) = a(0) : = 1
DIM c%(N%)
FOR I% = 0 TO N%-1
FOR J% = I%+1 TO N%
IF a(I%) = a(J%) c%(I%) += 1
NEXT
IF c%(I%) > max% max% = c%(I%)
NEXT I%
J% = 0
FOR I% = 0 TO N%
IF c%(I%) = max% J% += 1 : m(J%) = a(I%)
NEXT
= J%
|
http://rosettacode.org/wiki/Averages/Mode | Averages/Mode | Task[edit]
Write a program to find the mode value of a collection.
The case where the collection is empty may be ignored. Care must be taken to handle the case where the mode is non-unique.
If it is not appropriate or possible to support a general collection, use a vector (array), if possible. If it is not appropriate or possible to support an unspecified value type, use integers.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #BQN | BQN | Mode1 ← ⌈´⊸=∘⊒⊸/
Mode2 ← ⊏∘⊑˘·(⌈´⊸=≠¨)⊸/⊐⊸⊔
arr ← 1‿1‿1‿1‿2‿2‿2‿3‿3‿3‿3‿4‿4‿3‿2‿4‿4‿4‿5‿5‿5‿5‿5
•Show Mode1 arr
•Show Mode2 arr |
http://rosettacode.org/wiki/Averages/Simple_moving_average | Averages/Simple moving average | Computing the simple moving average of a series of numbers.
Task[edit]
Create a stateful function/class/instance that takes a period and returns a routine that takes a number as argument and returns a simple moving average of its arguments so far.
Description
A simple moving average is a method for computing an average of a stream of numbers by only averaging the last P numbers from the stream, where P is known as the period.
It can be implemented by calling an initialing routine with P as its argument, I(P), which should then return a routine that when called with individual, successive members of a stream of numbers, computes the mean of (up to), the last P of them, lets call this SMA().
The word stateful in the task description refers to the need for SMA() to remember certain information between calls to it:
The period, P
An ordered container of at least the last P numbers from each of its individual calls.
Stateful also means that successive calls to I(), the initializer, should return separate routines that do not share saved state so they could be used on two independent streams of data.
Pseudo-code for an implementation of SMA is:
function SMA(number: N):
stateful integer: P
stateful list: stream
number: average
stream.append_last(N)
if stream.length() > P:
# Only average the last P elements of the stream
stream.delete_first()
if stream.length() == 0:
average = 0
else:
average = sum( stream.values() ) / stream.length()
return average
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Mathematica_.2F_Wolfram_Language | Mathematica / Wolfram Language | MA[x_List, r_] := Join[Table[Mean[x[[1;;y]]],{y,r-1}], MovingAverage[x,r]] |
http://rosettacode.org/wiki/Averages/Pythagorean_means | Averages/Pythagorean means | Task[edit]
Compute all three of the Pythagorean means of the set of integers 1 through 10 (inclusive).
Show that
A
(
x
1
,
…
,
x
n
)
≥
G
(
x
1
,
…
,
x
n
)
≥
H
(
x
1
,
…
,
x
n
)
{\displaystyle A(x_{1},\ldots ,x_{n})\geq G(x_{1},\ldots ,x_{n})\geq H(x_{1},\ldots ,x_{n})}
for this set of positive integers.
The most common of the three means, the arithmetic mean, is the sum of the list divided by its length:
A
(
x
1
,
…
,
x
n
)
=
x
1
+
⋯
+
x
n
n
{\displaystyle A(x_{1},\ldots ,x_{n})={\frac {x_{1}+\cdots +x_{n}}{n}}}
The geometric mean is the
n
{\displaystyle n}
th root of the product of the list:
G
(
x
1
,
…
,
x
n
)
=
x
1
⋯
x
n
n
{\displaystyle G(x_{1},\ldots ,x_{n})={\sqrt[{n}]{x_{1}\cdots x_{n}}}}
The harmonic mean is
n
{\displaystyle n}
divided by the sum of the reciprocal of each item in the list:
H
(
x
1
,
…
,
x
n
)
=
n
1
x
1
+
⋯
+
1
x
n
{\displaystyle H(x_{1},\ldots ,x_{n})={\frac {n}{{\frac {1}{x_{1}}}+\cdots +{\frac {1}{x_{n}}}}}}
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #C.23 | C# | using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
namespace PythMean
{
static class Program
{
static void Main(string[] args) {
var nums = from n in Enumerable.Range(1, 10) select (double)n;
var a = nums.Average();
var g = nums.Gmean();
var h = nums.Hmean();
Console.WriteLine("Arithmetic mean {0}", a);
Console.WriteLine("Geometric mean {0}", g);
Console.WriteLine("Harmonic mean {0}", h);
Debug.Assert(a >= g && g >= h);
}
// Geometric mean extension method.
static double Gmean(this IEnumerable<double> n) {
return Math.Pow(n.Aggregate((s, i) => s * i), 1.0 / n.Count());
}
// Harmonic mean extension method.
static double Hmean(this IEnumerable<double> n) {
return n.Count() / n.Sum(i => 1.0 / i);
}
}
} |
http://rosettacode.org/wiki/Balanced_ternary | Balanced ternary | Balanced ternary is a way of representing numbers. Unlike the prevailing binary representation, a balanced ternary integer is in base 3, and each digit can have the values 1, 0, or −1.
Examples
Decimal 11 = 32 + 31 − 30, thus it can be written as "++−"
Decimal 6 = 32 − 31 + 0 × 30, thus it can be written as "+−0"
Task
Implement balanced ternary representation of integers with the following:
Support arbitrarily large integers, both positive and negative;
Provide ways to convert to and from text strings, using digits '+', '-' and '0' (unless you are already using strings to represent balanced ternary; but see requirement 5).
Provide ways to convert to and from native integer type (unless, improbably, your platform's native integer type is balanced ternary). If your native integers can't support arbitrary length, overflows during conversion must be indicated.
Provide ways to perform addition, negation and multiplication directly on balanced ternary integers; do not convert to native integers first.
Make your implementation efficient, with a reasonable definition of "efficient" (and with a reasonable definition of "reasonable").
Test case With balanced ternaries a from string "+-0++0+", b from native integer -436, c "+-++-":
write out a, b and c in decimal notation;
calculate a × (b − c), write out the result in both ternary and decimal notations.
Note: The pages generalised floating point addition and generalised floating point multiplication have code implementing arbitrary precision floating point balanced ternary.
| #Ada | Ada | with Ada.Finalization;
package BT is
type Balanced_Ternary is private;
-- conversions
function To_Balanced_Ternary (Num : Integer) return Balanced_Ternary;
function To_Balanced_Ternary (Str : String) return Balanced_Ternary;
function To_Integer (Num : Balanced_Ternary) return Integer;
function To_string (Num : Balanced_Ternary) return String;
-- Arithmetics
-- unary minus
function "-" (Left : in Balanced_Ternary)
return Balanced_Ternary;
-- subtraction
function "-" (Left, Right : in Balanced_Ternary)
return Balanced_Ternary;
-- addition
function "+" (Left, Right : in Balanced_Ternary)
return Balanced_Ternary;
-- multiplication
function "*" (Left, Right : in Balanced_Ternary)
return Balanced_Ternary;
private
-- a balanced ternary number is a unconstrained array of (1,0,-1)
-- dinamically allocated, least significant trit leftmost
type Trit is range -1..1;
type Trit_Array is array (Positive range <>) of Trit;
pragma Pack(Trit_Array);
type Trit_Access is access Trit_Array;
type Balanced_Ternary is new Ada.Finalization.Controlled
with record
Ref : Trit_access;
end record;
procedure Initialize (Object : in out Balanced_Ternary);
procedure Adjust (Object : in out Balanced_Ternary);
procedure Finalize (Object : in out Balanced_Ternary);
end BT; |
http://rosettacode.org/wiki/Babbage_problem | Babbage problem |
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.
For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].
Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.
| #Groovy | Groovy |
int n=104; ///starting point
while( (n**2)%1000000 != 269696 )
{ if (n%10==4) n=n+2;
if (n%10==6) n=n+8;
}
println n+"^2== "+n**2 ;
|
http://rosettacode.org/wiki/Balanced_brackets | Balanced brackets | Task:
Generate a string with N opening brackets [ and with N closing brackets ], in some arbitrary order.
Determine whether the generated string is balanced; that is, whether it consists entirely of pairs of opening/closing brackets (in that order), none of which mis-nest.
Examples
(empty) OK
[] OK
[][] OK
[[][]] OK
][ NOT OK
][][ NOT OK
[]][[] NOT OK
| #Action.21 | Action! | PROC Generate(BYTE size CHAR ARRAY s)
BYTE i,half
s(0)=size
half=size RSH 1
FOR i=1 TO half
DO s(i)='[ OD
FOR i=half+1 TO size
DO s(i)='] OD
RETURN
PROC Shuffle(CHAR ARRAY s)
BYTE i,j,k,n,len,tmp
len=s(0)
n=Rand(len+1)
FOR k=1 TO n
DO
i=Rand(len)+1
j=Rand(len)+1
tmp=s(i)
s(i)=s(j)
s(j)=tmp
OD
RETURN
BYTE FUNC Balanced(CHAR ARRAY s)
INT i,lev
lev=0
FOR i=1 TO s(0)
DO
IF s(i)='[ THEN
lev==+1
ELSE
lev==-1
FI
IF lev<0 THEN
RETURN (0)
FI
OD
IF lev#0 THEN
RETURN (0)
FI
RETURN (1)
PROC Main()
CHAR ARRAY s(20)
BYTE i,b
FOR i=0 TO 20 STEP 2
DO
Generate(i,s)
Shuffle(s)
b=Balanced(s)
IF s(0)=0 THEN
Print("(empty)")
ELSE
Print(s)
FI
Print(" is ")
IF b=0 THEN
Print("not ")
FI
PrintE("balanced")
OD
RETURN |
http://rosettacode.org/wiki/Averages/Mode | Averages/Mode | Task[edit]
Write a program to find the mode value of a collection.
The case where the collection is empty may be ignored. Care must be taken to handle the case where the mode is non-unique.
If it is not appropriate or possible to support a general collection, use a vector (array), if possible. If it is not appropriate or possible to support an unspecified value type, use integers.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #C | C | #include <stdio.h>
#include <stdlib.h>
typedef struct { double v; int c; } vcount;
int cmp_dbl(const void *a, const void *b)
{
double x = *(const double*)a - *(const double*)b;
return x < 0 ? -1 : x > 0;
}
int vc_cmp(const void *a, const void *b)
{
return ((const vcount*)b)->c - ((const vcount*)a)->c;
}
int get_mode(double* x, int len, vcount **list)
{
int i, j;
vcount *vc;
/* sort values */
qsort(x, len, sizeof(double), cmp_dbl);
/* count occurence of each value */
for (i = 0, j = 1; i < len - 1; i++, j += (x[i] != x[i + 1]));
*list = vc = malloc(sizeof(vcount) * j);
vc[0].v = x[0];
vc[0].c = 1;
/* generate list value-count pairs */
for (i = j = 0; i < len - 1; i++, vc[j].c++)
if (x[i] != x[i + 1]) vc[++j].v = x[i + 1];
/* sort that by count in descending order */
qsort(vc, j + 1, sizeof(vcount), vc_cmp);
/* the number of entries with same count as the highest */
for (i = 0; i <= j && vc[i].c == vc[0].c; i++);
return i;
}
int main()
{
double values[] = { 1, 3, 6, 6, 6, 6, 7, 7, 12, 12, 12, 12, 17 };
# define len sizeof(values)/sizeof(double)
vcount *vc;
int i, n_modes = get_mode(values, len, &vc);
printf("got %d modes:\n", n_modes);
for (i = 0; i < n_modes; i++)
printf("\tvalue = %g, count = %d\n", vc[i].v, vc[i].c);
free(vc);
return 0;
} |
http://rosettacode.org/wiki/Averages/Simple_moving_average | Averages/Simple moving average | Computing the simple moving average of a series of numbers.
Task[edit]
Create a stateful function/class/instance that takes a period and returns a routine that takes a number as argument and returns a simple moving average of its arguments so far.
Description
A simple moving average is a method for computing an average of a stream of numbers by only averaging the last P numbers from the stream, where P is known as the period.
It can be implemented by calling an initialing routine with P as its argument, I(P), which should then return a routine that when called with individual, successive members of a stream of numbers, computes the mean of (up to), the last P of them, lets call this SMA().
The word stateful in the task description refers to the need for SMA() to remember certain information between calls to it:
The period, P
An ordered container of at least the last P numbers from each of its individual calls.
Stateful also means that successive calls to I(), the initializer, should return separate routines that do not share saved state so they could be used on two independent streams of data.
Pseudo-code for an implementation of SMA is:
function SMA(number: N):
stateful integer: P
stateful list: stream
number: average
stream.append_last(N)
if stream.length() > P:
# Only average the last P elements of the stream
stream.delete_first()
if stream.length() == 0:
average = 0
else:
average = sum( stream.values() ) / stream.length()
return average
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #MATLAB_.2F_Octave | MATLAB / Octave | [m,z] = filter(ones(1,P),P,x); |
http://rosettacode.org/wiki/Averages/Pythagorean_means | Averages/Pythagorean means | Task[edit]
Compute all three of the Pythagorean means of the set of integers 1 through 10 (inclusive).
Show that
A
(
x
1
,
…
,
x
n
)
≥
G
(
x
1
,
…
,
x
n
)
≥
H
(
x
1
,
…
,
x
n
)
{\displaystyle A(x_{1},\ldots ,x_{n})\geq G(x_{1},\ldots ,x_{n})\geq H(x_{1},\ldots ,x_{n})}
for this set of positive integers.
The most common of the three means, the arithmetic mean, is the sum of the list divided by its length:
A
(
x
1
,
…
,
x
n
)
=
x
1
+
⋯
+
x
n
n
{\displaystyle A(x_{1},\ldots ,x_{n})={\frac {x_{1}+\cdots +x_{n}}{n}}}
The geometric mean is the
n
{\displaystyle n}
th root of the product of the list:
G
(
x
1
,
…
,
x
n
)
=
x
1
⋯
x
n
n
{\displaystyle G(x_{1},\ldots ,x_{n})={\sqrt[{n}]{x_{1}\cdots x_{n}}}}
The harmonic mean is
n
{\displaystyle n}
divided by the sum of the reciprocal of each item in the list:
H
(
x
1
,
…
,
x
n
)
=
n
1
x
1
+
⋯
+
1
x
n
{\displaystyle H(x_{1},\ldots ,x_{n})={\frac {n}{{\frac {1}{x_{1}}}+\cdots +{\frac {1}{x_{n}}}}}}
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #C.2B.2B | C++ | #include <vector>
#include <iostream>
#include <numeric>
#include <cmath>
#include <algorithm>
double toInverse ( int i ) {
return 1.0 / i ;
}
int main( ) {
std::vector<int> numbers ;
for ( int i = 1 ; i < 11 ; i++ )
numbers.push_back( i ) ;
double arithmetic_mean = std::accumulate( numbers.begin( ) , numbers.end( ) , 0 ) / 10.0 ;
double geometric_mean =
pow( std::accumulate( numbers.begin( ) , numbers.end( ) , 1 , std::multiplies<int>( ) ), 0.1 ) ;
std::vector<double> inverses ;
inverses.resize( numbers.size( ) ) ;
std::transform( numbers.begin( ) , numbers.end( ) , inverses.begin( ) , toInverse ) ;
double harmonic_mean = 10 / std::accumulate( inverses.begin( ) , inverses.end( ) , 0.0 ); //initial value of accumulate must be a double!
std::cout << "The arithmetic mean is " << arithmetic_mean << " , the geometric mean "
<< geometric_mean << " and the harmonic mean " << harmonic_mean << " !\n" ;
return 0 ;
} |
http://rosettacode.org/wiki/Balanced_ternary | Balanced ternary | Balanced ternary is a way of representing numbers. Unlike the prevailing binary representation, a balanced ternary integer is in base 3, and each digit can have the values 1, 0, or −1.
Examples
Decimal 11 = 32 + 31 − 30, thus it can be written as "++−"
Decimal 6 = 32 − 31 + 0 × 30, thus it can be written as "+−0"
Task
Implement balanced ternary representation of integers with the following:
Support arbitrarily large integers, both positive and negative;
Provide ways to convert to and from text strings, using digits '+', '-' and '0' (unless you are already using strings to represent balanced ternary; but see requirement 5).
Provide ways to convert to and from native integer type (unless, improbably, your platform's native integer type is balanced ternary). If your native integers can't support arbitrary length, overflows during conversion must be indicated.
Provide ways to perform addition, negation and multiplication directly on balanced ternary integers; do not convert to native integers first.
Make your implementation efficient, with a reasonable definition of "efficient" (and with a reasonable definition of "reasonable").
Test case With balanced ternaries a from string "+-0++0+", b from native integer -436, c "+-++-":
write out a, b and c in decimal notation;
calculate a × (b − c), write out the result in both ternary and decimal notations.
Note: The pages generalised floating point addition and generalised floating point multiplication have code implementing arbitrary precision floating point balanced ternary.
| #ALGOL_68 | ALGOL 68 | -- Build a balanced ternary, as text, from an integer value or acceptable AppleScript substitute.
on BTFromInteger(n)
try
if (n mod 1 is not 0) then error (n as text) & " isn't an integer value"
set n to n as integer
on error errMsg
display alert "BTFromInteger handler: parameter error" message errMsg buttons {"OK"} default button 1 as critical
error number -128
end try
if (n is 0) then return "0"
-- Positive numbers' digits will be indexed from the beginning of a list containing them, negatives' from the end.
-- AppleScript indices are 1-based, so get the appropriate 1 or -1 add-in.
set one to 1
if (n < 0) then set one to -1
set digits to {"0", "+", "-", "0"}
-- Build the text digit by digit.
set bt to ""
repeat until (n = 0)
set nMod3 to n mod 3
set bt to (item (nMod3 + one) of digits) & bt
set n to n div 3 + nMod3 div 2 -- + nMod3 div 2 adds in a carry when nMod3 is either 2 or -2.
end repeat
return bt
end BTFromInteger
-- Calculate a balanced ternary's integer value from its characters' Unicode numbers.
on integerFromBT(bt)
checkInput(bt, "integerFromBT")
set n to 0
repeat with thisID in (get bt's id)
set n to n * 3
-- Unicode 48 is "0", 43 is "+", 45 is "-".
if (thisID < 48) then set n to n + (44 - thisID)
end repeat
return n
end integerFromBT
-- Add two balanced ternaries together.
on addBTs(bt1, bt2)
checkInput({bt1, bt2}, "addBTs")
set {longerLength, shorterLength} to {(count bt1), (count bt2)}
if (longerLength < shorterLength) then set {bt1, bt2, longerLength, shorterLength} to {bt2, bt1, shorterLength, longerLength}
-- Add the shorter number's digits into a list of the longer number's digits, adding in carries too where appropriate.
set resultList to bt1's characters
repeat with i from -1 to -shorterLength by -1
set {carry, item i of resultList} to sumDigits(item i of resultList, character i of bt2)
repeat with j from (i - 1) to -longerLength by -1
if (carry is "0") then exit repeat
set {carry, item j of resultList} to sumDigits(carry, item j of resultList)
end repeat
if (carry is not "0") then set beginning of bt1 to carry
end repeat
-- Zap any leading zeros resulting from the cancelling out of the longer number's MSD(s).
set j to -(count resultList)
repeat while ((item j of resultList is "0") and (j < -1))
set item j of resultList to ""
set j to j + 1
end repeat
return join(resultList, "")
end addBTs
-- Multiply one balanced ternary by another.
on multiplyBTs(bt1, bt2)
checkInput({bt1, bt2}, "multiplyBTs")
-- Longer and shorter aren't critical here, but it's more efficient to loop through the lesser number of digits.
set {longerLength, shorterLength} to {(count bt1), (count bt2)}
if (longerLength < shorterLength) then set {bt1, bt2, shorterLength} to {bt2, bt1, longerLength}
set multiplicationResult to "0"
repeat with i from -1 to -shorterLength by -1
set d2 to character i of bt2
if (d2 is not "0") then
set subresult to ""
-- With each non-"0" subresult, begin with the appropriate number of trailing zeros.
repeat (-1 - i) times
set subresult to "0" & subresult
end repeat
-- Prepend the longer ternary as is.
set subresult to bt1 & subresult
-- Negate the result if the current multiplier from the shorter ternary is "-".
if (d2 is "-") then set subresult to negateBT(subresult)
-- Add the subresult to the total so far.
set multiplicationResult to addBTs(multiplicationResult, subresult)
end if
end repeat
return multiplicationResult
end multiplyBTs
-- Negate a balanced ternary by substituting the characters obtained through subtracting its sign characters' Unicode numbers from 88.
on negateBT(bt)
checkInput(bt, "negateBT")
set characterIDs to bt's id
repeat with thisID in characterIDs
if (thisID < 48) then set thisID's contents to 88 - thisID
end repeat
return string id characterIDs
end negateBT
(* Private handlers. *)
on checkInput(params as list, handlerName)
try
repeat with thisParam in params
if (thisParam's class is text) then
if (join(split(thisParam, {"-", "+", "0"}), "") > "") then error "\"" & thisParam & "\" isn't a balanced ternary number."
else
error "The parameter isn't text."
end if
end repeat
on error errMsg
display alert handlerName & " handler: parameter error" message errMsg buttons {"OK"} default button 1 as critical
error number -128
end try
end checkInput
-- "Add" two balanced ternaries and return both the carry and the result for the column.
on sumDigits(d1, d2)
if (d1 is "0") then
return {"0", d2}
else if (d2 is "0") then
return {"0", d1}
else if (d1 = d2) then
if (d1 = "+") then
return {"+", "-"}
else
return {"-", "+"}
end if
else
return {"0", "0"}
end if
end sumDigits
on join(lst, delimiter)
set astid to AppleScript's text item delimiters
set AppleScript's text item delimiters to delimiter
set txt to lst as text
set AppleScript's text item delimiters to astid
return txt
end join
on split(txt, delimiter)
set astid to AppleScript's text item delimiters
set AppleScript's text item delimiters to delimiter
set lst to txt's text items
set AppleScript's text item delimiters to astid
return lst
end split
-- Test code:
set a to "+-0++0+"
set b to BTFromInteger(-436) --> "-++-0--"
set c to "+-++-"
set line1 to "a = " & integerFromBT(a)
set line2 to "b = " & integerFromBT(b)
set line3 to "c = " & integerFromBT(c)
tell multiplyBTs(a, addBTs(b, negateBT(c))) to ¬
set line4 to "a * (b - c) = " & it & " or " & my integerFromBT(it)
return line1 & linefeed & line2 & linefeed & line3 & linefeed & line4 |
http://rosettacode.org/wiki/Babbage_problem | Babbage problem |
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.
For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].
Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.
| #Haskell | Haskell | --Calculate squares, testing for the last 6 digits
findBabbageNumber :: Integer
findBabbageNumber =
head (filter ((269696 ==) . flip mod 1000000 . (^ 2)) [1 ..])
main :: IO ()
main =
(putStrLn . unwords)
(zipWith
(++)
(show <$> ([id, (^ 2)] <*> [findBabbageNumber]))
[" ^ 2 equals", " !"]) |
http://rosettacode.org/wiki/Balanced_brackets | Balanced brackets | Task:
Generate a string with N opening brackets [ and with N closing brackets ], in some arbitrary order.
Determine whether the generated string is balanced; that is, whether it consists entirely of pairs of opening/closing brackets (in that order), none of which mis-nest.
Examples
(empty) OK
[] OK
[][] OK
[[][]] OK
][ NOT OK
][][ NOT OK
[]][[] NOT OK
| #Acurity_Architect | Acurity Architect | Using #HASH-OFF
|
http://rosettacode.org/wiki/Averages/Mode | Averages/Mode | Task[edit]
Write a program to find the mode value of a collection.
The case where the collection is empty may be ignored. Care must be taken to handle the case where the mode is non-unique.
If it is not appropriate or possible to support a general collection, use a vector (array), if possible. If it is not appropriate or possible to support an unspecified value type, use integers.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #C.23 | C# | using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
namespace Test
{
class Program
{
static void Main(string[] args)
{
/*
* We Use Linq To Determine The Mode
*/
List<int> myList = new List<int>() { 1, 1, 2, 4, 4 };
var query = from numbers in myList //select the numbers
group numbers by numbers //group them together so we can get the count
into groupedNumbers
select new { Number = groupedNumbers.Key, Count = groupedNumbers.Count() }; //so we got a query
//find the max of the occurence of the mode
int max = query.Max(g => g.Count);
IEnumerable<int> modes = query.Where(x => x.Count == max).Select(x => x.Number);//match the frequence and select the number
foreach (var item in modes)
{
Console.WriteLine(item);
}
Console.ReadLine();
}
}
}
|
http://rosettacode.org/wiki/Averages/Simple_moving_average | Averages/Simple moving average | Computing the simple moving average of a series of numbers.
Task[edit]
Create a stateful function/class/instance that takes a period and returns a routine that takes a number as argument and returns a simple moving average of its arguments so far.
Description
A simple moving average is a method for computing an average of a stream of numbers by only averaging the last P numbers from the stream, where P is known as the period.
It can be implemented by calling an initialing routine with P as its argument, I(P), which should then return a routine that when called with individual, successive members of a stream of numbers, computes the mean of (up to), the last P of them, lets call this SMA().
The word stateful in the task description refers to the need for SMA() to remember certain information between calls to it:
The period, P
An ordered container of at least the last P numbers from each of its individual calls.
Stateful also means that successive calls to I(), the initializer, should return separate routines that do not share saved state so they could be used on two independent streams of data.
Pseudo-code for an implementation of SMA is:
function SMA(number: N):
stateful integer: P
stateful list: stream
number: average
stream.append_last(N)
if stream.length() > P:
# Only average the last P elements of the stream
stream.delete_first()
if stream.length() == 0:
average = 0
else:
average = sum( stream.values() ) / stream.length()
return average
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Mercury | Mercury | % state(period, list of floats from [newest, ..., oldest])
:- type state ---> state(int, list(float)).
:- func init(int) = state.
init(Period) = state(Period, []).
:- pred sma(float::in, float::out, state::in, state::out) is det.
sma(N, Average, state(P, L0), state(P, L)) :-
take_upto(P, [N|L0], L),
Average = foldl((+), L, 0.0) / float(length(L)). |
http://rosettacode.org/wiki/Averages/Pythagorean_means | Averages/Pythagorean means | Task[edit]
Compute all three of the Pythagorean means of the set of integers 1 through 10 (inclusive).
Show that
A
(
x
1
,
…
,
x
n
)
≥
G
(
x
1
,
…
,
x
n
)
≥
H
(
x
1
,
…
,
x
n
)
{\displaystyle A(x_{1},\ldots ,x_{n})\geq G(x_{1},\ldots ,x_{n})\geq H(x_{1},\ldots ,x_{n})}
for this set of positive integers.
The most common of the three means, the arithmetic mean, is the sum of the list divided by its length:
A
(
x
1
,
…
,
x
n
)
=
x
1
+
⋯
+
x
n
n
{\displaystyle A(x_{1},\ldots ,x_{n})={\frac {x_{1}+\cdots +x_{n}}{n}}}
The geometric mean is the
n
{\displaystyle n}
th root of the product of the list:
G
(
x
1
,
…
,
x
n
)
=
x
1
⋯
x
n
n
{\displaystyle G(x_{1},\ldots ,x_{n})={\sqrt[{n}]{x_{1}\cdots x_{n}}}}
The harmonic mean is
n
{\displaystyle n}
divided by the sum of the reciprocal of each item in the list:
H
(
x
1
,
…
,
x
n
)
=
n
1
x
1
+
⋯
+
1
x
n
{\displaystyle H(x_{1},\ldots ,x_{n})={\frac {n}{{\frac {1}{x_{1}}}+\cdots +{\frac {1}{x_{n}}}}}}
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Clojure | Clojure | (use '[clojure.contrib.math :only (expt)])
(defn a-mean [coll]
(/ (apply + coll) (count coll)))
(defn g-mean [coll]
(expt (apply * coll) (/ (count coll))))
(defn h-mean [coll]
(/ (count coll) (apply + (map / coll))))
(let [numbers (range 1 11)
a (a-mean numbers) g (g-mean numbers) h (h-mean numbers)]
(println a ">=" g ">=" h)
(>= a g h)) |
http://rosettacode.org/wiki/Balanced_ternary | Balanced ternary | Balanced ternary is a way of representing numbers. Unlike the prevailing binary representation, a balanced ternary integer is in base 3, and each digit can have the values 1, 0, or −1.
Examples
Decimal 11 = 32 + 31 − 30, thus it can be written as "++−"
Decimal 6 = 32 − 31 + 0 × 30, thus it can be written as "+−0"
Task
Implement balanced ternary representation of integers with the following:
Support arbitrarily large integers, both positive and negative;
Provide ways to convert to and from text strings, using digits '+', '-' and '0' (unless you are already using strings to represent balanced ternary; but see requirement 5).
Provide ways to convert to and from native integer type (unless, improbably, your platform's native integer type is balanced ternary). If your native integers can't support arbitrary length, overflows during conversion must be indicated.
Provide ways to perform addition, negation and multiplication directly on balanced ternary integers; do not convert to native integers first.
Make your implementation efficient, with a reasonable definition of "efficient" (and with a reasonable definition of "reasonable").
Test case With balanced ternaries a from string "+-0++0+", b from native integer -436, c "+-++-":
write out a, b and c in decimal notation;
calculate a × (b − c), write out the result in both ternary and decimal notations.
Note: The pages generalised floating point addition and generalised floating point multiplication have code implementing arbitrary precision floating point balanced ternary.
| #AppleScript | AppleScript | -- Build a balanced ternary, as text, from an integer value or acceptable AppleScript substitute.
on BTFromInteger(n)
try
if (n mod 1 is not 0) then error (n as text) & " isn't an integer value"
set n to n as integer
on error errMsg
display alert "BTFromInteger handler: parameter error" message errMsg buttons {"OK"} default button 1 as critical
error number -128
end try
if (n is 0) then return "0"
-- Positive numbers' digits will be indexed from the beginning of a list containing them, negatives' from the end.
-- AppleScript indices are 1-based, so get the appropriate 1 or -1 add-in.
set one to 1
if (n < 0) then set one to -1
set digits to {"0", "+", "-", "0"}
-- Build the text digit by digit.
set bt to ""
repeat until (n = 0)
set nMod3 to n mod 3
set bt to (item (nMod3 + one) of digits) & bt
set n to n div 3 + nMod3 div 2 -- + nMod3 div 2 adds in a carry when nMod3 is either 2 or -2.
end repeat
return bt
end BTFromInteger
-- Calculate a balanced ternary's integer value from its characters' Unicode numbers.
on integerFromBT(bt)
checkInput(bt, "integerFromBT")
set n to 0
repeat with thisID in (get bt's id)
set n to n * 3
-- Unicode 48 is "0", 43 is "+", 45 is "-".
if (thisID < 48) then set n to n + (44 - thisID)
end repeat
return n
end integerFromBT
-- Add two balanced ternaries together.
on addBTs(bt1, bt2)
checkInput({bt1, bt2}, "addBTs")
set {longerLength, shorterLength} to {(count bt1), (count bt2)}
if (longerLength < shorterLength) then set {bt1, bt2, longerLength, shorterLength} to {bt2, bt1, shorterLength, longerLength}
-- Add the shorter number's digits into a list of the longer number's digits, adding in carries too where appropriate.
set resultList to bt1's characters
repeat with i from -1 to -shorterLength by -1
set {carry, item i of resultList} to sumDigits(item i of resultList, character i of bt2)
repeat with j from (i - 1) to -longerLength by -1
if (carry is "0") then exit repeat
set {carry, item j of resultList} to sumDigits(carry, item j of resultList)
end repeat
if (carry is not "0") then set beginning of bt1 to carry
end repeat
-- Zap any leading zeros resulting from the cancelling out of the longer number's MSD(s).
set j to -(count resultList)
repeat while ((item j of resultList is "0") and (j < -1))
set item j of resultList to ""
set j to j + 1
end repeat
return join(resultList, "")
end addBTs
-- Multiply one balanced ternary by another.
on multiplyBTs(bt1, bt2)
checkInput({bt1, bt2}, "multiplyBTs")
-- Longer and shorter aren't critical here, but it's more efficient to loop through the lesser number of digits.
set {longerLength, shorterLength} to {(count bt1), (count bt2)}
if (longerLength < shorterLength) then set {bt1, bt2, shorterLength} to {bt2, bt1, longerLength}
set multiplicationResult to "0"
repeat with i from -1 to -shorterLength by -1
set d2 to character i of bt2
if (d2 is not "0") then
set subresult to ""
-- With each non-"0" subresult, begin with the appropriate number of trailing zeros.
repeat (-1 - i) times
set subresult to "0" & subresult
end repeat
-- Prepend the longer ternary as is.
set subresult to bt1 & subresult
-- Negate the result if the current multiplier from the shorter ternary is "-".
if (d2 is "-") then set subresult to negateBT(subresult)
-- Add the subresult to the total so far.
set multiplicationResult to addBTs(multiplicationResult, subresult)
end if
end repeat
return multiplicationResult
end multiplyBTs
-- Negate a balanced ternary by substituting the characters obtained through subtracting its sign characters' Unicode numbers from 88.
on negateBT(bt)
checkInput(bt, "negateBT")
set characterIDs to bt's id
repeat with thisID in characterIDs
if (thisID < 48) then set thisID's contents to 88 - thisID
end repeat
return string id characterIDs
end negateBT
(* Private handlers. *)
on checkInput(params as list, handlerName)
try
repeat with thisParam in params
if (thisParam's class is text) then
if (join(split(thisParam, {"-", "+", "0"}), "") > "") then error "\"" & thisParam & "\" isn't a balanced ternary number."
else
error "The parameter isn't text."
end if
end repeat
on error errMsg
display alert handlerName & " handler: parameter error" message errMsg buttons {"OK"} default button 1 as critical
error number -128
end try
end checkInput
-- "Add" two balanced ternaries and return both the carry and the result for the column.
on sumDigits(d1, d2)
if (d1 is "0") then
return {"0", d2}
else if (d2 is "0") then
return {"0", d1}
else if (d1 = d2) then
if (d1 = "+") then
return {"+", "-"}
else
return {"-", "+"}
end if
else
return {"0", "0"}
end if
end sumDigits
on join(lst, delimiter)
set astid to AppleScript's text item delimiters
set AppleScript's text item delimiters to delimiter
set txt to lst as text
set AppleScript's text item delimiters to astid
return txt
end join
on split(txt, delimiter)
set astid to AppleScript's text item delimiters
set AppleScript's text item delimiters to delimiter
set lst to txt's text items
set AppleScript's text item delimiters to astid
return lst
end split
-- Test code:
set a to "+-0++0+"
set b to BTFromInteger(-436) --> "-++-0--"
set c to "+-++-"
set line1 to "a = " & integerFromBT(a)
set line2 to "b = " & integerFromBT(b)
set line3 to "c = " & integerFromBT(c)
tell multiplyBTs(a, addBTs(b, negateBT(c))) to ¬
set line4 to "a * (b - c) = " & it & " or " & my integerFromBT(it)
return line1 & linefeed & line2 & linefeed & line3 & linefeed & line4 |
http://rosettacode.org/wiki/Babbage_problem | Babbage problem |
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.
For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].
Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.
| #J | J | square=: ^&2
modulo1e6=: 1000000&|
trythese=: i. 1000000 NB. first million nonnegative integers
which=: I. NB. position of true values
which 269696=modulo1e6 square trythese NB. right to left <-
25264 99736 150264 224736 275264 349736 400264 474736 525264 599736 650264 724736 775264 849736 900264 974736 |
http://rosettacode.org/wiki/Balanced_brackets | Balanced brackets | Task:
Generate a string with N opening brackets [ and with N closing brackets ], in some arbitrary order.
Determine whether the generated string is balanced; that is, whether it consists entirely of pairs of opening/closing brackets (in that order), none of which mis-nest.
Examples
(empty) OK
[] OK
[][] OK
[[][]] OK
][ NOT OK
][][ NOT OK
[]][[] NOT OK
| #Ada | Ada | with Ada.Numerics.Discrete_Random;
with Ada.Text_IO;
with Ada.Strings.Fixed;
procedure Brackets is
package Random_Positive is new Ada.Numerics.Discrete_Random (Positive);
Positive_Generator : Random_Positive.Generator;
procedure Swap (Left, Right : in out Character) is
Temp : constant Character := Left;
begin
Left := Right;
Right := Temp;
end Swap;
function Generate_Brackets (Bracket_Count : Natural;
Opening_Bracket : Character := '[';
Closing_Bracket : Character := ']')
return String is
use Ada.Strings.Fixed;
All_Brackets : String := Bracket_Count * Opening_Bracket & Bracket_Count * Closing_Bracket;
begin
for I in All_Brackets'Range loop
Swap (All_Brackets (I), All_Brackets (Random_Positive.Random (Positive_Generator) mod (Bracket_Count * 2) + 1));
end loop;
return All_Brackets;
end Generate_Brackets;
function Check_Brackets (Test : String;
Opening_Bracket : Character := '[';
Closing_Bracket : Character := ']')
return Boolean is
Open : Natural := 0;
begin
for I in Test'Range loop
if Test (I) = Opening_Bracket then
Open := Open + 1;
elsif Test (I) = Closing_Bracket then
if Open = 0 then
return False;
else
Open := Open - 1;
end if;
end if;
end loop;
return True;
end Check_Brackets;
begin
Random_Positive.Reset (Positive_Generator);
Ada.Text_IO.Put_Line ("Brackets");
for I in 0 .. 4 loop
for J in 0 .. I loop
declare
My_String : constant String := Generate_Brackets (I);
begin
Ada.Text_IO.Put_Line (My_String & ": " & Boolean'Image (Check_Brackets (My_String)));
end;
end loop;
end loop;
end Brackets; |
http://rosettacode.org/wiki/Averages/Mode | Averages/Mode | Task[edit]
Write a program to find the mode value of a collection.
The case where the collection is empty may be ignored. Care must be taken to handle the case where the mode is non-unique.
If it is not appropriate or possible to support a general collection, use a vector (array), if possible. If it is not appropriate or possible to support an unspecified value type, use integers.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #C.2B.2B | C++ | #include <iterator>
#include <utility>
#include <algorithm>
#include <list>
#include <iostream>
// helper struct
template<typename T> struct referring
{
referring(T const& t): value(t) {}
template<typename Iter>
bool operator()(std::pair<Iter, int> const& p) const
{
return *p.first == value;
}
T const& value;
};
// requires:
// FwdIterator is a ForwardIterator
// The value_type of FwdIterator is EqualityComparable
// OutIterator is an output iterator
// the value_type of FwdIterator is convertible to the value_type of OutIterator
// [first, last) is a valid range
// provides:
// the mode is written to result
template<typename FwdIterator, typename OutIterator>
void mode(FwdIterator first, FwdIterator last, OutIterator result)
{
typedef typename std::iterator_traits<FwdIterator>::value_type value_type;
typedef std::list<std::pair<FwdIterator, int> > count_type;
typedef typename count_type::iterator count_iterator;
// count elements
count_type counts;
while (first != last)
{
count_iterator element = std::find_if(counts.begin(), counts.end(),
referring<value_type>(*first));
if (element == counts.end())
counts.push_back(std::make_pair(first, 1));
else
++element->second;
++first;
}
// find maximum
int max = 0;
for (count_iterator i = counts.begin(); i != counts.end(); ++i)
if (i->second > max)
max = i->second;
// copy corresponding elements to output sequence
for (count_iterator i = counts.begin(); i != counts.end(); ++i)
if (i->second == max)
*result++ = *i->first;
}
// example usage
int main()
{
int values[] = { 1, 2, 3, 1, 2, 4, 2, 5, 2, 3, 3, 1, 3, 6 };
median(values, values + sizeof(values)/sizeof(int),
std::ostream_iterator<int>(std::cout, " "));
std::cout << std::endl;
return 0;
} |
http://rosettacode.org/wiki/Averages/Simple_moving_average | Averages/Simple moving average | Computing the simple moving average of a series of numbers.
Task[edit]
Create a stateful function/class/instance that takes a period and returns a routine that takes a number as argument and returns a simple moving average of its arguments so far.
Description
A simple moving average is a method for computing an average of a stream of numbers by only averaging the last P numbers from the stream, where P is known as the period.
It can be implemented by calling an initialing routine with P as its argument, I(P), which should then return a routine that when called with individual, successive members of a stream of numbers, computes the mean of (up to), the last P of them, lets call this SMA().
The word stateful in the task description refers to the need for SMA() to remember certain information between calls to it:
The period, P
An ordered container of at least the last P numbers from each of its individual calls.
Stateful also means that successive calls to I(), the initializer, should return separate routines that do not share saved state so they could be used on two independent streams of data.
Pseudo-code for an implementation of SMA is:
function SMA(number: N):
stateful integer: P
stateful list: stream
number: average
stream.append_last(N)
if stream.length() > P:
# Only average the last P elements of the stream
stream.delete_first()
if stream.length() == 0:
average = 0
else:
average = sum( stream.values() ) / stream.length()
return average
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #MiniScript | MiniScript | SMA = {}
SMA.P = 5 // (a default; may be overridden)
SMA.buffer = null
SMA.next = function(n)
if self.buffer == null then self.buffer = []
self.buffer.push n
if self.buffer.len > self.P then self.buffer.pull
return self.buffer.sum / self.buffer.len
end function
sma3 = new SMA
sma3.P = 3
sma5 = new SMA
for i in range(10)
num = round(rnd*100)
print "num: " + num + " sma3: " + sma3.next(num) + " sma5: " + sma5.next(num)
end for |
http://rosettacode.org/wiki/Averages/Mean_time_of_day | Averages/Mean time of day | Task[edit]
A particular activity of bats occurs at these times of the day:
23:00:17, 23:40:20, 00:12:45, 00:17:19
Using the idea that there are twenty-four hours in a day,
which is analogous to there being 360 degrees in a circle,
map times of day to and from angles;
and using the ideas of Averages/Mean angle
compute and show the average time of the nocturnal activity
to an accuracy of one second of time.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #11l | 11l | F mean_angle(angles)
V x = sum(angles.map(a -> cos(radians(a)))) / angles.len
V y = sum(angles.map(a -> sin(radians(a)))) / angles.len
R degrees(atan2(y, x))
F mean_time(times)
V t = (times.map(time -> time.split(‘:’)))
V seconds = (t.map(hms -> (Float(hms[2]) + Int(hms[1]) * 60 + Int(hms[0]) * 3600)))
V day = 24 * 60 * 60
V to_angles = seconds.map(s -> s * 360.0 / @day)
V mean_as_angle = mean_angle(to_angles)
V mean_seconds = round(mean_as_angle * day / 360.0)
I mean_seconds < 0
mean_seconds += day
V h = mean_seconds I/ 3600
V m = mean_seconds % 3600
V s = m % 60
m = m I/ 60
R ‘#02:#02:#02’.format(h, m, s)
print(mean_time([‘23:00:17’, ‘23:40:20’, ‘00:12:45’, ‘00:17:19’])) |
http://rosettacode.org/wiki/Averages/Pythagorean_means | Averages/Pythagorean means | Task[edit]
Compute all three of the Pythagorean means of the set of integers 1 through 10 (inclusive).
Show that
A
(
x
1
,
…
,
x
n
)
≥
G
(
x
1
,
…
,
x
n
)
≥
H
(
x
1
,
…
,
x
n
)
{\displaystyle A(x_{1},\ldots ,x_{n})\geq G(x_{1},\ldots ,x_{n})\geq H(x_{1},\ldots ,x_{n})}
for this set of positive integers.
The most common of the three means, the arithmetic mean, is the sum of the list divided by its length:
A
(
x
1
,
…
,
x
n
)
=
x
1
+
⋯
+
x
n
n
{\displaystyle A(x_{1},\ldots ,x_{n})={\frac {x_{1}+\cdots +x_{n}}{n}}}
The geometric mean is the
n
{\displaystyle n}
th root of the product of the list:
G
(
x
1
,
…
,
x
n
)
=
x
1
⋯
x
n
n
{\displaystyle G(x_{1},\ldots ,x_{n})={\sqrt[{n}]{x_{1}\cdots x_{n}}}}
The harmonic mean is
n
{\displaystyle n}
divided by the sum of the reciprocal of each item in the list:
H
(
x
1
,
…
,
x
n
)
=
n
1
x
1
+
⋯
+
1
x
n
{\displaystyle H(x_{1},\ldots ,x_{n})={\frac {n}{{\frac {1}{x_{1}}}+\cdots +{\frac {1}{x_{n}}}}}}
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #CoffeeScript | CoffeeScript | a = [ 1..10 ]
arithmetic_mean = (a) -> a.reduce(((s, x) -> s + x), 0) / a.length
geometic_mean = (a) -> Math.pow(a.reduce(((s, x) -> s * x), 1), (1 / a.length))
harmonic_mean = (a) -> a.length / a.reduce(((s, x) -> s + 1 / x), 0)
A = arithmetic_mean a
G = geometic_mean a
H = harmonic_mean a
console.log "A = ", A, " G = ", G, " H = ", H
console.log "A >= G : ", A >= G, " G >= H : ", G >= H |
http://rosettacode.org/wiki/Balanced_ternary | Balanced ternary | Balanced ternary is a way of representing numbers. Unlike the prevailing binary representation, a balanced ternary integer is in base 3, and each digit can have the values 1, 0, or −1.
Examples
Decimal 11 = 32 + 31 − 30, thus it can be written as "++−"
Decimal 6 = 32 − 31 + 0 × 30, thus it can be written as "+−0"
Task
Implement balanced ternary representation of integers with the following:
Support arbitrarily large integers, both positive and negative;
Provide ways to convert to and from text strings, using digits '+', '-' and '0' (unless you are already using strings to represent balanced ternary; but see requirement 5).
Provide ways to convert to and from native integer type (unless, improbably, your platform's native integer type is balanced ternary). If your native integers can't support arbitrary length, overflows during conversion must be indicated.
Provide ways to perform addition, negation and multiplication directly on balanced ternary integers; do not convert to native integers first.
Make your implementation efficient, with a reasonable definition of "efficient" (and with a reasonable definition of "reasonable").
Test case With balanced ternaries a from string "+-0++0+", b from native integer -436, c "+-++-":
write out a, b and c in decimal notation;
calculate a × (b − c), write out the result in both ternary and decimal notations.
Note: The pages generalised floating point addition and generalised floating point multiplication have code implementing arbitrary precision floating point balanced ternary.
| #ATS | ATS |
(*
** This one is
** translated into ATS from the Ocaml entry
*)
(* ****** ****** *)
//
// How to compile:
// patscc -DATS_MEMALLOC_LIBC -o bternary bternary.dats
//
(* ****** ****** *)
#include
"share/atspre_staload.hats"
(* ****** ****** *)
datatype btd = P | Z | N; typedef btern = List0(btd)
(* ****** ****** *)
fun
btd2int (d: btd): int =
(case+ d of P() => 1 | Z() => 0 | N() => ~1)
(* ****** ****** *)
fun
btd2string (d:btd): string =
(
case+ d of P() => "+" | Z() => "0" | N() => "-"
)
(* ****** ****** *)
fun
btern2string
(
ds: btern
) : string =
strptr2string(res) where
{
val xs = list_map_cloref (ds, lam d => btd2string(d))
val xs = list_vt_reverse (xs)
val res = stringlst_concat($UNSAFE.castvwtp1{List(string)}(xs))
val () = list_vt_free<string> (xs)
}
(* ****** ****** *)
fun
from_string
(inp: string): btern = let
//
fun
loop{n:nat}
(
inp: string(n), ds: btern
) : btern =
(
//
if isneqz(inp)
then let
val c = inp.head()
val d =
(case- c of '+' => P | '0' => Z | '-' => N): btd
// end of [val]
in
loop (inp.tail(), list_cons(d, ds))
end // end of [then]
else ds // end of [else]
//
) (* end of [loop] *)
//
in
loop (g1ofg0(inp), list_nil)
end // end of [from_string]
(* ****** ****** *)
fun
to_int (ds: btern): int =
(
case+ ds of
| list_nil () => 0
| list_cons (d, ds) => 3*to_int(ds) + btd2int(d)
) (* end of [to_int] *)
fun
from_int (n: int): btern =
(
if
n = 0
then list_nil
else let
val r = n mod 3
in
if r = 0
then list_cons (Z, from_int (n/3))
else if (r = 1 || r = ~2)
then list_cons (P, from_int ((n-1)/3))
else list_cons (N, from_int ((n+1)/3))
end // end of [else]
) (* end of [from_int] *)
(* ****** ****** *)
fun
neg_btern
(ds: btern): btern =
list_vt2t
(
list_map_cloref<btd><btd>
(ds, lam d => case+ d of P() => N() | Z() => Z() | N() => P())
) (* end of [neg_btern] *)
overload ~ with neg_btern
(* ****** ****** *)
//
extern
fun
add_btern_btern: (btern, btern) -> btern
and
sub_btern_btern: (btern, btern) -> btern
overload + with add_btern_btern of 100
overload - with sub_btern_btern of 100
//
extern
fun
mul_btern_btern: (btern, btern) -> btern
overload * with mul_btern_btern of 110
//
(* ****** ****** *)
#define :: list_cons
(* ****** ****** *)
local
fun aux0 (ds: btern): btern =
(
case+ ds of nil() => ds | _ => Z()::ds
)
fun succ(ds:btern) = ds+list_sing(P())
fun pred(ds:btern) = ds+list_sing(N())
in (* in-of-local *)
implement
add_btern_btern
(ds1, ds2) =
(
case+ (ds1, ds2) of
| (nil(), _) => ds2
| (_, nil()) => ds1
| (P()::ds1, N()::ds2) => aux0 (ds1+ds2)
| (Z()::ds1, Z()::ds2) => aux0 (ds1+ds2)
| (N()::ds1, P()::ds2) => aux0 (ds1+ds2)
| (P()::ds1, P()::ds2) => N() :: succ(ds1 + ds2)
| (N()::ds1, N()::ds2) => P() :: pred(ds1 + ds2)
| (Z()::ds1, btd::ds2) => btd :: (ds1 + ds2)
| (btd::ds1, Z()::ds2) => btd :: (ds1 + ds2)
)
implement
sub_btern_btern (ds1, ds2) = ds1 + (~ds2)
implement
mul_btern_btern (ds1, ds2) =
(
case+ ds2 of
| nil() => nil()
| Z()::ds2 => aux0 (ds1 * ds2)
| P()::ds2 => aux0 (ds1 * ds2) + ds1
| N()::ds2 => aux0 (ds1 * ds2) - ds1
)
end // end of [local]
(* ****** ****** *)
typedef charptr = $extype"char*"
(* ****** ****** *)
implement main0 () =
{
//
val a =
from_string "+-0++0+"
//
val b = from_int (~436)
val c = from_string "+-++-"
//
val d = a * (b - c)
//
val () =
$extfcall
(
void
, "printf"
, "a = %d\nb = %d\nc = %d\na * (b - c) = %s = %d\n"
, to_int(a)
, to_int(b)
, to_int(c)
, $UNSAFE.cast{charptr}(btern2string(d))
, to_int(d)
) (* end of [val] *)
//
} (* end of [main0] *)
|
http://rosettacode.org/wiki/Babbage_problem | Babbage problem |
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.
For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].
Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.
| #Java | Java | public class Test {
public static void main(String[] args) {
// let n be zero
int n = 0;
// repeat the following action
do {
// increase n by 1
n++;
// while the modulo of n times n is not equal to 269696
} while (n * n % 1000_000 != 269696);
// show the result
System.out.println(n);
}
} |
http://rosettacode.org/wiki/Balanced_brackets | Balanced brackets | Task:
Generate a string with N opening brackets [ and with N closing brackets ], in some arbitrary order.
Determine whether the generated string is balanced; that is, whether it consists entirely of pairs of opening/closing brackets (in that order), none of which mis-nest.
Examples
(empty) OK
[] OK
[][] OK
[[][]] OK
][ NOT OK
][][ NOT OK
[]][[] NOT OK
| #Aime | Aime | unbalanced(data s)
{
integer b, i;
b = i = 0;
while (i + ~s && -1 < b) {
b += s[i -= 1] == '[' ? -1 : 1;
}
b;
}
generate(data b, integer d)
{
if (d) {
d.times(l_bill, list(), -1, '[', ']').l_rand().ucall(b_append, 1, b);
}
}
main(void)
{
integer i;
i = 0;
while (i < 10) {
data s;
generate(s, i);
o_(s, " is ", unbalanced(s) ? "un" : "", "balanced\n");
i += 1;
}
0;
} |
http://rosettacode.org/wiki/Averages/Mode | Averages/Mode | Task[edit]
Write a program to find the mode value of a collection.
The case where the collection is empty may be ignored. Care must be taken to handle the case where the mode is non-unique.
If it is not appropriate or possible to support a general collection, use a vector (array), if possible. If it is not appropriate or possible to support an unspecified value type, use integers.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Clojure | Clojure | (defn modes [coll]
(let [distrib (frequencies coll)
[value freq] [first second] ; name the key/value pairs in the distrib (map) entries
sorted (sort-by (comp - freq) distrib)
maxfq (freq (first sorted))]
(map value (take-while #(= maxfq (freq %)) sorted)))) |
http://rosettacode.org/wiki/Averages/Simple_moving_average | Averages/Simple moving average | Computing the simple moving average of a series of numbers.
Task[edit]
Create a stateful function/class/instance that takes a period and returns a routine that takes a number as argument and returns a simple moving average of its arguments so far.
Description
A simple moving average is a method for computing an average of a stream of numbers by only averaging the last P numbers from the stream, where P is known as the period.
It can be implemented by calling an initialing routine with P as its argument, I(P), which should then return a routine that when called with individual, successive members of a stream of numbers, computes the mean of (up to), the last P of them, lets call this SMA().
The word stateful in the task description refers to the need for SMA() to remember certain information between calls to it:
The period, P
An ordered container of at least the last P numbers from each of its individual calls.
Stateful also means that successive calls to I(), the initializer, should return separate routines that do not share saved state so they could be used on two independent streams of data.
Pseudo-code for an implementation of SMA is:
function SMA(number: N):
stateful integer: P
stateful list: stream
number: average
stream.append_last(N)
if stream.length() > P:
# Only average the last P elements of the stream
stream.delete_first()
if stream.length() == 0:
average = 0
else:
average = sum( stream.values() ) / stream.length()
return average
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #NetRexx | NetRexx | /* NetRexx */
options replace format comments java crossref symbols nobinary
numeric digits 20
class RAvgSimpleMoving public
properties private
window = java.util.Queue
period
sum
properties constant
exMsg = 'Period must be a positive integer'
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method RAvgSimpleMoving(period_) public
if \period_.datatype('w') then signal RuntimeException(exMsg)
if period_ <= 0 then signal RuntimeException(exMsg)
window = LinkedList()
period = period_
sum = 0
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method newNum(num) public
sum = sum + num
window.add(num)
if window.size() > period then do
rmv = (Rexx window.remove())
sum = sum - rmv
end
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method getAvg() public returns Rexx
if window.isEmpty() then do
avg = 0
end
else do
avg = sum / window.size()
end
return avg
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method run_samples(args = String[]) public static
testData = [Rexx 1, 2, 3, 4, 5, 5, 4, 3, 2, 1]
windowSizes = [Rexx 3, 5]
loop windSize over windowSizes
ma = RAvgSimpleMoving(windSize)
loop xVal over testData
ma.newNum(xVal)
say 'Next number =' xVal.right(5)', SMA =' ma.getAvg().format(10, 9)
end xVal
say
end windSize
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method main(args = String[]) public static
run_samples(args)
return
|
http://rosettacode.org/wiki/Averages/Mean_time_of_day | Averages/Mean time of day | Task[edit]
A particular activity of bats occurs at these times of the day:
23:00:17, 23:40:20, 00:12:45, 00:17:19
Using the idea that there are twenty-four hours in a day,
which is analogous to there being 360 degrees in a circle,
map times of day to and from angles;
and using the ideas of Averages/Mean angle
compute and show the average time of the nocturnal activity
to an accuracy of one second of time.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Action.21 | Action! | INCLUDE "H6:REALMATH.ACT"
DEFINE PTR="CARD"
TYPE Time=[BYTE s,m,h]
REAL r60
PROC PrintB2(BYTE b)
IF b<10 THEN Put('0) FI
PrintB(b)
RETURN
PROC PrintTime(Time POINTER t)
PrintB2(t.h) Put(':)
PrintB2(t.m) Put(':)
PrintB2(t.s)
RETURN
PROC Decode(CHAR ARRAY st Time POINTER t)
CHAR ARRAY tmp
IF st(0)#8 THEN Break() FI
SCopyS(tmp,st,1,2) t.h=ValB(tmp)
SCopyS(tmp,st,4,5) t.m=ValB(tmp)
SCopyS(tmp,st,7,8) t.s=ValB(tmp)
RETURN
PROC TimeToSeconds(Time POINTER t REAL POINTER seconds)
REAL r
IntToReal(t.h,seconds)
RealMult(seconds,r60,seconds)
IntToReal(t.m,r)
RealAdd(seconds,r,seconds)
RealMult(seconds,r60,seconds)
IntToReal(t.s,r)
RealAdd(seconds,r,seconds)
RETURN
PROC SecondsToTime(REAL POINTER seconds Time POINTER t)
REAL tmp1,tmp2
RealAssign(seconds,tmp1)
RealMod(tmp1,r60,tmp2)
t.s=RealToInt(tmp2)
RealDivInt(tmp1,r60,tmp2)
RealMod(tmp2,r60,tmp1)
t.m=RealToInt(tmp1)
RealDivInt(tmp2,r60,tmp1)
t.h=RealToInt(tmp1)
RETURN
PROC AverageTime(PTR ARRAY times BYTE count Time POINTER res)
BYTE i
Time t
REAL avg,rcount,seconds,halfDay,day
IntToReal(0,avg)
IntToReal(count,rcount)
ValR("43200",halfDay) ;seconds in the half of day
ValR("86400",day) ;seconds in the whole day
FOR i=0 TO count-1
DO
Decode(times(i),t)
TimeToSeconds(t,seconds)
IF RealLess(seconds,halfDay) THEN
RealAdd(seconds,day,seconds) ;correction of time
FI
RealAdd(avg,seconds,avg)
OD
RealDivInt(avg,rcount,avg)
WHILE RealGreaterOrEqual(avg,day)
DO
RealSub(avg,day,avg) ;correction of time
OD
SecondsToTime(avg,res)
RETURN
PROC Main()
DEFINE COUNT="4"
PTR ARRAY times(COUNT)
Time t
Put(125) PutE() ;clear the screen
IntToReal(60,r60)
times(0)="23:00:17" times(1)="23:40:20"
times(2)="00:12:45" times(3)="00:17:19"
AverageTime(times,COUNT,t)
Print("Mean time is ") PrintTime(t)
RETURN |
http://rosettacode.org/wiki/Averages/Mean_time_of_day | Averages/Mean time of day | Task[edit]
A particular activity of bats occurs at these times of the day:
23:00:17, 23:40:20, 00:12:45, 00:17:19
Using the idea that there are twenty-four hours in a day,
which is analogous to there being 360 degrees in a circle,
map times of day to and from angles;
and using the ideas of Averages/Mean angle
compute and show the average time of the nocturnal activity
to an accuracy of one second of time.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Ada | Ada | with Ada.Calendar.Formatting;
with Ada.Command_Line;
with Ada.Numerics.Elementary_Functions;
with Ada.Strings.Fixed;
with Ada.Text_IO;
procedure Mean_Time_Of_Day is
subtype Time is Ada.Calendar.Time;
subtype Time_Of_Day is Ada.Calendar.Day_Duration;
subtype Time_String is String (1 .. 8); -- "HH:MM:SS"
type Time_List is array (Positive range <>) of Time_String;
function Average_Time (List : Time_List) return Time_String is
function To_Time (Time_Image : Time_String) return Time
is (Ada.Calendar.Formatting.Value ("2000-01-01 " & Time_Image));
function To_Time_Of_Day (TS : Time) return Time_Of_Day is
use Ada.Calendar.Formatting;
Hour_Part : constant Time_Of_Day := 60.0 * 60.0 * Hour (TS);
Min_Part : constant Time_Of_Day := 60.0 * Minute (TS);
Sec_Part : constant Time_Of_Day := Time_Of_Day (Second (TS));
begin
return Hour_Part + Min_Part + Sec_Part;
end To_Time_Of_Day;
function To_Time_Image (Angle : Time_Of_Day) return Time_String
is
use Ada.Calendar.Formatting;
TOD : constant Time := Time_Of
(Year => 2000, Month => 1, Day => 1, -- Not used
Seconds => Angle);
begin
return Ada.Strings.Fixed.Tail (Image (TOD), Time_String'Length);
end To_Time_Image;
function Average_Time_Of_Day (List : Time_List) return Time_Of_Day is
use Ada.Numerics.Elementary_Functions;
Cycle : constant Float := Float (Time_Of_Day'Last);
X_Sum, Y_Sum : Float := 0.0;
Angle : Float;
begin
for Time_Stamp of List loop
Angle := Float (To_Time_Of_Day (To_Time (Time_Stamp)));
X_Sum := X_Sum + Cos (Angle, Cycle => Cycle);
Y_Sum := Y_Sum + Sin (Angle, Cycle => Cycle);
end loop;
Angle := Arctan (Y_Sum, X_Sum, Cycle => Cycle);
if Angle < 0.0 then
Angle := Angle + Cycle;
elsif Angle > Cycle then
Angle := Angle - Cycle;
end if;
return Time_Of_Day (Angle);
end Average_Time_Of_Day;
begin
return To_Time_Image (Average_Time_Of_Day (List));
end Average_Time;
use Ada.Command_Line;
List : Time_List (1 .. Argument_Count);
begin
if Argument_Count = 0 then
raise Constraint_Error;
end if;
for A in 1 .. Argument_Count loop
List (A) := Argument (A);
end loop;
Ada.Text_IO.Put_Line (Average_Time (List));
exception
when others =>
Ada.Text_IO.Put_Line ("Usage: mean_time_of_day <time-1> ...");
Ada.Text_IO.Put_Line (" <time-1> ... 'HH:MM:SS' format");
end Mean_Time_Of_Day; |
http://rosettacode.org/wiki/Averages/Pythagorean_means | Averages/Pythagorean means | Task[edit]
Compute all three of the Pythagorean means of the set of integers 1 through 10 (inclusive).
Show that
A
(
x
1
,
…
,
x
n
)
≥
G
(
x
1
,
…
,
x
n
)
≥
H
(
x
1
,
…
,
x
n
)
{\displaystyle A(x_{1},\ldots ,x_{n})\geq G(x_{1},\ldots ,x_{n})\geq H(x_{1},\ldots ,x_{n})}
for this set of positive integers.
The most common of the three means, the arithmetic mean, is the sum of the list divided by its length:
A
(
x
1
,
…
,
x
n
)
=
x
1
+
⋯
+
x
n
n
{\displaystyle A(x_{1},\ldots ,x_{n})={\frac {x_{1}+\cdots +x_{n}}{n}}}
The geometric mean is the
n
{\displaystyle n}
th root of the product of the list:
G
(
x
1
,
…
,
x
n
)
=
x
1
⋯
x
n
n
{\displaystyle G(x_{1},\ldots ,x_{n})={\sqrt[{n}]{x_{1}\cdots x_{n}}}}
The harmonic mean is
n
{\displaystyle n}
divided by the sum of the reciprocal of each item in the list:
H
(
x
1
,
…
,
x
n
)
=
n
1
x
1
+
⋯
+
1
x
n
{\displaystyle H(x_{1},\ldots ,x_{n})={\frac {n}{{\frac {1}{x_{1}}}+\cdots +{\frac {1}{x_{n}}}}}}
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Common_Lisp | Common Lisp | (defun generic-mean (nums reduce-op final-op)
(funcall final-op (reduce reduce-op nums)))
(defun a-mean (nums)
(generic-mean nums #'+ (lambda (x) (/ x (length nums)))))
(defun g-mean (nums)
(generic-mean nums #'* (lambda (x) (expt x (/ 1 (length nums))))))
(defun h-mean (nums)
(generic-mean nums
(lambda (x y) (+ x
(/ 1 y)))
(lambda (x) (/ (length nums) x))))
(let ((numbers (loop for i from 1 to 10 collect i)))
(let ((a-mean (a-mean numbers))
(g-mean (g-mean numbers))
(h-mean (h-mean numbers)))
(assert (> a-mean g-mean h-mean))
(format t "a-mean ~a~%" a-mean)
(format t "g-mean ~a~%" g-mean)
(format t "h-mean ~a~%" h-mean))) |
http://rosettacode.org/wiki/Balanced_ternary | Balanced ternary | Balanced ternary is a way of representing numbers. Unlike the prevailing binary representation, a balanced ternary integer is in base 3, and each digit can have the values 1, 0, or −1.
Examples
Decimal 11 = 32 + 31 − 30, thus it can be written as "++−"
Decimal 6 = 32 − 31 + 0 × 30, thus it can be written as "+−0"
Task
Implement balanced ternary representation of integers with the following:
Support arbitrarily large integers, both positive and negative;
Provide ways to convert to and from text strings, using digits '+', '-' and '0' (unless you are already using strings to represent balanced ternary; but see requirement 5).
Provide ways to convert to and from native integer type (unless, improbably, your platform's native integer type is balanced ternary). If your native integers can't support arbitrary length, overflows during conversion must be indicated.
Provide ways to perform addition, negation and multiplication directly on balanced ternary integers; do not convert to native integers first.
Make your implementation efficient, with a reasonable definition of "efficient" (and with a reasonable definition of "reasonable").
Test case With balanced ternaries a from string "+-0++0+", b from native integer -436, c "+-++-":
write out a, b and c in decimal notation;
calculate a × (b − c), write out the result in both ternary and decimal notations.
Note: The pages generalised floating point addition and generalised floating point multiplication have code implementing arbitrary precision floating point balanced ternary.
| #AutoHotkey | AutoHotkey | BalancedTernary(n){
k = 0
if abs(n)<2
return n=1?"+":n=0?"0":"-"
if n<1
negative := true, n:= -1*n
while !break {
d := Mod(n, 3**(k+1)) / 3**k
d := d=2?-1:d
n := n - (d * 3**k)
r := (d=-1?"-":d=1?"+":0) . r
k++
if (n = 3**k)
r := "+" . r , break := true
}
if negative {
StringReplace, r, r, -,n, all
StringReplace, r, r, `+,-, all
StringReplace, r, r, n,+, all
}
return r
} |
http://rosettacode.org/wiki/Babbage_problem | Babbage problem |
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.
For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].
Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.
| #JavaScript | JavaScript | // Every line starting with a double slash will be ignored by the processing machine,
// just like these two.
//
// Since the square root of 269,696 is approximately 519, we create a variable named "n"
// and give it this value.
n = 519
// The while-condition is in parentheses
// * is for multiplication
// % is for modulo operation
// != is for "not equal"
while ( ((n * n) % 1000000) != 269696 )
n = n + 1
// n is incremented until the while-condition is met, so n should finally be the
// smallest positive integer whose square ends in the digits 269,696. To see n, we
// need to send it to the monitoring device (named console).
console.log(n)
|
http://rosettacode.org/wiki/Balanced_brackets | Balanced brackets | Task:
Generate a string with N opening brackets [ and with N closing brackets ], in some arbitrary order.
Determine whether the generated string is balanced; that is, whether it consists entirely of pairs of opening/closing brackets (in that order), none of which mis-nest.
Examples
(empty) OK
[] OK
[][] OK
[[][]] OK
][ NOT OK
][][ NOT OK
[]][[] NOT OK
| #ALGOL_68 | ALGOL 68 | # generates a string of random opening and closing brackets. The number of #
# each type of brackets is speccified in length #
PROC get brackets = ( INT length ) STRING:
BEGIN
INT result length = length * 2;
[ 1 : result length ]CHAR result;
# initialise the brackets to all open brackets #
FOR char pos TO result length DO result[ char pos ] := "[" OD;
# set half of the brackets to close brackets #
INT close count := 0;
WHILE close count < length
DO
INT random pos = 1 + ENTIER ( next random * result length );
IF result[ random pos ] = "["
THEN
close count +:= 1;
result[ random pos ] := "]"
FI
OD;
result
END # get brackets # ;
# returns TRUE if the brackets string contains a correctly nested sequence #
# of brackets, FALSE otherwise #
PROC check brackets = ( STRING brackets ) BOOL:
BEGIN
INT depth := 0;
FOR char pos FROM LWB brackets TO UPB brackets
WHILE
IF brackets[ char pos ] = "["
THEN
depth +:= 1
ELSE
depth -:= 1
FI;
depth >= 0
DO
SKIP
OD;
# depth will be 0 if we reached the end of the string and it was #
# correct, non-0 otherwise #
depth = 0
END # check brackets # ;
# procedure to test check brackets #
PROC test check brackets = ( STRING brackets ) VOID:
print( ( ( brackets
+ ": "
+ IF check brackets( brackets ) THEN "ok" ELSE "not ok" FI
)
, newline
)
) ;
# test the bracket generation and checking PROCs #
test check brackets( get brackets( 0 ) );
FOR length TO 12
DO
TO 2
DO
test check brackets( get brackets( length ) )
OD
OD |
http://rosettacode.org/wiki/Averages/Mode | Averages/Mode | Task[edit]
Write a program to find the mode value of a collection.
The case where the collection is empty may be ignored. Care must be taken to handle the case where the mode is non-unique.
If it is not appropriate or possible to support a general collection, use a vector (array), if possible. If it is not appropriate or possible to support an unspecified value type, use integers.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #CoffeeScript | CoffeeScript | mode = (arr) ->
# returns an array with the modes of arr, i.e. the
# elements that appear most often in arr
counts = {}
for elem in arr
counts[elem] ||= 0
counts[elem] += 1
max = 0
for key, cnt of counts
max = cnt if cnt > max
(key for key, cnt of counts when cnt == max)
console.log mode [1, 2, 2, 2, 3, 3, 3, 4, 4] |
http://rosettacode.org/wiki/Averages/Simple_moving_average | Averages/Simple moving average | Computing the simple moving average of a series of numbers.
Task[edit]
Create a stateful function/class/instance that takes a period and returns a routine that takes a number as argument and returns a simple moving average of its arguments so far.
Description
A simple moving average is a method for computing an average of a stream of numbers by only averaging the last P numbers from the stream, where P is known as the period.
It can be implemented by calling an initialing routine with P as its argument, I(P), which should then return a routine that when called with individual, successive members of a stream of numbers, computes the mean of (up to), the last P of them, lets call this SMA().
The word stateful in the task description refers to the need for SMA() to remember certain information between calls to it:
The period, P
An ordered container of at least the last P numbers from each of its individual calls.
Stateful also means that successive calls to I(), the initializer, should return separate routines that do not share saved state so they could be used on two independent streams of data.
Pseudo-code for an implementation of SMA is:
function SMA(number: N):
stateful integer: P
stateful list: stream
number: average
stream.append_last(N)
if stream.length() > P:
# Only average the last P elements of the stream
stream.delete_first()
if stream.length() == 0:
average = 0
else:
average = sum( stream.values() ) / stream.length()
return average
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Nim | Nim | import deques
proc simplemovingaverage(period: int): auto =
assert period > 0
var
summ, n = 0.0
values: Deque[float]
for i in 1..period:
values.addLast(0)
proc sma(x: float): float =
values.addLast(x)
summ += x - values.popFirst()
n = min(n+1, float(period))
result = summ / n
return sma
var sma = simplemovingaverage(3)
for i in 1..5: echo sma(float(i))
for i in countdown(5,1): echo sma(float(i))
echo ""
var sma2 = simplemovingaverage(5)
for i in 1..5: echo sma2(float(i))
for i in countdown(5,1): echo sma2(float(i)) |
http://rosettacode.org/wiki/Averages/Mean_time_of_day | Averages/Mean time of day | Task[edit]
A particular activity of bats occurs at these times of the day:
23:00:17, 23:40:20, 00:12:45, 00:17:19
Using the idea that there are twenty-four hours in a day,
which is analogous to there being 360 degrees in a circle,
map times of day to and from angles;
and using the ideas of Averages/Mean angle
compute and show the average time of the nocturnal activity
to an accuracy of one second of time.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #AutoHotkey | AutoHotkey | MsgBox, % "The mean time is: " MeanTime(["23:00:17", "23:40:20", "00:12:45", "00:17:19"])
MeanTime(t, x=0, y=0) {
static c := ATan(1) / 45
for k, v in t {
n := StrSplit(v, ":")
r := c * (n[1] * 3600 + n[2] * 60 + n[3]) / 240
x += Cos(r)
y += Sin(r)
}
r := atan2(x, y) / c
r := (r < 0 ? r + 360 : r) / 15
h := SubStr("00" Round(r // 1, 0), -1)
s := SubStr("00" Round(Mod(m := Mod(r, 1) * 60, 1) * 60, 0), -1)
m := SubStr("00" Round(m // 1, 0), -1)
return, h ":" m ":" s
}
atan2(x, y) {
return dllcall("msvcrt\atan2", "Double",y, "Double",x, "CDECL Double")
} |
http://rosettacode.org/wiki/Averages/Pythagorean_means | Averages/Pythagorean means | Task[edit]
Compute all three of the Pythagorean means of the set of integers 1 through 10 (inclusive).
Show that
A
(
x
1
,
…
,
x
n
)
≥
G
(
x
1
,
…
,
x
n
)
≥
H
(
x
1
,
…
,
x
n
)
{\displaystyle A(x_{1},\ldots ,x_{n})\geq G(x_{1},\ldots ,x_{n})\geq H(x_{1},\ldots ,x_{n})}
for this set of positive integers.
The most common of the three means, the arithmetic mean, is the sum of the list divided by its length:
A
(
x
1
,
…
,
x
n
)
=
x
1
+
⋯
+
x
n
n
{\displaystyle A(x_{1},\ldots ,x_{n})={\frac {x_{1}+\cdots +x_{n}}{n}}}
The geometric mean is the
n
{\displaystyle n}
th root of the product of the list:
G
(
x
1
,
…
,
x
n
)
=
x
1
⋯
x
n
n
{\displaystyle G(x_{1},\ldots ,x_{n})={\sqrt[{n}]{x_{1}\cdots x_{n}}}}
The harmonic mean is
n
{\displaystyle n}
divided by the sum of the reciprocal of each item in the list:
H
(
x
1
,
…
,
x
n
)
=
n
1
x
1
+
⋯
+
1
x
n
{\displaystyle H(x_{1},\ldots ,x_{n})={\frac {n}{{\frac {1}{x_{1}}}+\cdots +{\frac {1}{x_{n}}}}}}
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #D | D | import std.stdio, std.algorithm, std.range, std.functional;
auto aMean(T)(T data) pure nothrow @nogc {
return data.sum / data.length;
}
auto gMean(T)(T data) pure /*@nogc*/ {
return data.reduce!q{a * b} ^^ (1.0 / data.length);
}
auto hMean(T)(T data) pure /*@nogc*/ {
return data.length / data.reduce!q{ 1.0 / a + b };
}
void main() {
immutable m = [adjoin!(hMean, gMean, aMean)(iota(1.0L, 11.0L))[]];
writefln("%(%.19f %)", m);
assert(m.isSorted);
} |
http://rosettacode.org/wiki/Balanced_ternary | Balanced ternary | Balanced ternary is a way of representing numbers. Unlike the prevailing binary representation, a balanced ternary integer is in base 3, and each digit can have the values 1, 0, or −1.
Examples
Decimal 11 = 32 + 31 − 30, thus it can be written as "++−"
Decimal 6 = 32 − 31 + 0 × 30, thus it can be written as "+−0"
Task
Implement balanced ternary representation of integers with the following:
Support arbitrarily large integers, both positive and negative;
Provide ways to convert to and from text strings, using digits '+', '-' and '0' (unless you are already using strings to represent balanced ternary; but see requirement 5).
Provide ways to convert to and from native integer type (unless, improbably, your platform's native integer type is balanced ternary). If your native integers can't support arbitrary length, overflows during conversion must be indicated.
Provide ways to perform addition, negation and multiplication directly on balanced ternary integers; do not convert to native integers first.
Make your implementation efficient, with a reasonable definition of "efficient" (and with a reasonable definition of "reasonable").
Test case With balanced ternaries a from string "+-0++0+", b from native integer -436, c "+-++-":
write out a, b and c in decimal notation;
calculate a × (b − c), write out the result in both ternary and decimal notations.
Note: The pages generalised floating point addition and generalised floating point multiplication have code implementing arbitrary precision floating point balanced ternary.
| #C | C | #include <stdio.h>
#include <string.h>
void reverse(char *p) {
size_t len = strlen(p);
char *r = p + len - 1;
while (p < r) {
*p ^= *r;
*r ^= *p;
*p++ ^= *r--;
}
}
void to_bt(int n, char *b) {
static char d[] = { '0', '+', '-' };
static int v[] = { 0, 1, -1 };
char *ptr = b;
*ptr = 0;
while (n) {
int r = n % 3;
if (r < 0) {
r += 3;
}
*ptr = d[r];
*(++ptr) = 0;
n -= v[r];
n /= 3;
}
reverse(b);
}
int from_bt(const char *a) {
int n = 0;
while (*a != '\0') {
n *= 3;
if (*a == '+') {
n++;
} else if (*a == '-') {
n--;
}
a++;
}
return n;
}
char last_char(char *ptr) {
char c;
if (ptr == NULL || *ptr == '\0') {
return '\0';
}
while (*ptr != '\0') {
ptr++;
}
ptr--;
c = *ptr;
*ptr = 0;
return c;
}
void add(const char *b1, const char *b2, char *out) {
if (*b1 != '\0' && *b2 != '\0') {
char c1[16];
char c2[16];
char ob1[16];
char ob2[16];
char d[3] = { 0, 0, 0 };
char L1, L2;
strcpy(c1, b1);
strcpy(c2, b2);
L1 = last_char(c1);
L2 = last_char(c2);
if (L2 < L1) {
L2 ^= L1;
L1 ^= L2;
L2 ^= L1;
}
if (L1 == '-') {
if (L2 == '0') {
d[0] = '-';
}
if (L2 == '-') {
d[0] = '+';
d[1] = '-';
}
}
if (L1 == '+') {
if (L2 == '0') {
d[0] = '+';
}
if (L2 == '-') {
d[0] = '0';
}
if (L2 == '+') {
d[0] = '-';
d[1] = '+';
}
}
if (L1 == '0') {
if (L2 == '0') {
d[0] = '0';
}
}
add(c1, &d[1], ob1);
add(ob1, c2, ob2);
strcpy(out, ob2);
d[1] = 0;
strcat(out, d);
} else if (*b1 != '\0') {
strcpy(out, b1);
} else if (*b2 != '\0') {
strcpy(out, b2);
} else {
*out = '\0';
}
}
void unary_minus(const char *b, char *out) {
while (*b != '\0') {
if (*b == '-') {
*out++ = '+';
b++;
} else if (*b == '+') {
*out++ = '-';
b++;
} else {
*out++ = *b++;
}
}
*out = '\0';
}
void subtract(const char *b1, const char *b2, char *out) {
char buf[16];
unary_minus(b2, buf);
add(b1, buf, out);
}
void mult(const char *b1, const char *b2, char *out) {
char r[16] = "0";
char t[16];
char c1[16];
char c2[16];
char *ptr = c2;
strcpy(c1, b1);
strcpy(c2, b2);
reverse(c2);
while (*ptr != '\0') {
if (*ptr == '+') {
add(r, c1, t);
strcpy(r, t);
}
if (*ptr == '-') {
subtract(r, c1, t);
strcpy(r, t);
}
strcat(c1, "0");
ptr++;
}
ptr = r;
while (*ptr == '0') {
ptr++;
}
strcpy(out, ptr);
}
int main() {
const char *a = "+-0++0+";
char b[16];
const char *c = "+-++-";
char t[16];
char d[16];
to_bt(-436, b);
subtract(b, c, t);
mult(a, t, d);
printf(" a: %14s %10d\n", a, from_bt(a));
printf(" b: %14s %10d\n", b, from_bt(b));
printf(" c: %14s %10d\n", c, from_bt(c));
printf("a*(b-c): %14s %10d\n", d, from_bt(d));
return 0;
} |
http://rosettacode.org/wiki/Babbage_problem | Babbage problem |
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.
For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].
Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.
| #jq | jq | $ jq -n '1 | until( .*. | tostring | test("269696$"); .+1)'
25264 |
http://rosettacode.org/wiki/Babbage_problem | Babbage problem |
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.
For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].
Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.
| #Julia | Julia |
function babbage(x::Integer)
i = big(0)
d = floor(log10(x)) + 1
while i ^ 2 % 10 ^ d != x
i += 1
end
return i
end
|
http://rosettacode.org/wiki/Balanced_brackets | Balanced brackets | Task:
Generate a string with N opening brackets [ and with N closing brackets ], in some arbitrary order.
Determine whether the generated string is balanced; that is, whether it consists entirely of pairs of opening/closing brackets (in that order), none of which mis-nest.
Examples
(empty) OK
[] OK
[][] OK
[[][]] OK
][ NOT OK
][][ NOT OK
[]][[] NOT OK
| #ANTLR | ANTLR |
grammar balancedBrackets ;
options {
language = Java;
}
bb : {System.out.print("input is: ");} (balancedBrackets {System.out.print($balancedBrackets.text);})* NEWLINE {System.out.println();}
;
balancedBrackets
: OpenBracket balancedBrackets* CloseBracket
;
OpenBracket
: '['
;
CloseBracket
: ']'
;
NEWLINE : '\r'? '\n'
;
|
http://rosettacode.org/wiki/Averages/Mode | Averages/Mode | Task[edit]
Write a program to find the mode value of a collection.
The case where the collection is empty may be ignored. Care must be taken to handle the case where the mode is non-unique.
If it is not appropriate or possible to support a general collection, use a vector (array), if possible. If it is not appropriate or possible to support an unspecified value type, use integers.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Common_Lisp | Common Lisp | (defun mode (sequence &rest hash-table-options)
(let ((frequencies (apply #'make-hash-table hash-table-options)))
(map nil (lambda (element)
(incf (gethash element frequencies 0)))
sequence)
(let ((modes '())
(hifreq 0 ))
(maphash (lambda (element frequency)
(cond ((> frequency hifreq)
(setf hifreq frequency
modes (list element)))
((= frequency hifreq)
(push element modes))))
frequencies)
(values modes hifreq)))) |
http://rosettacode.org/wiki/Averages/Simple_moving_average | Averages/Simple moving average | Computing the simple moving average of a series of numbers.
Task[edit]
Create a stateful function/class/instance that takes a period and returns a routine that takes a number as argument and returns a simple moving average of its arguments so far.
Description
A simple moving average is a method for computing an average of a stream of numbers by only averaging the last P numbers from the stream, where P is known as the period.
It can be implemented by calling an initialing routine with P as its argument, I(P), which should then return a routine that when called with individual, successive members of a stream of numbers, computes the mean of (up to), the last P of them, lets call this SMA().
The word stateful in the task description refers to the need for SMA() to remember certain information between calls to it:
The period, P
An ordered container of at least the last P numbers from each of its individual calls.
Stateful also means that successive calls to I(), the initializer, should return separate routines that do not share saved state so they could be used on two independent streams of data.
Pseudo-code for an implementation of SMA is:
function SMA(number: N):
stateful integer: P
stateful list: stream
number: average
stream.append_last(N)
if stream.length() > P:
# Only average the last P elements of the stream
stream.delete_first()
if stream.length() == 0:
average = 0
else:
average = sum( stream.values() ) / stream.length()
return average
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Objeck | Objeck |
use Collection;
class MovingAverage {
@window : FloatQueue;
@period : Int;
@sum : Float;
New(period : Int) {
@window := FloatQueue->New();
@period := period;
}
method : NewNum(num : Float) ~ Nil {
@sum += num;
@window->Add(num);
if(@window->Size() > @period) {
@sum -= @window->Remove();
};
}
method : GetAvg() ~ Float {
if(@window->IsEmpty()) {
return 0; # technically the average is undefined
};
return @sum / @window->Size();
}
function : Main(args : String[]) ~ Nil {
testData := [1.0, 2.0, 3.0, 4.0, 5.0, 5.0, 4.0, 3.0, 2.0, 1.0];
windowSizes := [3.0, 5.0];
each(i : windowSizes) {
windSize := windowSizes[i];
ma := MovingAverage->New(windSize);
each(j : testData) {
x := testData[j];
ma->NewNum(x);
avg := ma->GetAvg();
"Next number = {$x}, SMA = {$avg}"->PrintLine();
};
IO.Console->PrintLine();
};
}
}
|
http://rosettacode.org/wiki/Averages/Mean_time_of_day | Averages/Mean time of day | Task[edit]
A particular activity of bats occurs at these times of the day:
23:00:17, 23:40:20, 00:12:45, 00:17:19
Using the idea that there are twenty-four hours in a day,
which is analogous to there being 360 degrees in a circle,
map times of day to and from angles;
and using the ideas of Averages/Mean angle
compute and show the average time of the nocturnal activity
to an accuracy of one second of time.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #AWK | AWK | #!/usr/bin/awk -f
{
c = atan2(0,-1)/(12*60*60);
x=0.0; y=0.0;
for (i=1; i<=NF; i++) {
split($i,a,":");
p = (a[1]*3600+a[2]*60+a[3])*c;
x += sin(p);
y += cos(p);
}
p = atan2(x,y)/c;
if (p<0) p += 24*60*60;
print strftime("%T",p,1);
} |
http://rosettacode.org/wiki/AVL_tree | AVL tree |
This page uses content from Wikipedia. The original article was at AVL tree. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
In computer science, an AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; at no time do they differ by more than one because rebalancing is done ensure this is the case. Lookup, insertion, and deletion all take O(log n) time in both the average and worst cases, where n is the number of nodes in the tree prior to the operation. Insertions and deletions may require the tree to be rebalanced by one or more tree rotations. Note the tree of nodes comprise a set, so duplicate node keys are not allowed.
AVL trees are often compared with red-black trees because they support the same set of operations and because red-black trees also take O(log n) time for the basic operations. Because AVL trees are more rigidly balanced, they are faster than red-black trees for lookup-intensive applications. Similar to red-black trees, AVL trees are height-balanced, but in general not weight-balanced nor μ-balanced; that is, sibling nodes can have hugely differing numbers of descendants.
Task
Implement an AVL tree in the language of choice, and provide at least basic operations.
| #AArch64_Assembly | AArch64 Assembly |
/* ARM assembly AARCH64 Raspberry PI 3B */
/* program avltree64.s */
/*******************************************/
/* Constantes file */
/*******************************************/
/* for this file see task include a file in language AArch64 assembly*/
.include "../includeConstantesARM64.inc"
.equ NBVAL, 12
/*******************************************/
/* Structures */
/********************************************/
/* structure tree */
.struct 0
tree_root: // root pointer (or node right)
.struct tree_root + 8
tree_size: // number of element of tree
.struct tree_size + 8
tree_suite:
.struct tree_suite + 24 // for alignement to node
tree_fin:
/* structure node tree */
.struct 0
node_right: // right pointer
.struct node_right + 8
node_left: // left pointer
.struct node_left + 8
node_value: // element value
.struct node_value + 8
node_height: // element value
.struct node_height + 8
node_parent: // element value
.struct node_parent + 8
node_fin:
/*******************************************/
/* Initialized data */
/*******************************************/
.data
szMessPreOrder: .asciz "PreOrder :\n"
szCarriageReturn: .asciz "\n"
/* datas error display */
szMessErreur: .asciz "Error detected.\n"
szMessKeyDbl: .asciz "Key exists in tree.\n"
szMessInsInv: .asciz "Insertion in inverse order.\n"
/* datas message display */
szMessResult: .asciz "Ele: @ G: @ D: @ val @ h @ \npere @\n"
/*******************************************/
/* UnInitialized data */
/*******************************************/
.bss
sZoneConv: .skip 24
stTree: .skip tree_fin // place to structure tree
stTree1: .skip tree_fin // place to structure tree
/*******************************************/
/* code section */
/*******************************************/
.text
.global main
main:
mov x20,#1 // node tree value
1: // loop insertion in order
ldr x0,qAdrstTree // structure tree address
mov x1,x20
bl insertElement // add element value x1
cmp x0,-1
beq 99f
add x20,x20,1 // increment value
cmp x20,NBVAL // end ?
ble 1b // no -> loop
ldr x0,qAdrstTree // structure tree address
mov x1,11 // verif key dobble
bl insertElement // add element value x1
cmp x0,-1
bne 2f
ldr x0,qAdrszMessErreur
bl affichageMess
2:
ldr x0,qAdrszMessPreOrder // load verification
bl affichageMess
ldr x3,qAdrstTree // tree root address (begin structure)
ldr x0,[x3,tree_root]
ldr x1,qAdrdisplayElement // function to execute
bl preOrder
ldr x0,qAdrszMessInsInv
bl affichageMess
mov x20,NBVAL // node tree value
3: // loop insertion inverse order
ldr x0,qAdrstTree1 // structure tree address
mov x1,x20
bl insertElement // add element value x1
cmp x0,-1
beq 99f
sub x20,x20,1 // increment value
cmp x20,0 // end ?
bgt 3b // no -> loop
ldr x0,qAdrszMessPreOrder // load verification
bl affichageMess
ldr x3,qAdrstTree1 // tree root address (begin structure)
ldr x0,[x3,tree_root]
ldr x1,qAdrdisplayElement // function to execute
bl preOrder
// search value
ldr x0,qAdrstTree1 // tree root address (begin structure)
mov x1,11 // value to search
bl searchTree
cmp x0,-1
beq 100f
mov x2,x0
ldr x0,qAdrszMessKeyDbl // key exists
bl affichageMess
// suppresssion previous value
mov x0,x2
ldr x1,qAdrstTree1
bl supprimer
ldr x0,qAdrszMessPreOrder // verification
bl affichageMess
ldr x3,qAdrstTree1 // tree root address (begin structure)
ldr x0,[x3,tree_root]
ldr x1,qAdrdisplayElement // function to execute
bl preOrder
b 100f
99: // display error
ldr x0,qAdrszMessErreur
bl affichageMess
100: // standard end of the program
mov x8, #EXIT // request to exit program
svc 0 // perform system call
qAdrszMessPreOrder: .quad szMessPreOrder
qAdrszMessErreur: .quad szMessErreur
qAdrszCarriageReturn: .quad szCarriageReturn
qAdrstTree: .quad stTree
qAdrstTree1: .quad stTree1
qAdrdisplayElement: .quad displayElement
qAdrszMessInsInv: .quad szMessInsInv
/******************************************************************/
/* insert element in the tree */
/******************************************************************/
/* x0 contains the address of the tree structure */
/* x1 contains the value of element */
/* x0 returns address of element or - 1 if error */
insertElement: // INFO: insertElement
stp x1,lr,[sp,-16]! // save registers
mov x6,x0 // save head
mov x0,#node_fin // reservation place one element
bl allocHeap
cmp x0,#-1 // allocation error
beq 100f
mov x5,x0
str x1,[x5,#node_value] // store value in address heap
mov x3,#0
str x3,[x5,#node_left] // init left pointer with zero
str x3,[x5,#node_right] // init right pointer with zero
str x3,[x5,#node_height] // init balance with zero
ldr x2,[x6,#tree_size] // load tree size
cmp x2,#0 // 0 element ?
bne 1f
str x5,[x6,#tree_root] // yes -> store in root
b 4f
1: // else search free address in tree
ldr x3,[x6,#tree_root] // start with address root
2: // begin loop to insertion
ldr x4,[x3,#node_value] // load key
cmp x1,x4
beq 6f // key equal
blt 3f // key <
// key > insertion right
ldr x8,[x3,#node_right] // node empty ?
cmp x8,#0
csel x3,x8,x3,ne // current = right node if not
//movne x3,x8 // no -> next node
bne 2b // and loop
str x5,[x3,#node_right] // store node address in right pointer
b 4f
3: // left
ldr x8,[x3,#node_left] // left pointer empty ?
cmp x8,#0
csel x3,x8,x3,ne // current = left node if not
//movne x3,x8 //
bne 2b // no -> loop
str x5,[x3,#node_left] // store node address in left pointer
4:
str x3,[x5,#node_parent] // store parent
mov x4,#1
str x4,[x5,#node_height] // store height = 1
mov x0,x5 // begin node to requilbrate
mov x1,x6 // head address
bl equilibrer
5:
add x2,x2,#1 // increment tree size
str x2,[x6,#tree_size]
mov x0,#0
b 100f
6: // key equal ?
ldr x0,qAdrszMessKeyDbl
bl affichageMess
mov x0,#-1
b 100f
100:
ldp x1,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
qAdrszMessKeyDbl: .quad szMessKeyDbl
/******************************************************************/
/* equilibrer after insertion */
/******************************************************************/
/* x0 contains the address of the node */
/* x1 contains the address of head */
equilibrer: // INFO: equilibrer
stp x1,lr,[sp,-16]! // save registers
stp x2,x3,[sp,-16]! // save registers
stp x4,x5,[sp,-16]! // save registers
stp x6,x7,[sp,-16]! // save registers
mov x3,#0 // balance factor
1: // begin loop
ldr x5,[x0,#node_parent] // load father
cmp x5,#0 // end ?
beq 8f
cmp x3,#2 // right tree too long
beq 8f
cmp x3,#-2 // left tree too long
beq 8f
mov x6,x0 // s = current
ldr x0,[x6,#node_parent] // current = father
ldr x7,[x0,#node_left]
mov x4,#0
cmp x7,#0
beq 2f
ldr x4,[x7,#node_height] // height left tree
2:
ldr x7,[x0,#node_right]
mov x2,#0
cmp x7,#0
beq 3f
ldr x2,[x7,#node_height] // height right tree
3:
cmp x4,x2
ble 4f
add x4,x4,#1
str x4,[x0,#node_height]
b 5f
4:
add x2,x2,#1
str x2,[x0,#node_height]
5:
ldr x7,[x0,#node_right]
mov x4,0
cmp x7,#0
beq 6f
ldr x4,[x7,#node_height]
6:
ldr x7,[x0,#node_left]
mov x2,0
cmp x7,#0
beq 7f
ldr x2,[x7,#node_height]
7:
sub x3,x4,x2 // compute balance factor
b 1b
8:
cmp x3,#2
beq 9f
cmp x3,#-2
beq 9f
b 100f
9:
mov x3,x1
mov x4,x0
mov x1,x6
bl equiUnSommet
// change head address ?
ldr x2,[x3,#tree_root]
cmp x2,x4
bne 100f
str x6,[x3,#tree_root]
100:
ldp x6,x7,[sp],16 // restaur 2 registers
ldp x4,x5,[sp],16 // restaur 2 registers
ldp x2,x3,[sp],16 // restaur 2 registers
ldp x1,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/******************************************************************/
/* equilibre 1 sommet */
/******************************************************************/
/* x0 contains the address of the node */
/* x1 contains the address of the node */
equiUnSommet: // INFO: equiUnSommet
stp x1,lr,[sp,-16]! // save registers
stp x2,x3,[sp,-16]! // save registers
stp x4,x5,[sp,-16]! // save registers
stp x6,x7,[sp,-16]! // save registers
mov x5,x0 // save p
mov x6,x1 // s
ldr x2,[x5,#node_left]
cmp x2,x6
bne 6f
ldr x7,[x5,#node_right]
mov x4,#0
cmp x7,#0
beq 1f
ldr x4,[x7,#node_height]
1:
ldr x7,[x5,#node_left]
mov x2,0
cmp x7,#0
beq 2f
ldr x2,[x7,#node_height]
2:
sub x3,x4,x2
cmp x3,#-2
bne 100f
ldr x7,[x6,#node_right]
mov x4,0
cmp x7,#0
beq 3f
ldr x4,[x7,#node_height]
3:
ldr x7,[x6,#node_left]
mov x2,0
cmp x7,#0
beq 4f
ldr x2,[x7,#node_height]
4:
sub x3,x4,x2
cmp x3,#1
bge 5f
mov x0,x5
bl rotRight
b 100f
5:
mov x0,x6
bl rotLeft
mov x0,x5
bl rotRight
b 100f
6:
ldr x7,[x5,#node_right]
mov x4,0
cmp x7,#0
beq 7f
ldr x4,[x7,#node_height]
7:
ldr x7,[x5,#node_left]
mov x2,0
cmp x7,#0
beq 8f
ldr x2,[x7,#node_height]
8:
sub x3,x4,x2
cmp x3,2
bne 100f
ldr x7,[x6,#node_right]
mov x4,0
cmp x7,#0
beq 9f
ldr x4,[x7,#node_height]
9:
ldr x7,[x6,#node_left]
mov x2,0
cmp x7,#0
beq 10f
ldr x2,[x7,#node_height]
10:
sub x3,x4,x2
cmp x3,#-1
ble 11f
mov x0,x5
bl rotLeft
b 100f
11:
mov x0,x6
bl rotRight
mov x0,x5
bl rotLeft
100:
ldp x6,x7,[sp],16 // restaur 2 registers
ldp x4,x5,[sp],16 // restaur 2 registers
ldp x2,x3,[sp],16 // restaur 2 registers
ldp x1,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/******************************************************************/
/* right rotation */
/******************************************************************/
/* x0 contains the address of the node */
rotRight: // INFO: rotRight
stp x1,lr,[sp,-16]! // save registers
stp x2,x3,[sp,-16]! // save registers
stp x4,x5,[sp,-16]! // save registers
// x2 x2
// x0 x1
// x1 x0
// x3 x3
ldr x1,[x0,#node_left] // load left children
ldr x2,[x0,#node_parent] // load father
cmp x2,#0 // no father ???
beq 2f
ldr x3,[x2,#node_left] // load left node father
cmp x3,x0 // equal current node ?
bne 1f
str x1,[x2,#node_left] // yes store left children
b 2f
1:
str x1,[x2,#node_right] // no store right
2:
str x2,[x1,#node_parent] // change parent
str x1,[x0,#node_parent]
ldr x3,[x1,#node_right]
str x3,[x0,#node_left]
cmp x3,#0
beq 3f
str x0,[x3,#node_parent] // change parent node left
3:
str x0,[x1,#node_right]
ldr x3,[x0,#node_left] // compute newbalance factor
mov x4,0
cmp x3,#0
beq 4f
ldr x4,[x3,#node_height]
4:
ldr x3,[x0,#node_right]
mov x5,0
cmp x3,#0
beq 5f
ldr x5,[x3,#node_height]
5:
cmp x4,x5
ble 6f
add x4,x4,#1
str x4,[x0,#node_height]
b 7f
6:
add x5,x5,#1
str x5,[x0,#node_height]
7:
//
ldr x3,[x1,#node_left] // compute new balance factor
mov x4,0
cmp x3,#0
beq 8f
ldr x4,[x3,#node_height]
8:
ldr x3,[x1,#node_right]
mov x5,0
cmp x3,#0
beq 9f
ldr x5,[x3,#node_height]
9:
cmp x4,x5
ble 10f
add x4,x4,#1
str x4,[x1,#node_height]
b 100f
10:
add x5,x5,#1
str x5,[x1,#node_height]
100:
ldp x4,x5,[sp],16 // restaur 2 registers
ldp x2,x3,[sp],16 // restaur 2 registers
ldp x1,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/******************************************************************/
/* left rotation */
/******************************************************************/
/* x0 contains the address of the node sommet */
rotLeft: // INFO: rotLeft
stp x1,lr,[sp,-16]! // save registers
stp x2,x3,[sp,-16]! // save registers
stp x4,x5,[sp,-16]! // save registers
// x2 x2
// x0 x1
// x1 x0
// x3 x3
ldr x1,[x0,#node_right] // load right children
ldr x2,[x0,#node_parent] // load father (racine)
cmp x2,#0 // no father ???
beq 2f
ldr x3,[x2,#node_left] // load left node father
cmp x3,x0 // equal current node ?
bne 1f
str x1,[x2,#node_left] // yes store left children
b 2f
1:
str x1,[x2,#node_right] // no store to right
2:
str x2,[x1,#node_parent] // change parent of right children
str x1,[x0,#node_parent] // change parent of sommet
ldr x3,[x1,#node_left] // left children
str x3,[x0,#node_right] // left children pivot exists ?
cmp x3,#0
beq 3f
str x0,[x3,#node_parent] // yes store in
3:
str x0,[x1,#node_left]
//
ldr x3,[x0,#node_left] // compute new height for old summit
mov x4,0
cmp x3,#0
beq 4f
ldr x4,[x3,#node_height] // left height
4:
ldr x3,[x0,#node_right]
mov x5,0
cmp x3,#0
beq 5f
ldr x5,[x3,#node_height] // right height
5:
cmp x4,x5
ble 6f
add x4,x4,#1
str x4,[x0,#node_height] // if right > left
b 7f
6:
add x5,x5,#1
str x5,[x0,#node_height] // if left > right
7:
//
ldr x3,[x1,#node_left] // compute new height for new
mov x4,0
cmp x3,#0
beq 8f
ldr x4,[x3,#node_height]
8:
ldr x3,[x1,#node_right]
mov x5,0
cmp x3,#0
beq 9f
ldr x5,[x3,#node_height]
9:
cmp x4,x5
ble 10f
add x4,x4,#1
str x4,[x1,#node_height]
b 100f
10:
add x5,x5,#1
str x5,[x1,#node_height]
100:
ldp x4,x5,[sp],16 // restaur 2 registers
ldp x2,x3,[sp],16 // restaur 2 registers
ldp x1,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/******************************************************************/
/* search value in tree */
/******************************************************************/
/* x0 contains the address of structure of tree */
/* x1 contains the value to search */
searchTree: // INFO: searchTree
stp x2,lr,[sp,-16]! // save registers
stp x3,x4,[sp,-16]! // save registers
ldr x2,[x0,#tree_root]
1: // begin loop
ldr x4,[x2,#node_value] // load key
cmp x1,x4
beq 3f // key equal
blt 2f // key <
// key > insertion right
ldr x3,[x2,#node_right] // node empty ?
cmp x3,#0
csel x2,x3,x2,ne
//movne x2,x3 // no -> next node
bne 1b // and loop
mov x0,#-1 // not find
b 100f
2: // left
ldr x3,[x2,#node_left] // left pointer empty ?
cmp x3,#0
csel x2,x3,x2,ne
bne 1b // no -> loop
mov x0,#-1 // not find
b 100f
3:
mov x0,x2 // return node address
100:
ldp x3,x4,[sp],16 // restaur 2 registers
ldp x2,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/******************************************************************/
/* suppression node */
/******************************************************************/
/* x0 contains the address of the node */
/* x1 contains structure tree address */
supprimer: // INFO: supprimer
stp x1,lr,[sp,-16]! // save registers
stp x2,x3,[sp,-16]! // save registers
stp x4,x5,[sp,-16]! // save registers
stp x6,x7,[sp,-16]! // save registers
ldr x1,[x0,#node_left]
cmp x1,#0
bne 5f
ldr x1,[x0,#node_right]
cmp x1,#0
bne 5f
// is a leaf
mov x4,#0
ldr x3,[x0,#node_parent] // father
cmp x3,#0
bne 11f
str x4,[x1,#tree_root]
b 100f
11:
ldr x1,[x3,#node_left]
cmp x1,x0
bne 2f
str x4,[x3,#node_left] // suppression left children
ldr x5,[x3,#node_right]
mov x6,#0
cmp x5,#0
beq 12f
ldr x6,[x5,#node_height]
12:
add x6,x6,#1
str x6,[x3,#node_height]
b 3f
2: // suppression right children
str x4,[x3,#node_right]
ldr x5,[x3,#node_left]
mov x6,#0
cmp x5,#0
beq 21f
ldr x6,[x5,#node_height]
21:
add x6,x6,#1
str x6,[x3,#node_height]
3: // new balance
mov x0,x3
bl equilibrerSupp
b 100f
5: // is not à leaf
ldr x7,[x0,#node_right]
cmp x7,#0
beq 7f
mov x2,x0
mov x0,x7
6:
ldr x6,[x0,#node_left] // search the litle element
cmp x6,#0
beq 9f
mov x0,x6
b 6b
7:
ldr x7,[x0,#node_left]
cmp x7,#0
beq 9f
mov x2,x0
mov x0,x7
8:
ldr x6,[x0,#node_right] // search the great element
cmp x6,#0
beq 9f
mov x0,x6
b 8b
9:
ldr x5,[x0,#node_value] // copy value
str x5,[x2,#node_value]
bl supprimer // suppression node x0
100:
ldp x6,x7,[sp],16 // restaur 2 registers
ldp x4,x5,[sp],16 // restaur 2 registers
ldp x2,x3,[sp],16 // restaur 2 registers
ldp x1,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/******************************************************************/
/* equilibrer after suppression */
/******************************************************************/
/* x0 contains the address of the node */
/* x1 contains the address of head */
equilibrerSupp: // INFO: equilibrerSupp
stp x1,lr,[sp,-16]! // save registers
stp x2,x3,[sp,-16]! // save registers
stp x4,x5,[sp,-16]! // save registers
stp x6,x7,[sp,-16]! // save registers
mov x3,#1 // balance factor
ldr x2,[x1,#tree_root]
1:
ldr x5,[x0,#node_parent] // load father
cmp x5,#0 // no father
beq 100f
cmp x3,#0 // balance equilibred
beq 100f
mov x6,x0 // save entry node
ldr x0,[x6,#node_parent] // current = father
ldr x7,[x0,#node_left]
mov x4,#0
cmp x7,#0
b 11f
ldr x4,[x7,#node_height] // height left tree
11:
ldr x7,[x0,#node_right]
mov x5,#0
cmp x7,#0
beq 12f
ldr x5,[x7,#node_height] // height right tree
12:
cmp x4,x5
ble 13f
add x4,x4,1
str x4,[x0,#node_height]
b 14f
13:
add x5,x5,1
str x5,[x0,#node_height]
14:
ldr x7,[x0,#node_right]
mov x4,#0
cmp x7,#0
beq 15f
ldr x4,[x7,#node_height]
15:
ldr x7,[x0,#node_left]
mov x5,0
cmp x7,#0
beq 16f
ldr x5,[x7,#node_height]
16:
sub x3,x4,x5 // compute balance factor
mov x2,x1
mov x7,x0 // save current
mov x1,x6
bl equiUnSommet
// change head address ?
cmp x2,x7
bne 17f
str x6,[x3,#tree_root]
17:
mov x0,x7 // restaur current
b 1b
100:
ldp x6,x7,[sp],16 // restaur 2 registers
ldp x4,x5,[sp],16 // restaur 2 registers
ldp x2,x3,[sp],16 // restaur 2 registers
ldp x1,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/******************************************************************/
/* preOrder */
/******************************************************************/
/* x0 contains the address of the node */
/* x1 function address */
preOrder: // INFO: preOrder
stp x2,lr,[sp,-16]! // save registers
cmp x0,#0
beq 100f
mov x2,x0
blr x1 // call function
ldr x0,[x2,#node_left]
bl preOrder
ldr x0,[x2,#node_right]
bl preOrder
100:
ldp x2,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/******************************************************************/
/* display node */
/******************************************************************/
/* x0 contains node address */
displayElement: // INFO: displayElement
stp x1,lr,[sp,-16]! // save registers
stp x2,x3,[sp,-16]! // save registers
stp x4,x5,[sp,-16]! // save registers
mov x2,x0
ldr x1,qAdrsZoneConv
bl conversion16
//strb wzr,[x1,x0]
ldr x0,qAdrszMessResult
ldr x1,qAdrsZoneConv
bl strInsertAtCharInc
mov x3,x0
ldr x0,[x2,#node_left]
ldr x1,qAdrsZoneConv
bl conversion16
//strb wzr,[x1,x0]
mov x0,x3
ldr x1,qAdrsZoneConv
bl strInsertAtCharInc
mov x3,x0
ldr x0,[x2,#node_right]
ldr x1,qAdrsZoneConv
bl conversion16
//strb wzr,[x1,x0]
mov x0,x3
ldr x1,qAdrsZoneConv
bl strInsertAtCharInc
mov x3,x0
ldr x0,[x2,#node_value]
ldr x1,qAdrsZoneConv
bl conversion10
//strb wzr,[x1,x0]
mov x0,x3
ldr x1,qAdrsZoneConv
bl strInsertAtCharInc
mov x3,x0
ldr x0,[x2,#node_height]
ldr x1,qAdrsZoneConv
bl conversion10
//strb wzr,[x1,x0]
mov x0,x3
ldr x1,qAdrsZoneConv
bl strInsertAtCharInc
mov x3,x0
ldr x0,[x2,#node_parent]
ldr x1,qAdrsZoneConv
bl conversion16
//strb wzr,[x1,x0]
mov x0,x3
ldr x1,qAdrsZoneConv
bl strInsertAtCharInc
bl affichageMess
100:
ldp x4,x5,[sp],16 // restaur 2 registers
ldp x2,x3,[sp],16 // restaur 2 registers
ldp x1,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
qAdrszMessResult: .quad szMessResult
qAdrsZoneConv: .quad sZoneConv
/******************************************************************/
/* memory allocation on the heap */
/******************************************************************/
/* x0 contains the size to allocate */
/* x0 returns address of memory heap or - 1 if error */
/* CAUTION : The size of the allowance must be a multiple of 4 */
allocHeap:
stp x1,lr,[sp,-16]! // save registers
stp x2,x8,[sp,-16]! // save registers
// allocation
mov x1,x0 // save size
mov x0,0 // read address start heap
mov x8,BRK // call system 'brk'
svc 0
mov x2,x0 // save address heap for return
add x0,x0,x1 // reservation place for size
mov x8,BRK // call system 'brk'
svc 0
cmp x0,-1 // allocation error
beq 100f
mov x0,x2 // return address memory heap
100:
ldp x2,x8,[sp],16 // restaur 2 registers
ldp x1,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/********************************************************/
/* File Include fonctions */
/********************************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeARM64.inc"
|
http://rosettacode.org/wiki/Averages/Mean_angle | Averages/Mean angle | When calculating the average or mean of an angle one has to take into account how angles wrap around so that any angle in degrees plus any integer multiple of 360 degrees is a measure of the same angle.
If one wanted an average direction of the wind over two readings where the first reading was of 350 degrees and the second was of 10 degrees then the average of the numbers is 180 degrees, whereas if you can note that 350 degrees is equivalent to -10 degrees and so you have two readings at 10 degrees either side of zero degrees leading to a more fitting mean angle of zero degrees.
To calculate the mean angle of several angles:
Assume all angles are on the unit circle and convert them to complex numbers expressed in real and imaginary form.
Compute the mean of the complex numbers.
Convert the complex mean to polar coordinates whereupon the phase of the complex mean is the required angular mean.
(Note that, since the mean is the sum divided by the number of numbers, and division by a positive real number does not affect the angle, you can also simply compute the sum for step 2.)
You can alternatively use this formula:
Given the angles
α
1
,
…
,
α
n
{\displaystyle \alpha _{1},\dots ,\alpha _{n}}
the mean is computed by
α
¯
=
atan2
(
1
n
⋅
∑
j
=
1
n
sin
α
j
,
1
n
⋅
∑
j
=
1
n
cos
α
j
)
{\displaystyle {\bar {\alpha }}=\operatorname {atan2} \left({\frac {1}{n}}\cdot \sum _{j=1}^{n}\sin \alpha _{j},{\frac {1}{n}}\cdot \sum _{j=1}^{n}\cos \alpha _{j}\right)}
Task[edit]
write a function/method/subroutine/... that given a list of angles in degrees returns their mean angle.
(You should use a built-in function if you have one that does this for degrees or radians).
Use the function to compute the means of these lists of angles (in degrees):
[350, 10]
[90, 180, 270, 360]
[10, 20, 30]
Show your output here.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #11l | 11l | F mean_angle(angles)
V x = sum(angles.map(a -> cos(radians(a)))) / angles.len
V y = sum(angles.map(a -> sin(radians(a)))) / angles.len
R degrees(atan2(y, x))
print(mean_angle([350, 10]))
print(mean_angle([90, 180, 270, 360]))
print(mean_angle([10, 20, 30])) |
http://rosettacode.org/wiki/Averages/Median | Averages/Median | Task[edit]
Write a program to find the median value of a vector of floating-point numbers.
The program need not handle the case where the vector is empty, but must handle the case where there are an even number of elements. In that case, return the average of the two middle values.
There are several approaches to this. One is to sort the elements, and then pick the element(s) in the middle.
Sorting would take at least O(n logn). Another approach would be to build a priority queue from the elements, and then extract half of the elements to get to the middle element(s). This would also take O(n logn). The best solution is to use the selection algorithm to find the median in O(n) time.
See also
Quickselect_algorithm
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #11l | 11l | F median(aray)
V srtd = sorted(aray)
V alen = srtd.len
R 0.5 * (srtd[(alen - 1) I/ 2] + srtd[alen I/ 2])
print(median([4.1, 5.6, 7.2, 1.7, 9.3, 4.4, 3.2]))
print(median([4.1, 7.2, 1.7, 9.3, 4.4, 3.2])) |
http://rosettacode.org/wiki/Averages/Pythagorean_means | Averages/Pythagorean means | Task[edit]
Compute all three of the Pythagorean means of the set of integers 1 through 10 (inclusive).
Show that
A
(
x
1
,
…
,
x
n
)
≥
G
(
x
1
,
…
,
x
n
)
≥
H
(
x
1
,
…
,
x
n
)
{\displaystyle A(x_{1},\ldots ,x_{n})\geq G(x_{1},\ldots ,x_{n})\geq H(x_{1},\ldots ,x_{n})}
for this set of positive integers.
The most common of the three means, the arithmetic mean, is the sum of the list divided by its length:
A
(
x
1
,
…
,
x
n
)
=
x
1
+
⋯
+
x
n
n
{\displaystyle A(x_{1},\ldots ,x_{n})={\frac {x_{1}+\cdots +x_{n}}{n}}}
The geometric mean is the
n
{\displaystyle n}
th root of the product of the list:
G
(
x
1
,
…
,
x
n
)
=
x
1
⋯
x
n
n
{\displaystyle G(x_{1},\ldots ,x_{n})={\sqrt[{n}]{x_{1}\cdots x_{n}}}}
The harmonic mean is
n
{\displaystyle n}
divided by the sum of the reciprocal of each item in the list:
H
(
x
1
,
…
,
x
n
)
=
n
1
x
1
+
⋯
+
1
x
n
{\displaystyle H(x_{1},\ldots ,x_{n})={\frac {n}{{\frac {1}{x_{1}}}+\cdots +{\frac {1}{x_{n}}}}}}
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Delphi | Delphi | program AveragesPythagoreanMeans;
{$APPTYPE CONSOLE}
uses Types, Math;
function ArithmeticMean(aArray: TDoubleDynArray): Double;
var
lValue: Double;
begin
Result := 0;
for lValue in aArray do
Result := Result + lValue;
if Result > 0 then
Result := Result / Length(aArray);
end;
function GeometricMean(aArray: TDoubleDynArray): Double;
var
lValue: Double;
begin
Result := 1;
for lValue in aArray do
Result := Result * lValue;
Result := Power(Result, 1 / Length(aArray));
end;
function HarmonicMean(aArray: TDoubleDynArray): Double;
var
lValue: Double;
begin
Result := 0;
for lValue in aArray do
Result := Result + 1 / lValue;
Result := Length(aArray) / Result;
end;
var
lSourceArray: TDoubleDynArray;
AMean, GMean, HMean: Double;
begin
lSourceArray := TDoubleDynArray.Create(1,2,3,4,5,6,7,8,9,10);
AMean := ArithmeticMean(lSourceArray));
GMean := GeometricMean(lSourceArray));
HMean := HarmonicMean(lSourceArray));
if (AMean >= GMean) and (GMean >= HMean) then
Writeln(AMean, " ≥ ", GMean, " ≥ ", HMean)
else
writeln("Error!");
end. |
http://rosettacode.org/wiki/Balanced_ternary | Balanced ternary | Balanced ternary is a way of representing numbers. Unlike the prevailing binary representation, a balanced ternary integer is in base 3, and each digit can have the values 1, 0, or −1.
Examples
Decimal 11 = 32 + 31 − 30, thus it can be written as "++−"
Decimal 6 = 32 − 31 + 0 × 30, thus it can be written as "+−0"
Task
Implement balanced ternary representation of integers with the following:
Support arbitrarily large integers, both positive and negative;
Provide ways to convert to and from text strings, using digits '+', '-' and '0' (unless you are already using strings to represent balanced ternary; but see requirement 5).
Provide ways to convert to and from native integer type (unless, improbably, your platform's native integer type is balanced ternary). If your native integers can't support arbitrary length, overflows during conversion must be indicated.
Provide ways to perform addition, negation and multiplication directly on balanced ternary integers; do not convert to native integers first.
Make your implementation efficient, with a reasonable definition of "efficient" (and with a reasonable definition of "reasonable").
Test case With balanced ternaries a from string "+-0++0+", b from native integer -436, c "+-++-":
write out a, b and c in decimal notation;
calculate a × (b − c), write out the result in both ternary and decimal notations.
Note: The pages generalised floating point addition and generalised floating point multiplication have code implementing arbitrary precision floating point balanced ternary.
| #C.23 | C# | using System;
using System.Text;
using System.Collections.Generic;
public class BalancedTernary
{
public static void Main()
{
BalancedTernary a = new BalancedTernary("+-0++0+");
System.Console.WriteLine("a: " + a + " = " + a.ToLong());
BalancedTernary b = new BalancedTernary(-436);
System.Console.WriteLine("b: " + b + " = " + b.ToLong());
BalancedTernary c = new BalancedTernary("+-++-");
System.Console.WriteLine("c: " + c + " = " + c.ToLong());
BalancedTernary d = a * (b - c);
System.Console.WriteLine("a * (b - c): " + d + " = " + d.ToLong());
}
private enum BalancedTernaryDigit
{
MINUS = -1,
ZERO = 0,
PLUS = 1
}
private BalancedTernaryDigit[] value;
// empty = 0
public BalancedTernary()
{
this.value = new BalancedTernaryDigit[0];
}
// create from String
public BalancedTernary(String str)
{
this.value = new BalancedTernaryDigit[str.Length];
for (int i = 0; i < str.Length; ++i)
{
switch (str[i])
{
case '-':
this.value[i] = BalancedTernaryDigit.MINUS;
break;
case '0':
this.value[i] = BalancedTernaryDigit.ZERO;
break;
case '+':
this.value[i] = BalancedTernaryDigit.PLUS;
break;
default:
throw new ArgumentException("Unknown Digit: " + str[i]);
}
}
Array.Reverse(this.value);
}
// convert long integer
public BalancedTernary(long l)
{
List<BalancedTernaryDigit> value = new List<BalancedTernaryDigit>();
int sign = Math.Sign(l);
l = Math.Abs(l);
while (l != 0)
{
byte rem = (byte)(l % 3);
switch (rem)
{
case 0:
case 1:
value.Add((BalancedTernaryDigit)rem);
l /= 3;
break;
case 2:
value.Add(BalancedTernaryDigit.MINUS);
l = (l + 1) / 3;
break;
}
}
this.value = value.ToArray();
if (sign < 0)
{
this.Invert();
}
}
// copy constructor
public BalancedTernary(BalancedTernary origin)
{
this.value = new BalancedTernaryDigit[origin.value.Length];
Array.Copy(origin.value, this.value, origin.value.Length);
}
// only for internal use
private BalancedTernary(BalancedTernaryDigit[] value)
{
int end = value.Length - 1;
while (value[end] == BalancedTernaryDigit.ZERO)
--end;
this.value = new BalancedTernaryDigit[end + 1];
Array.Copy(value, this.value, end + 1);
}
// invert the values
private void Invert()
{
for (int i=0; i < this.value.Length; ++i)
{
this.value[i] = (BalancedTernaryDigit)(-(int)this.value[i]);
}
}
// convert to string
override public String ToString()
{
StringBuilder result = new StringBuilder();
for (int i = this.value.Length - 1; i >= 0; --i)
{
switch (this.value[i])
{
case BalancedTernaryDigit.MINUS:
result.Append('-');
break;
case BalancedTernaryDigit.ZERO:
result.Append('0');
break;
case BalancedTernaryDigit.PLUS:
result.Append('+');
break;
}
}
return result.ToString();
}
// convert to long
public long ToLong()
{
long result = 0;
int digit;
for (int i = 0; i < this.value.Length; ++i)
{
result += (long)this.value[i] * (long)Math.Pow(3.0, (double)i);
}
return result;
}
// unary minus
public static BalancedTernary operator -(BalancedTernary origin)
{
BalancedTernary result = new BalancedTernary(origin);
result.Invert();
return result;
}
// addition of digits
private static BalancedTernaryDigit carry = BalancedTernaryDigit.ZERO;
private static BalancedTernaryDigit Add(BalancedTernaryDigit a, BalancedTernaryDigit b)
{
if (a != b)
{
carry = BalancedTernaryDigit.ZERO;
return (BalancedTernaryDigit)((int)a + (int)b);
}
else
{
carry = a;
return (BalancedTernaryDigit)(-(int)b);
}
}
// addition of balanced ternary numbers
public static BalancedTernary operator +(BalancedTernary a, BalancedTernary b)
{
int maxLength = Math.Max(a.value.Length, b.value.Length);
BalancedTernaryDigit[] resultValue = new BalancedTernaryDigit[maxLength + 1];
for (int i=0; i < maxLength; ++i)
{
if (i < a.value.Length)
{
resultValue[i] = Add(resultValue[i], a.value[i]);
resultValue[i+1] = carry;
}
else
{
carry = BalancedTernaryDigit.ZERO;
}
if (i < b.value.Length)
{
resultValue[i] = Add(resultValue[i], b.value[i]);
resultValue[i+1] = Add(resultValue[i+1], carry);
}
}
return new BalancedTernary(resultValue);
}
// subtraction of balanced ternary numbers
public static BalancedTernary operator -(BalancedTernary a, BalancedTernary b)
{
return a + (-b);
}
// multiplication of balanced ternary numbers
public static BalancedTernary operator *(BalancedTernary a, BalancedTernary b)
{
BalancedTernaryDigit[] longValue = a.value;
BalancedTernaryDigit[] shortValue = b.value;
BalancedTernary result = new BalancedTernary();
if (a.value.Length < b.value.Length)
{
longValue = b.value;
shortValue = a.value;
}
for (int i = 0; i < shortValue.Length; ++i)
{
if (shortValue[i] != BalancedTernaryDigit.ZERO)
{
BalancedTernaryDigit[] temp = new BalancedTernaryDigit[i + longValue.Length];
for (int j = 0; j < longValue.Length; ++j)
{
temp[i+j] = (BalancedTernaryDigit)((int)shortValue[i] * (int)longValue[j]);
}
result = result + new BalancedTernary(temp);
}
}
return result;
}
} |
http://rosettacode.org/wiki/Babbage_problem | Babbage problem |
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.
For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].
Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.
| #Kotlin | Kotlin | fun main(args: Array<String>) {
var number = 520L
var square = 520 * 520L
while (true) {
val last6 = square.toString().takeLast(6)
if (last6 == "269696") {
println("The smallest number is $number whose square is $square")
return
}
number += 2
square = number * number
}
} |
http://rosettacode.org/wiki/Balanced_brackets | Balanced brackets | Task:
Generate a string with N opening brackets [ and with N closing brackets ], in some arbitrary order.
Determine whether the generated string is balanced; that is, whether it consists entirely of pairs of opening/closing brackets (in that order), none of which mis-nest.
Examples
(empty) OK
[] OK
[][] OK
[[][]] OK
][ NOT OK
][][ NOT OK
[]][[] NOT OK
| #APL | APL | gen ← (⊂+?+)⍨ ⌷ ('[]'/⍨⊢)
bal ← (((|≡⊢)+\) ∧ 0=+/)(+⌿1 ¯1×[1]'[]'∘.=⊢) |
http://rosettacode.org/wiki/Averages/Mode | Averages/Mode | Task[edit]
Write a program to find the mode value of a collection.
The case where the collection is empty may be ignored. Care must be taken to handle the case where the mode is non-unique.
If it is not appropriate or possible to support a general collection, use a vector (array), if possible. If it is not appropriate or possible to support an unspecified value type, use integers.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #D | D | import std.stdio, std.algorithm, std.array;
auto mode(T)(T[] items) pure /*nothrow @safe*/ {
int[T] aa;
foreach (item; items)
aa[item]++;
immutable m = aa.byValue.reduce!max;
return aa.byKey.filter!(k => aa[k] == m);
}
void main() /*@safe*/ {
auto data = [1, 2, 3, 1, 2, 4, 2, 5, 3, 3, 1, 3, 6];
writeln("Mode: ", data.mode);
data ~= 2;
writeln("Mode: ", data.mode);
} |
http://rosettacode.org/wiki/Averages/Simple_moving_average | Averages/Simple moving average | Computing the simple moving average of a series of numbers.
Task[edit]
Create a stateful function/class/instance that takes a period and returns a routine that takes a number as argument and returns a simple moving average of its arguments so far.
Description
A simple moving average is a method for computing an average of a stream of numbers by only averaging the last P numbers from the stream, where P is known as the period.
It can be implemented by calling an initialing routine with P as its argument, I(P), which should then return a routine that when called with individual, successive members of a stream of numbers, computes the mean of (up to), the last P of them, lets call this SMA().
The word stateful in the task description refers to the need for SMA() to remember certain information between calls to it:
The period, P
An ordered container of at least the last P numbers from each of its individual calls.
Stateful also means that successive calls to I(), the initializer, should return separate routines that do not share saved state so they could be used on two independent streams of data.
Pseudo-code for an implementation of SMA is:
function SMA(number: N):
stateful integer: P
stateful list: stream
number: average
stream.append_last(N)
if stream.length() > P:
# Only average the last P elements of the stream
stream.delete_first()
if stream.length() == 0:
average = 0
else:
average = sum( stream.values() ) / stream.length()
return average
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Objective-C | Objective-C | #import <Foundation/Foundation.h>
@interface MovingAverage : NSObject {
unsigned int period;
NSMutableArray *window;
double sum;
}
- (instancetype)initWithPeriod:(unsigned int)thePeriod;
@end
@implementation MovingAverage
// init with default period
- (instancetype)init {
self = [super init];
if(self) {
period = 10;
window = [[NSMutableArray alloc] init];
sum = 0.0;
}
return self;
}
// init with specified period
- (instancetype)initWithPeriod:(unsigned int)thePeriod {
self = [super init];
if(self) {
period = thePeriod;
window = [[NSMutableArray alloc] init];
sum = 0.0;
}
return self;
}
// add a new number to the window
- (void)add:(double)val {
sum += val;
[window addObject:@(val)];
if([window count] > period) {
NSNumber *n = window[0];
sum -= [n doubleValue];
[window removeObjectAtIndex:0];
}
}
// get the average value
- (double)avg {
if([window count] == 0) {
return 0; // technically the average is undefined
}
return sum / [window count];
}
// set the period, resizes current window
- (void)setPeriod:(unsigned int)thePeriod {
// make smaller?
if(thePeriod < [window count]) {
for(int i = 0; i < thePeriod; ++i) {
NSNumber *n = window[0];
sum -= [n doubleValue];
[window removeObjectAtIndex:0];
}
}
period = thePeriod;
}
// get the period (window size)
- (unsigned int)period {
return period;
}
// clear the window and current sum
- (void)clear {
[window removeAllObjects];
sum = 0;
}
@end
int main (int argc, const char * argv[]) {
@autoreleasepool {
double testData[10] = {1,2,3,4,5,5,4,3,2,1};
int periods[2] = {3,5};
for(int i = 0; i < 2; ++i) {
MovingAverage *ma = [[MovingAverage alloc] initWithPeriod:periods[i]];
for(int j = 0; j < 10; ++j) {
[ma add:testData[j]];
NSLog(@"Next number = %f, SMA = %f", testData[j], [ma avg]);
}
NSLog(@"\n");
}
}
return 0;
} |
http://rosettacode.org/wiki/Averages/Mean_time_of_day | Averages/Mean time of day | Task[edit]
A particular activity of bats occurs at these times of the day:
23:00:17, 23:40:20, 00:12:45, 00:17:19
Using the idea that there are twenty-four hours in a day,
which is analogous to there being 360 degrees in a circle,
map times of day to and from angles;
and using the ideas of Averages/Mean angle
compute and show the average time of the nocturnal activity
to an accuracy of one second of time.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #BBC_BASIC | BBC BASIC | nTimes% = 4
DATA 23:00:17, 23:40:20, 00:12:45, 00:17:19
DIM angles(nTimes%-1)
FOR N% = 0 TO nTimes%-1
READ tim$
angles(N%) = FNtimetoangle(tim$)
NEXT
PRINT "Mean time is " FNangletotime(FNmeanangle(angles(), nTimes%))
END
DEF FNtimetoangle(t$)
LOCAL A%, I%
REPEAT
A% = A% * 60 + VAL(t$)
I% = INSTR(t$, ":")
t$ = MID$(t$, I%+1)
UNTIL I% = 0
= A% / 240 - 180
DEF FNangletotime(a)
LOCAL A%, I%, t$
A% = INT((a + 180) * 240 + 0.5)
FOR I% = 1 TO 3
t$ = RIGHT$("0" + STR$(A% MOD 60), 2) + ":" + t$
A% DIV= 60
NEXT
= LEFT$(t$)
DEF FNmeanangle(angles(), N%)
LOCAL I%, addsin, addcos
FOR I% = 0 TO N%-1
addsin += SINRADangles(I%)
addcos += COSRADangles(I%)
NEXT
= DEGFNatan2(addsin, addcos)
DEF FNatan2(y,x) : ON ERROR LOCAL = SGN(y)*PI/2
IF x>0 THEN = ATN(y/x) ELSE IF y>0 THEN = ATN(y/x)+PI ELSE = ATN(y/x)-PI |
http://rosettacode.org/wiki/Averages/Mean_time_of_day | Averages/Mean time of day | Task[edit]
A particular activity of bats occurs at these times of the day:
23:00:17, 23:40:20, 00:12:45, 00:17:19
Using the idea that there are twenty-four hours in a day,
which is analogous to there being 360 degrees in a circle,
map times of day to and from angles;
and using the ideas of Averages/Mean angle
compute and show the average time of the nocturnal activity
to an accuracy of one second of time.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #C | C | #include<stdlib.h>
#include<math.h>
#include<stdio.h>
typedef struct
{
int hour, minute, second;
} digitime;
double
timeToDegrees (digitime time)
{
return (360 * time.hour / 24.0 + 360 * time.minute / (24 * 60.0) +
360 * time.second / (24 * 3600.0));
}
digitime
timeFromDegrees (double angle)
{
digitime d;
double totalSeconds = 24 * 60 * 60 * angle / 360;
d.second = (int) totalSeconds % 60;
d.minute = ((int) totalSeconds % 3600 - d.second) / 60;
d.hour = (int) totalSeconds / 3600;
return d;
}
double
meanAngle (double *angles, int size)
{
double y_part = 0, x_part = 0;
int i;
for (i = 0; i < size; i++)
{
x_part += cos (angles[i] * M_PI / 180);
y_part += sin (angles[i] * M_PI / 180);
}
return atan2 (y_part / size, x_part / size) * 180 / M_PI;
}
int
main ()
{
digitime *set, meanTime;
int inputs, i;
double *angleSet, angleMean;
printf ("Enter number of inputs : ");
scanf ("%d", &inputs);
set = malloc (inputs * sizeof (digitime));
angleSet = malloc (inputs * sizeof (double));
printf ("\n\nEnter the data separated by a space between each unit : ");
for (i = 0; i < inputs; i++)
{
scanf ("%d:%d:%d", &set[i].hour, &set[i].minute, &set[i].second);
angleSet[i] = timeToDegrees (set[i]);
}
meanTime = timeFromDegrees (360 + meanAngle (angleSet, inputs));
printf ("\n\nThe mean time is : %d:%d:%d", meanTime.hour, meanTime.minute,
meanTime.second);
return 0;
} |
http://rosettacode.org/wiki/AVL_tree | AVL tree |
This page uses content from Wikipedia. The original article was at AVL tree. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
In computer science, an AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; at no time do they differ by more than one because rebalancing is done ensure this is the case. Lookup, insertion, and deletion all take O(log n) time in both the average and worst cases, where n is the number of nodes in the tree prior to the operation. Insertions and deletions may require the tree to be rebalanced by one or more tree rotations. Note the tree of nodes comprise a set, so duplicate node keys are not allowed.
AVL trees are often compared with red-black trees because they support the same set of operations and because red-black trees also take O(log n) time for the basic operations. Because AVL trees are more rigidly balanced, they are faster than red-black trees for lookup-intensive applications. Similar to red-black trees, AVL trees are height-balanced, but in general not weight-balanced nor μ-balanced; that is, sibling nodes can have hugely differing numbers of descendants.
Task
Implement an AVL tree in the language of choice, and provide at least basic operations.
| #Ada | Ada |
with Ada.Text_IO, Ada.Finalization, Ada.Unchecked_Deallocation;
procedure Main is
generic
type Key_Type is private;
with function "<"(a, b : Key_Type) return Boolean is <>;
with function "="(a, b : Key_Type) return Boolean is <>;
with function "<="(a, b : Key_Type) return Boolean is <>;
package AVL_Tree is
type Tree is tagged limited private;
function insert(self : in out Tree; key : Key_Type) return Boolean;
procedure delete(self : in out Tree; key : Key_Type);
procedure print_balance(self : in out Tree);
private
type Height_Amt is range -1 .. Integer'Last;
-- Since only one key is inserted before each rebalance, the balance of
-- all trees/subtrees will stay in range -2 .. 2
type Balance_Amt is range -2 .. 2;
type Node;
type Node_Ptr is access Node;
type Node is new Ada.Finalization.Limited_Controlled with record
left, right, parent : Node_Ptr := null;
key : Key_Type;
balance : Balance_Amt := 0;
end record;
overriding procedure Finalize(self : in out Node);
subtype Node_Parent is Ada.Finalization.Limited_Controlled;
type Tree is new Ada.Finalization.Limited_Controlled with record
root : Node_Ptr := null;
end record;
overriding procedure Finalize(self : in out Tree);
end AVL_Tree;
package body AVL_Tree is
procedure Free_Node is new Ada.Unchecked_Deallocation(Node, Node_Ptr);
overriding procedure Finalize(self : in out Node) is
begin
Free_Node(self.left);
Free_Node(self.right);
end Finalize;
overriding procedure Finalize(self : in out Tree) is
begin
Free_Node(self.root);
end Finalize;
function height(n : Node_Ptr) return Height_Amt is
begin
if n = null then
return -1;
else
return 1 + Height_Amt'Max(height(n.left), height(n.right));
end if;
end height;
procedure set_balance(n : not null Node_Ptr) is
begin
n.balance := Balance_Amt(height(n.right) - height(n.left));
end set_balance;
procedure update_parent(parent : Node_Ptr; new_child : Node_Ptr; old_child : Node_Ptr) is
begin
if parent /= null then
if parent.right = old_child then
parent.right := new_child;
else
parent.left := new_child;
end if;
end if;
end update_parent;
function rotate_left(a : not null Node_Ptr) return Node_Ptr is
b : Node_Ptr := a.right;
begin
b.parent := a.parent;
a.right := b.left;
if a.right /= null then
a.right.parent := a;
end if;
b.left := a;
a.parent := b;
update_parent(parent => b.parent, new_child => b, old_child => a);
set_balance(a);
set_balance(b);
return b;
end rotate_left;
function rotate_right(a : not null Node_Ptr) return Node_Ptr is
b : Node_Ptr := a.left;
begin
b.parent := a.parent;
a.left := b.right;
if a.left /= null then
a.left.parent := a;
end if;
b.right := a;
a.parent := b;
update_parent(parent => b.parent, new_child => b, old_child => a);
set_balance(a);
set_balance(b);
return b;
end rotate_right;
function rotate_left_right(n : not null Node_Ptr) return Node_Ptr is
begin
n.left := rotate_left(n.left);
return rotate_right(n);
end rotate_left_right;
function rotate_right_left(n : not null Node_Ptr) return Node_Ptr is
begin
n.right := rotate_right(n.right);
return rotate_left(n);
end rotate_right_left;
procedure rebalance(self : in out Tree; n : not null Node_Ptr) is
new_n : Node_Ptr := n;
begin
set_balance(new_n);
if new_n.balance = -2 then
if height(new_n.left.left) >= height(new_n.left.right) then
new_n := rotate_right(new_n);
else
new_n := rotate_left_right(new_n);
end if;
elsif new_n.balance = 2 then
if height(new_n.right.right) >= height(new_n.right.left) then
new_n := rotate_left(new_n);
else
new_n := rotate_right_left(new_n);
end if;
end if;
if new_n.parent /= null then
rebalance(self, new_n.parent);
else
self.root := new_n;
end if;
end rebalance;
function new_node(key : Key_Type) return Node_Ptr is
(new Node'(Node_Parent with key => key, others => <>));
function insert(self : in out Tree; key : Key_Type) return Boolean is
curr, parent : Node_Ptr;
go_left : Boolean;
begin
if self.root = null then
self.root := new_node(key);
return True;
end if;
curr := self.root;
while curr.key /= key loop
parent := curr;
go_left := key < curr.key;
curr := (if go_left then curr.left else curr.right);
if curr = null then
if go_left then
parent.left := new_node(key);
parent.left.parent := parent;
else
parent.right := new_node(key);
parent.right.parent := parent;
end if;
rebalance(self, parent);
return True;
end if;
end loop;
return False;
end insert;
procedure delete(self : in out Tree; key : Key_Type) is
successor, parent, child : Node_Ptr := self.root;
to_delete : Node_Ptr := null;
begin
if self.root = null then
return;
end if;
while child /= null loop
parent := successor;
successor := child;
child := (if successor.key <= key then successor.right else successor.left);
if successor.key = key then
to_delete := successor;
end if;
end loop;
if to_delete = null then
return;
end if;
to_delete.key := successor.key;
child := (if successor.left = null then successor.right else successor.left);
if self.root.key = key then
self.root := child;
else
update_parent(parent => parent, new_child => child, old_child => successor);
rebalance(self, parent);
end if;
Free_Node(successor);
end delete;
procedure print_balance(n : Node_Ptr) is
begin
if n /= null then
print_balance(n.left);
Ada.Text_IO.Put(n.balance'Image);
print_balance(n.right);
end if;
end print_balance;
procedure print_balance(self : in out Tree) is
begin
print_balance(self.root);
end print_balance;
end AVL_Tree;
package Int_AVL_Tree is new AVL_Tree(Integer);
tree : Int_AVL_Tree.Tree;
success : Boolean;
begin
for i in 1 .. 10 loop
success := tree.insert(i);
end loop;
Ada.Text_IO.Put("Printing balance: ");
tree.print_balance;
Ada.Text_IO.New_Line;
end Main;
|
http://rosettacode.org/wiki/Averages/Mean_angle | Averages/Mean angle | When calculating the average or mean of an angle one has to take into account how angles wrap around so that any angle in degrees plus any integer multiple of 360 degrees is a measure of the same angle.
If one wanted an average direction of the wind over two readings where the first reading was of 350 degrees and the second was of 10 degrees then the average of the numbers is 180 degrees, whereas if you can note that 350 degrees is equivalent to -10 degrees and so you have two readings at 10 degrees either side of zero degrees leading to a more fitting mean angle of zero degrees.
To calculate the mean angle of several angles:
Assume all angles are on the unit circle and convert them to complex numbers expressed in real and imaginary form.
Compute the mean of the complex numbers.
Convert the complex mean to polar coordinates whereupon the phase of the complex mean is the required angular mean.
(Note that, since the mean is the sum divided by the number of numbers, and division by a positive real number does not affect the angle, you can also simply compute the sum for step 2.)
You can alternatively use this formula:
Given the angles
α
1
,
…
,
α
n
{\displaystyle \alpha _{1},\dots ,\alpha _{n}}
the mean is computed by
α
¯
=
atan2
(
1
n
⋅
∑
j
=
1
n
sin
α
j
,
1
n
⋅
∑
j
=
1
n
cos
α
j
)
{\displaystyle {\bar {\alpha }}=\operatorname {atan2} \left({\frac {1}{n}}\cdot \sum _{j=1}^{n}\sin \alpha _{j},{\frac {1}{n}}\cdot \sum _{j=1}^{n}\cos \alpha _{j}\right)}
Task[edit]
write a function/method/subroutine/... that given a list of angles in degrees returns their mean angle.
(You should use a built-in function if you have one that does this for degrees or radians).
Use the function to compute the means of these lists of angles (in degrees):
[350, 10]
[90, 180, 270, 360]
[10, 20, 30]
Show your output here.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Ada | Ada | with Ada.Text_IO, Ada.Numerics.Generic_Elementary_Functions;
procedure Mean_Angles is
type X_Real is digits 4; -- or more digits for improved precision
subtype Real is X_Real range 0.0 .. 360.0; -- the range of interest
type Angles is array(Positive range <>) of Real;
procedure Put(R: Real) is
package IO is new Ada.Text_IO.Float_IO(Real);
begin
IO.Put(R, Fore => 3, Aft => 2, Exp => 0);
end Put;
function Mean_Angle(A: Angles) return Real is
Sin_Sum, Cos_Sum: X_Real := 0.0; -- X_Real since sums might exceed 360.0
package Math is new Ada.Numerics.Generic_Elementary_Functions(Real);
use Math;
begin
for I in A'Range loop
Sin_Sum := Sin_Sum + Sin(A(I), Cycle => 360.0);
Cos_Sum := Cos_Sum + Cos(A(I), Cycle => 360.0);
end loop;
return Arctan(Sin_Sum / X_Real(A'Length), Cos_Sum / X_Real(A'Length),
Cycle => 360.0);
-- may raise Ada.Numerics.Argument_Error if inputs are
-- numerically instable, e.g., when Cos_Sum is 0.0
end Mean_Angle;
begin
Put(Mean_Angle((10.0, 20.0, 30.0))); Ada.Text_IO.New_Line; -- 20.00
Put(Mean_Angle((10.0, 350.0))); Ada.Text_IO.New_Line; -- 0.00
Put(Mean_Angle((90.0, 180.0, 270.0, 360.0))); -- Ada.Numerics.Argument_Error!
end Mean_Angles; |
http://rosettacode.org/wiki/Averages/Median | Averages/Median | Task[edit]
Write a program to find the median value of a vector of floating-point numbers.
The program need not handle the case where the vector is empty, but must handle the case where there are an even number of elements. In that case, return the average of the two middle values.
There are several approaches to this. One is to sort the elements, and then pick the element(s) in the middle.
Sorting would take at least O(n logn). Another approach would be to build a priority queue from the elements, and then extract half of the elements to get to the middle element(s). This would also take O(n logn). The best solution is to use the selection algorithm to find the median in O(n) time.
See also
Quickselect_algorithm
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Action.21 | Action! | INCLUDE "H6:REALMATH.ACT"
DEFINE PTR="CARD"
PROC Sort(PTR ARRAY a INT count)
INT i,j,minpos
REAL POINTER tmp
FOR i=0 TO count-2
DO
minpos=i
FOR j=i+1 TO count-1
DO
IF RealGreaterOrEqual(a(minpos),a(j)) THEN
minpos=j
FI
OD
IF minpos#i THEN
tmp=a(i)
a(i)=a(minpos)
a(minpos)=tmp
FI
OD
RETURN
PROC Median(PTR ARRAY a INT count REAL POINTER res)
IF count=0 THEN Break() FI
Sort(a,count)
IF (count&1)=0 THEN
RealAdd(a(count RSH 1-1),a(count RSH 1),res)
RealMult(res,half,res)
ELSE
RealAssign(a(count RSH 1),res)
FI
RETURN
PROC Test(PTR ARRAY a INT count)
INT i
REAL res
FOR i=0 TO count-1
DO
PrintR(a(i)) Put(32)
OD
Median(a,count,res)
Print("-> ")
PrintRE(res)
RETURN
PROC Main()
PTR ARRAY a(8)
REAL r1,r2,r3,r4,r5,r6,r7,r8
BYTE i
Put(125) PutE() ;clear the screen
MathInit()
ValR("3.2",r1) ValR("-4.1",r2)
ValR("0.6",r3) ValR("9.8",r4)
ValR("5.1",r5) ValR("-1.4",r6)
ValR("0.3",r7) ValR("2.2",r8)
FOR i=1 TO 8
DO
a(0)=r1 a(1)=r2 a(2)=r3 a(3)=r4
a(4)=r5 a(5)=r6 a(6)=r7 a(7)=r8
Test(a,i)
OD
RETURN |
http://rosettacode.org/wiki/Averages/Pythagorean_means | Averages/Pythagorean means | Task[edit]
Compute all three of the Pythagorean means of the set of integers 1 through 10 (inclusive).
Show that
A
(
x
1
,
…
,
x
n
)
≥
G
(
x
1
,
…
,
x
n
)
≥
H
(
x
1
,
…
,
x
n
)
{\displaystyle A(x_{1},\ldots ,x_{n})\geq G(x_{1},\ldots ,x_{n})\geq H(x_{1},\ldots ,x_{n})}
for this set of positive integers.
The most common of the three means, the arithmetic mean, is the sum of the list divided by its length:
A
(
x
1
,
…
,
x
n
)
=
x
1
+
⋯
+
x
n
n
{\displaystyle A(x_{1},\ldots ,x_{n})={\frac {x_{1}+\cdots +x_{n}}{n}}}
The geometric mean is the
n
{\displaystyle n}
th root of the product of the list:
G
(
x
1
,
…
,
x
n
)
=
x
1
⋯
x
n
n
{\displaystyle G(x_{1},\ldots ,x_{n})={\sqrt[{n}]{x_{1}\cdots x_{n}}}}
The harmonic mean is
n
{\displaystyle n}
divided by the sum of the reciprocal of each item in the list:
H
(
x
1
,
…
,
x
n
)
=
n
1
x
1
+
⋯
+
1
x
n
{\displaystyle H(x_{1},\ldots ,x_{n})={\frac {n}{{\frac {1}{x_{1}}}+\cdots +{\frac {1}{x_{n}}}}}}
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #E | E | def makeMean(base, include, finish) {
return def mean(numbers) {
var count := 0
var acc := base
for x in numbers {
acc := include(acc, x)
count += 1
}
return finish(acc, count)
}
}
def A := makeMean(0, fn b,x { b+x }, fn acc,n { acc / n })
def G := makeMean(1, fn b,x { b*x }, fn acc,n { acc ** (1/n) })
def H := makeMean(0, fn b,x { b+1/x }, fn acc,n { n / acc }) |
http://rosettacode.org/wiki/Balanced_ternary | Balanced ternary | Balanced ternary is a way of representing numbers. Unlike the prevailing binary representation, a balanced ternary integer is in base 3, and each digit can have the values 1, 0, or −1.
Examples
Decimal 11 = 32 + 31 − 30, thus it can be written as "++−"
Decimal 6 = 32 − 31 + 0 × 30, thus it can be written as "+−0"
Task
Implement balanced ternary representation of integers with the following:
Support arbitrarily large integers, both positive and negative;
Provide ways to convert to and from text strings, using digits '+', '-' and '0' (unless you are already using strings to represent balanced ternary; but see requirement 5).
Provide ways to convert to and from native integer type (unless, improbably, your platform's native integer type is balanced ternary). If your native integers can't support arbitrary length, overflows during conversion must be indicated.
Provide ways to perform addition, negation and multiplication directly on balanced ternary integers; do not convert to native integers first.
Make your implementation efficient, with a reasonable definition of "efficient" (and with a reasonable definition of "reasonable").
Test case With balanced ternaries a from string "+-0++0+", b from native integer -436, c "+-++-":
write out a, b and c in decimal notation;
calculate a × (b − c), write out the result in both ternary and decimal notations.
Note: The pages generalised floating point addition and generalised floating point multiplication have code implementing arbitrary precision floating point balanced ternary.
| #C.2B.2B | C++ | #include <iostream>
#include <string>
#include <climits>
using namespace std;
class BalancedTernary {
protected:
// Store the value as a reversed string of +, 0 and - characters
string value;
// Helper function to change a balanced ternary character to an integer
int charToInt(char c) const {
if (c == '0')
return 0;
return 44 - c;
}
// Helper function to negate a string of ternary characters
string negate(string s) const {
for (int i = 0; i < s.length(); ++i) {
if (s[i] == '+')
s[i] = '-';
else if (s[i] == '-')
s[i] = '+';
}
return s;
}
public:
// Default constructor
BalancedTernary() {
value = "0";
}
// Construct from a string
BalancedTernary(string s) {
value = string(s.rbegin(), s.rend());
}
// Construct from an integer
BalancedTernary(long long n) {
if (n == 0) {
value = "0";
return;
}
bool neg = n < 0;
if (neg)
n = -n;
value = "";
while (n != 0) {
int r = n % 3;
if (r == 0)
value += "0";
else if (r == 1)
value += "+";
else {
value += "-";
++n;
}
n /= 3;
}
if (neg)
value = negate(value);
}
// Copy constructor
BalancedTernary(const BalancedTernary &n) {
value = n.value;
}
// Addition operators
BalancedTernary operator+(BalancedTernary n) const {
n += *this;
return n;
}
BalancedTernary& operator+=(const BalancedTernary &n) {
static char *add = "0+-0+-0";
static char *carry = "--000++";
int lastNonZero = 0;
char c = '0';
for (int i = 0; i < value.length() || i < n.value.length(); ++i) {
char a = i < value.length() ? value[i] : '0';
char b = i < n.value.length() ? n.value[i] : '0';
int sum = charToInt(a) + charToInt(b) + charToInt(c) + 3;
c = carry[sum];
if (i < value.length())
value[i] = add[sum];
else
value += add[sum];
if (add[sum] != '0')
lastNonZero = i;
}
if (c != '0')
value += c;
else
value = value.substr(0, lastNonZero + 1); // Chop off leading zeroes
return *this;
}
// Negation operator
BalancedTernary operator-() const {
BalancedTernary result;
result.value = negate(value);
return result;
}
// Subtraction operators
BalancedTernary operator-(const BalancedTernary &n) const {
return operator+(-n);
}
BalancedTernary& operator-=(const BalancedTernary &n) {
return operator+=(-n);
}
// Multiplication operators
BalancedTernary operator*(BalancedTernary n) const {
n *= *this;
return n;
}
BalancedTernary& operator*=(const BalancedTernary &n) {
BalancedTernary pos = *this;
BalancedTernary neg = -pos; // Storing an extra copy to avoid negating repeatedly
value = "0";
for (int i = 0; i < n.value.length(); ++i) {
if (n.value[i] == '+')
operator+=(pos);
else if (n.value[i] == '-')
operator+=(neg);
pos.value = '0' + pos.value;
neg.value = '0' + neg.value;
}
return *this;
}
// Stream output operator
friend ostream& operator<<(ostream &out, const BalancedTernary &n) {
out << n.toString();
return out;
}
// Convert to string
string toString() const {
return string(value.rbegin(), value.rend());
}
// Convert to integer
long long toInt() const {
long long result = 0;
for (long long i = 0, pow = 1; i < value.length(); ++i, pow *= 3)
result += pow * charToInt(value[i]);
return result;
}
// Convert to integer if possible
bool tryInt(long long &out) const {
long long result = 0;
bool ok = true;
for (long long i = 0, pow = 1; i < value.length() && ok; ++i, pow *= 3) {
if (value[i] == '+') {
ok &= LLONG_MAX - pow >= result; // Clear ok if the result overflows
result += pow;
} else if (value[i] == '-') {
ok &= LLONG_MIN + pow <= result; // Clear ok if the result overflows
result -= pow;
}
}
if (ok)
out = result;
return ok;
}
};
int main() {
BalancedTernary a("+-0++0+");
BalancedTernary b(-436);
BalancedTernary c("+-++-");
cout << "a = " << a << " = " << a.toInt() << endl;
cout << "b = " << b << " = " << b.toInt() << endl;
cout << "c = " << c << " = " << c.toInt() << endl;
BalancedTernary d = a * (b - c);
cout << "a * (b - c) = " << d << " = " << d.toInt() << endl;
BalancedTernary e("+++++++++++++++++++++++++++++++++++++++++");
long long n;
if (e.tryInt(n))
cout << "e = " << e << " = " << n << endl;
else
cout << "e = " << e << " is too big to fit in a long long" << endl;
return 0;
}
|
http://rosettacode.org/wiki/Babbage_problem | Babbage problem |
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.
For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].
Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.
| #Liberty_BASIC | Liberty BASIC |
[start]
if right$(str$(n*n),6)="269696" then
print "n = "; using("###,###", n);
print " n*n = "; using("###,###,###,###", n*n)
end if
if n<100000 then n=n+1: goto [start]
print "Program complete."
|
http://rosettacode.org/wiki/Balanced_brackets | Balanced brackets | Task:
Generate a string with N opening brackets [ and with N closing brackets ], in some arbitrary order.
Determine whether the generated string is balanced; that is, whether it consists entirely of pairs of opening/closing brackets (in that order), none of which mis-nest.
Examples
(empty) OK
[] OK
[][] OK
[[][]] OK
][ NOT OK
][][ NOT OK
[]][[] NOT OK
| #AppleScript | AppleScript | -- CHECK NESTING OF SQUARE BRACKET SEQUENCES ---------------------------------
-- Zero-based index of the first problem (-1 if none found):
-- imbalance :: String -> Integer
on imbalance(strBrackets)
script
on errorIndex(xs, iDepth, iIndex)
set lngChars to length of xs
if lngChars > 0 then
set iNext to iDepth + cond(item 1 of xs = "[", 1, -1)
if iNext < 0 then -- closing bracket unmatched
iIndex
else
if lngChars > 1 then -- continue recursively
errorIndex(items 2 thru -1 of xs, iNext, iIndex + 1)
else -- end of string
cond(iNext = 0, -1, iIndex)
end if
end if
else
cond(iDepth = 0, -1, iIndex)
end if
end errorIndex
end script
result's errorIndex(characters of strBrackets, 0, 0)
end imbalance
-- TEST ----------------------------------------------------------------------
-- Random bracket sequences for testing
-- brackets :: Int -> String
on randomBrackets(n)
-- bracket :: () -> String
script bracket
on |λ|(_)
cond((random number) < 0.5, "[", "]")
end |λ|
end script
intercalate("", map(bracket, enumFromTo(1, n)))
end randomBrackets
on run
set nPairs to 6
-- report :: Int -> String
script report
property strPad : concat(replicate(nPairs * 2 + 4, space))
on |λ|(n)
set w to n * 2
set s to randomBrackets(w)
set i to imbalance(s)
set blnOK to (i = -1)
set strStatus to cond(blnOK, "OK", "problem")
set strLine to "'" & s & "'" & ¬
(items (w + 2) thru -1 of strPad) & strStatus
set strPointer to cond(blnOK, ¬
"", linefeed & concat(replicate(i + 1, space)) & "^")
intercalate("", {strLine, strPointer})
end |λ|
end script
linefeed & ¬
intercalate(linefeed, ¬
map(report, enumFromTo(1, nPairs))) & linefeed
end run
-- GENERIC FUNCTIONS ---------------------------------------------------------
-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map
-- foldl :: (a -> b -> a) -> a -> [b] -> a
on foldl(f, startValue, xs)
tell mReturn(f)
set v to startValue
set lng to length of xs
repeat with i from 1 to lng
set v to |λ|(v, item i of xs, i, xs)
end repeat
return v
end tell
end foldl
-- Text -> [Text] -> Text
on intercalate(strText, lstText)
set {dlm, my text item delimiters} to {my text item delimiters, strText}
set strJoined to lstText as text
set my text item delimiters to dlm
return strJoined
end intercalate
-- concat :: [[a]] -> [a] | [String] -> String
on concat(xs)
script append
on |λ|(a, b)
a & b
end |λ|
end script
if length of xs > 0 and class of (item 1 of xs) is string then
set empty to ""
else
set empty to {}
end if
foldl(append, empty, xs)
end concat
-- Egyptian multiplication - progressively doubling a list, appending
-- stages of doubling to an accumulator where needed for binary
-- assembly of a target length
-- replicate :: Int -> a -> [a]
on replicate(n, a)
set out to {}
if n < 1 then return out
set dbl to {a}
repeat while (n > 1)
if (n mod 2) > 0 then set out to out & dbl
set n to (n div 2)
set dbl to (dbl & dbl)
end repeat
return out & dbl
end replicate
-- Value of one of two expressions
-- cond :: Bool -> a -> b -> c
on cond(bln, f, g)
if bln then
set e to f
else
set e to g
end if
if class of e is handler then
mReturn(e)'s |λ|()
else
e
end if
end cond
-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
if m > n then
set d to -1
else
set d to 1
end if
set lst to {}
repeat with i from m to n by d
set end of lst to i
end repeat
return lst
end enumFromTo
-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: Handler -> Script
on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn |
http://rosettacode.org/wiki/Averages/Mode | Averages/Mode | Task[edit]
Write a program to find the mode value of a collection.
The case where the collection is empty may be ignored. Care must be taken to handle the case where the mode is non-unique.
If it is not appropriate or possible to support a general collection, use a vector (array), if possible. If it is not appropriate or possible to support an unspecified value type, use integers.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Delphi | Delphi |
program AveragesMode;
{$APPTYPE CONSOLE}
uses
System.SysUtils,
System.Generics.Collections,
System.Generics.Defaults;
type
TCounts = TDictionary<Integer, Integer>;
TPair = record
value, count: Integer;
constructor Create(value, count: Integer);
end;
TPairs = TArray<TPair>;
var
dict: TCounts;
Pairs: TPairs;
list: TArray<Integer>;
i, key, max: Integer;
p: TPair;
{ TPair }
constructor TPair.Create(value, count: Integer);
begin
self.value := value;
self.count := count;
end;
function SortByCount(const left, right: TPair): Integer;
begin
Result := right.count - left.count;
end;
begin
list := [1, 3, 6, 6, 6, 6, 7, 7, 12, 12, 12, 12, 17];
dict := TCounts.Create;
for i in list do
begin
if dict.ContainsKey(i) then
dict[i] := dict[i] + 1
else
begin
dict.Add(i, 1);
end;
end;
SetLength(Pairs, dict.Count);
i := 0;
for key in dict.Keys do
begin
Pairs[i] := TPair.Create(key, dict[key]);
inc(i);
end;
TArray.Sort<TPair>(Pairs, TComparer<TPair>.Construct(SortByCount));
Writeln('Modes:');
max := Pairs[0].count;
for p in Pairs do
if p.count = max then
Writeln(' Value: ', p.value, ', Count: ', p.count);
dict.Free;
Readln;
end. |
http://rosettacode.org/wiki/Averages/Simple_moving_average | Averages/Simple moving average | Computing the simple moving average of a series of numbers.
Task[edit]
Create a stateful function/class/instance that takes a period and returns a routine that takes a number as argument and returns a simple moving average of its arguments so far.
Description
A simple moving average is a method for computing an average of a stream of numbers by only averaging the last P numbers from the stream, where P is known as the period.
It can be implemented by calling an initialing routine with P as its argument, I(P), which should then return a routine that when called with individual, successive members of a stream of numbers, computes the mean of (up to), the last P of them, lets call this SMA().
The word stateful in the task description refers to the need for SMA() to remember certain information between calls to it:
The period, P
An ordered container of at least the last P numbers from each of its individual calls.
Stateful also means that successive calls to I(), the initializer, should return separate routines that do not share saved state so they could be used on two independent streams of data.
Pseudo-code for an implementation of SMA is:
function SMA(number: N):
stateful integer: P
stateful list: stream
number: average
stream.append_last(N)
if stream.length() > P:
# Only average the last P elements of the stream
stream.delete_first()
if stream.length() == 0:
average = 0
else:
average = sum( stream.values() ) / stream.length()
return average
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #OCaml | OCaml | let sma (n, s, q) x =
let l = Queue.length q and s = s +. x in
Queue.push x q;
if l < n then
(n, s, q), s /. float (l + 1)
else (
let s = s -. Queue.pop q in
(n, s, q), s /. float l
)
let _ =
let periodLst = [ 3; 5 ] in
let series = [ 1.; 2.; 3.; 4.; 5.; 5.; 4.; 3.; 2.; 1. ] in
List.iter (fun d ->
Printf.printf "SIMPLE MOVING AVERAGE: PERIOD = %d\n" d;
ignore (
List.fold_left (fun o x ->
let o, m = sma o x in
Printf.printf "Next number = %-2g, SMA = %g\n" x m;
o
) (d, 0., Queue.create ()) series;
);
print_newline ();
) periodLst |
http://rosettacode.org/wiki/Averages/Mean_time_of_day | Averages/Mean time of day | Task[edit]
A particular activity of bats occurs at these times of the day:
23:00:17, 23:40:20, 00:12:45, 00:17:19
Using the idea that there are twenty-four hours in a day,
which is analogous to there being 360 degrees in a circle,
map times of day to and from angles;
and using the ideas of Averages/Mean angle
compute and show the average time of the nocturnal activity
to an accuracy of one second of time.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #C.23 | C# | using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
namespace RosettaCode
{
class Program
{
static void Main(string[] args)
{
Func<TimeSpan, double> TimeToDegrees = (time) =>
360 * time.Hours / 24.0 +
360 * time.Minutes / (24 * 60.0) +
360 * time.Seconds / (24 * 3600.0);
Func<List<double>, double> MeanAngle = (angles) =>
{
double y_part = 0.0d, x_part = 0.0d;
int numItems = angles.Count;
for (int i = 0; i < numItems; i++)
{
x_part += Math.Cos(angles[i] * Math.PI / 180);
y_part += Math.Sin(angles[i] * Math.PI / 180);
}
return Math.Atan2(y_part / numItems, x_part / numItems) * 180 / Math.PI;
};
Func<double, TimeSpan> TimeFromDegrees = (angle) =>
new TimeSpan(
(int)(24 * 60 * 60 * angle / 360) / 3600,
((int)(24 * 60 * 60 * angle / 360) % 3600 - (int)(24 * 60 * 60 * angle / 360) % 60) / 60,
(int)(24 * 60 * 60 * angle / 360) % 60);
List<double> digitimes = new List<double>();
TimeSpan digitime;
string input;
Console.WriteLine("Enter times, end with no input: ");
do
{
input = Console.ReadLine();
if (!(string.IsNullOrWhiteSpace(input)))
{
if (TimeSpan.TryParse(input, out digitime))
digitimes.Add(TimeToDegrees(digitime));
else
Console.WriteLine("Seems this is wrong input: ignoring time");
}
} while (!string.IsNullOrWhiteSpace(input));
if(digitimes.Count() > 0)
Console.WriteLine("The mean time is : {0}", TimeFromDegrees(360 + MeanAngle(digitimes)));
}
}
}
|
http://rosettacode.org/wiki/AVL_tree | AVL tree |
This page uses content from Wikipedia. The original article was at AVL tree. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
In computer science, an AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; at no time do they differ by more than one because rebalancing is done ensure this is the case. Lookup, insertion, and deletion all take O(log n) time in both the average and worst cases, where n is the number of nodes in the tree prior to the operation. Insertions and deletions may require the tree to be rebalanced by one or more tree rotations. Note the tree of nodes comprise a set, so duplicate node keys are not allowed.
AVL trees are often compared with red-black trees because they support the same set of operations and because red-black trees also take O(log n) time for the basic operations. Because AVL trees are more rigidly balanced, they are faster than red-black trees for lookup-intensive applications. Similar to red-black trees, AVL trees are height-balanced, but in general not weight-balanced nor μ-balanced; that is, sibling nodes can have hugely differing numbers of descendants.
Task
Implement an AVL tree in the language of choice, and provide at least basic operations.
| #Agda | Agda |
module Avl where
-- The Peano naturals
data Nat : Set where
z : Nat
s : Nat -> Nat
-- An AVL tree's type is indexed by a natural.
-- Avl N is the type of AVL trees of depth N. There arj 3 different
-- node constructors:
-- Left: The left subtree is one level deeper than the right
-- Balanced: The subtrees have the same depth
-- Right: The right Subtree is one level deeper than the left
-- Since the AVL invariant is that the depths of a node's subtrees
-- always differ by at most 1, this perfectly encodes the AVL depth invariant.
data Avl : Nat -> Set where
Empty : Avl z
Left : {X : Nat} -> Nat -> Avl (s X) -> Avl X -> Avl (s (s X))
Balanced : {X : Nat} -> Nat -> Avl X -> Avl X -> Avl (s X)
Right : {X : Nat} -> Nat -> Avl X -> Avl (s X) -> Avl (s (s X))
-- A wrapper type that hides the AVL tree invariant. This is the interface
-- exposed to the user.
data Tree : Set where
avl : {N : Nat} -> Avl N -> Tree
-- Comparison result
data Ord : Set where
Less : Ord
Equal : Ord
Greater : Ord
-- Comparison function
cmp : Nat -> Nat -> Ord
cmp z (s X) = Less
cmp z z = Equal
cmp (s X) z = Greater
cmp (s X) (s Y) = cmp X Y
-- Insertions can either leave the depth the same or
-- increase it by one. Encode this in the type.
data InsertResult : Nat -> Set where
Same : {X : Nat} -> Avl X -> InsertResult X
Bigger : {X : Nat} -> Avl (s X) -> InsertResult X
-- If the left subtree is 2 levels deeper than the right, rotate to the right.
-- balance-left X L R means X is the root, L is the left subtree and R is the right.
balance-left : {N : Nat} -> Nat -> Avl (s (s N)) -> Avl N -> InsertResult (s (s N))
balance-left X (Right Y A (Balanced Z B C)) D = Same (Balanced Z (Balanced X A B) (Balanced Y C D))
balance-left X (Right Y A (Left Z B C)) D = Same (Balanced Z (Balanced X A B) (Right Y C D))
balance-left X (Right Y A (Right Z B C)) D = Same (Balanced Z (Left X A B) (Balanced Y C D))
balance-left X (Left Y (Balanced Z A B) C) D = Same (Balanced Z (Balanced X A B) (Balanced Y C D))
balance-left X (Left Y (Left Z A B) C) D = Same (Balanced Z (Left X A B) (Balanced Y C D))
balance-left X (Left Y (Right Z A B) C) D = Same (Balanced Z (Right X A B) (Balanced Y C D))
balance-left X (Balanced Y (Balanced Z A B) C) D = Bigger (Right Z (Balanced X A B) (Left Y C D))
balance-left X (Balanced Y (Left Z A B) C) D = Bigger (Right Z (Left X A B) (Left Y C D))
balance-left X (Balanced Y (Right Z A B) C) D = Bigger (Right Z (Right X A B) (Left Y C D))
-- Symmetric with balance-left
balance-right : {N : Nat} -> Nat -> Avl N -> Avl (s (s N)) -> InsertResult (s (s N))
balance-right X A (Left Y (Left Z B C) D) = Same (Balanced Z (Balanced X A B) (Right Y C D))
balance-right X A (Left Y (Balanced Z B C) D) = Same(Balanced Z (Balanced X A B) (Balanced Y C D))
balance-right X A (Left Y (Right Z B C) D) = Same(Balanced Z (Left X A B) (Balanced Y C D))
balance-right X A (Balanced Z B (Left Y C D)) = Bigger(Left Z (Right X A B) (Left Y C D))
balance-right X A (Balanced Z B (Balanced Y C D)) = Bigger (Left Z (Right X A B) (Balanced Y C D))
balance-right X A (Balanced Z B (Right Y C D)) = Bigger (Left Z (Right X A B) (Right Y C D))
balance-right X A (Right Z B (Left Y C D)) = Same (Balanced Z (Balanced X A B) (Left Y C D))
balance-right X A (Right Z B (Balanced Y C D)) = Same (Balanced Z (Balanced X A B) (Balanced Y C D))
balance-right X A (Right Z B (Right Y C D)) = Same (Balanced Z (Balanced X A B) (Right Y C D))
-- insert' T N does all the work of inserting the element N into the tree T.
insert' : {N : Nat} -> Avl N -> Nat -> InsertResult N
insert' Empty N = Bigger (Balanced N Empty Empty)
insert' (Left Y L R) X with cmp X Y
insert' (Left Y L R) X | Less with insert' L X
insert' (Left Y L R) X | Less | Same L' = Same (Left Y L' R)
insert' (Left Y L R) X | Less | Bigger L' = balance-left Y L' R
insert' (Left Y L R) X | Equal = Same (Left Y L R)
insert' (Left Y L R) X | Greater with insert' R X
insert' (Left Y L R) X | Greater | Same R' = Same (Left Y L R')
insert' (Left Y L R) X | Greater | Bigger R' = Same (Balanced Y L R')
insert' (Balanced Y L R) X with cmp X Y
insert' (Balanced Y L R) X | Less with insert' L X
insert' (Balanced Y L R) X | Less | Same L' = Same (Balanced Y L' R)
insert' (Balanced Y L R) X | Less | Bigger L' = Bigger (Left Y L' R)
insert' (Balanced Y L R) X | Equal = Same (Balanced Y L R)
insert' (Balanced Y L R) X | Greater with insert' R X
insert' (Balanced Y L R) X | Greater | Same R' = Same (Balanced Y L R')
insert' (Balanced Y L R) X | Greater | Bigger R' = Bigger (Right Y L R')
insert' (Right Y L R) X with cmp X Y
insert' (Right Y L R) X | Less with insert' L X
insert' (Right Y L R) X | Less | Same L' = Same (Right Y L' R)
insert' (Right Y L R) X | Less | Bigger L' = Same (Balanced Y L' R)
insert' (Right Y L R) X | Equal = Same (Right Y L R)
insert' (Right Y L R) X | Greater with insert' R X
insert' (Right Y L R) X | Greater | Same R' = Same (Right Y L R')
insert' (Right Y L R) X | Greater | Bigger R' = balance-right Y L R'
-- Wrapper around insert' to use the depth-agnostic type Tree.
insert : Tree -> Nat -> Tree
insert (avl T) X with insert' T X
... | Same T' = avl T'
... | Bigger T' = avl T'
|
http://rosettacode.org/wiki/Averages/Mean_angle | Averages/Mean angle | When calculating the average or mean of an angle one has to take into account how angles wrap around so that any angle in degrees plus any integer multiple of 360 degrees is a measure of the same angle.
If one wanted an average direction of the wind over two readings where the first reading was of 350 degrees and the second was of 10 degrees then the average of the numbers is 180 degrees, whereas if you can note that 350 degrees is equivalent to -10 degrees and so you have two readings at 10 degrees either side of zero degrees leading to a more fitting mean angle of zero degrees.
To calculate the mean angle of several angles:
Assume all angles are on the unit circle and convert them to complex numbers expressed in real and imaginary form.
Compute the mean of the complex numbers.
Convert the complex mean to polar coordinates whereupon the phase of the complex mean is the required angular mean.
(Note that, since the mean is the sum divided by the number of numbers, and division by a positive real number does not affect the angle, you can also simply compute the sum for step 2.)
You can alternatively use this formula:
Given the angles
α
1
,
…
,
α
n
{\displaystyle \alpha _{1},\dots ,\alpha _{n}}
the mean is computed by
α
¯
=
atan2
(
1
n
⋅
∑
j
=
1
n
sin
α
j
,
1
n
⋅
∑
j
=
1
n
cos
α
j
)
{\displaystyle {\bar {\alpha }}=\operatorname {atan2} \left({\frac {1}{n}}\cdot \sum _{j=1}^{n}\sin \alpha _{j},{\frac {1}{n}}\cdot \sum _{j=1}^{n}\cos \alpha _{j}\right)}
Task[edit]
write a function/method/subroutine/... that given a list of angles in degrees returns their mean angle.
(You should use a built-in function if you have one that does this for degrees or radians).
Use the function to compute the means of these lists of angles (in degrees):
[350, 10]
[90, 180, 270, 360]
[10, 20, 30]
Show your output here.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Aime | Aime | real
mean(list l)
{
integer i;
real x, y;
x = y = 0;
i = 0;
while (i < l_length(l)) {
x += Gcos(l[i]);
y += Gsin(l[i]);
i += 1;
}
return Gatan2(y / l_length(l), x / l_length(l));
}
integer
main(void)
{
o_form("mean of 1st set: /d6/\n", mean(l_effect(350, 10)));
o_form("mean of 2nd set: /d6/\n", mean(l_effect(90, 180, 270, 360)));
o_form("mean of 3rd set: /d6/\n", mean(l_effect(10, 20, 30)));
return 0;
} |
http://rosettacode.org/wiki/Averages/Mean_angle | Averages/Mean angle | When calculating the average or mean of an angle one has to take into account how angles wrap around so that any angle in degrees plus any integer multiple of 360 degrees is a measure of the same angle.
If one wanted an average direction of the wind over two readings where the first reading was of 350 degrees and the second was of 10 degrees then the average of the numbers is 180 degrees, whereas if you can note that 350 degrees is equivalent to -10 degrees and so you have two readings at 10 degrees either side of zero degrees leading to a more fitting mean angle of zero degrees.
To calculate the mean angle of several angles:
Assume all angles are on the unit circle and convert them to complex numbers expressed in real and imaginary form.
Compute the mean of the complex numbers.
Convert the complex mean to polar coordinates whereupon the phase of the complex mean is the required angular mean.
(Note that, since the mean is the sum divided by the number of numbers, and division by a positive real number does not affect the angle, you can also simply compute the sum for step 2.)
You can alternatively use this formula:
Given the angles
α
1
,
…
,
α
n
{\displaystyle \alpha _{1},\dots ,\alpha _{n}}
the mean is computed by
α
¯
=
atan2
(
1
n
⋅
∑
j
=
1
n
sin
α
j
,
1
n
⋅
∑
j
=
1
n
cos
α
j
)
{\displaystyle {\bar {\alpha }}=\operatorname {atan2} \left({\frac {1}{n}}\cdot \sum _{j=1}^{n}\sin \alpha _{j},{\frac {1}{n}}\cdot \sum _{j=1}^{n}\cos \alpha _{j}\right)}
Task[edit]
write a function/method/subroutine/... that given a list of angles in degrees returns their mean angle.
(You should use a built-in function if you have one that does this for degrees or radians).
Use the function to compute the means of these lists of angles (in degrees):
[350, 10]
[90, 180, 270, 360]
[10, 20, 30]
Show your output here.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #ALGOL_68 | ALGOL 68 | #!/usr/bin/a68g --script #
# -*- coding: utf-8 -*- #
PROC mean angle = ([]#LONG# REAL angles)#LONG# REAL:
(
INT size = UPB angles - LWB angles + 1;
#LONG# REAL y part := 0, x part := 0;
FOR i FROM LWB angles TO UPB angles DO
x part +:= #long# cos (angles[i] * #long# pi / 180);
y part +:= #long# sin (angles[i] * #long# pi / 180)
OD;
#long# arc tan2 (y part / size, x part / size) * 180 / #long# pi
);
main:
(
[]#LONG# REAL angle set 1 = ( 350, 10 );
[]#LONG# REAL angle set 2 = ( 90, 180, 270, 360);
[]#LONG# REAL angle set 3 = ( 10, 20, 30);
FORMAT summary fmt=$"Mean angle for "g" set :"-zd.ddddd" degrees"l$;
printf ((summary fmt,"1st", mean angle (angle set 1)));
printf ((summary fmt,"2nd", mean angle (angle set 2)));
printf ((summary fmt,"3rd", mean angle (angle set 3)))
) |
http://rosettacode.org/wiki/Averages/Median | Averages/Median | Task[edit]
Write a program to find the median value of a vector of floating-point numbers.
The program need not handle the case where the vector is empty, but must handle the case where there are an even number of elements. In that case, return the average of the two middle values.
There are several approaches to this. One is to sort the elements, and then pick the element(s) in the middle.
Sorting would take at least O(n logn). Another approach would be to build a priority queue from the elements, and then extract half of the elements to get to the middle element(s). This would also take O(n logn). The best solution is to use the selection algorithm to find the median in O(n) time.
See also
Quickselect_algorithm
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Ada | Ada | with Ada.Text_IO, Ada.Float_Text_IO;
procedure FindMedian is
f: array(1..10) of float := ( 4.4, 2.3, -1.7, 7.5, 6.6, 0.0, 1.9, 8.2, 9.3, 4.5 );
min_idx: integer;
min_val, median_val, swap: float;
begin
for i in f'range loop
min_idx := i;
min_val := f(i);
for j in i+1 .. f'last loop
if f(j) < min_val then
min_idx := j;
min_val := f(j);
end if;
end loop;
swap := f(i); f(i) := f(min_idx); f(min_idx) := swap;
end loop;
if f'length mod 2 /= 0 then
median_val := f( f'length/2+1 );
else
median_val := ( f(f'length/2) + f(f'length/2+1) ) / 2.0;
end if;
Ada.Text_IO.Put( "Median value: " );
Ada.Float_Text_IO.Put( median_val );
Ada.Text_IO.New_line;
end FindMedian; |
http://rosettacode.org/wiki/Averages/Pythagorean_means | Averages/Pythagorean means | Task[edit]
Compute all three of the Pythagorean means of the set of integers 1 through 10 (inclusive).
Show that
A
(
x
1
,
…
,
x
n
)
≥
G
(
x
1
,
…
,
x
n
)
≥
H
(
x
1
,
…
,
x
n
)
{\displaystyle A(x_{1},\ldots ,x_{n})\geq G(x_{1},\ldots ,x_{n})\geq H(x_{1},\ldots ,x_{n})}
for this set of positive integers.
The most common of the three means, the arithmetic mean, is the sum of the list divided by its length:
A
(
x
1
,
…
,
x
n
)
=
x
1
+
⋯
+
x
n
n
{\displaystyle A(x_{1},\ldots ,x_{n})={\frac {x_{1}+\cdots +x_{n}}{n}}}
The geometric mean is the
n
{\displaystyle n}
th root of the product of the list:
G
(
x
1
,
…
,
x
n
)
=
x
1
⋯
x
n
n
{\displaystyle G(x_{1},\ldots ,x_{n})={\sqrt[{n}]{x_{1}\cdots x_{n}}}}
The harmonic mean is
n
{\displaystyle n}
divided by the sum of the reciprocal of each item in the list:
H
(
x
1
,
…
,
x
n
)
=
n
1
x
1
+
⋯
+
1
x
n
{\displaystyle H(x_{1},\ldots ,x_{n})={\frac {n}{{\frac {1}{x_{1}}}+\cdots +{\frac {1}{x_{n}}}}}}
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #EchoLisp | EchoLisp |
(define (A xs) (// (for/sum ((x xs)) x) (length xs)))
(define (G xs) (expt (for/product ((x xs)) x) (// (length xs))))
(define (H xs) (// (length xs) (for/sum ((x xs)) (// x))))
(define xs (range 1 11))
(and (>= (A xs) (G xs)) (>= (G xs) (H xs)))
→ #t
|
http://rosettacode.org/wiki/Balanced_ternary | Balanced ternary | Balanced ternary is a way of representing numbers. Unlike the prevailing binary representation, a balanced ternary integer is in base 3, and each digit can have the values 1, 0, or −1.
Examples
Decimal 11 = 32 + 31 − 30, thus it can be written as "++−"
Decimal 6 = 32 − 31 + 0 × 30, thus it can be written as "+−0"
Task
Implement balanced ternary representation of integers with the following:
Support arbitrarily large integers, both positive and negative;
Provide ways to convert to and from text strings, using digits '+', '-' and '0' (unless you are already using strings to represent balanced ternary; but see requirement 5).
Provide ways to convert to and from native integer type (unless, improbably, your platform's native integer type is balanced ternary). If your native integers can't support arbitrary length, overflows during conversion must be indicated.
Provide ways to perform addition, negation and multiplication directly on balanced ternary integers; do not convert to native integers first.
Make your implementation efficient, with a reasonable definition of "efficient" (and with a reasonable definition of "reasonable").
Test case With balanced ternaries a from string "+-0++0+", b from native integer -436, c "+-++-":
write out a, b and c in decimal notation;
calculate a × (b − c), write out the result in both ternary and decimal notations.
Note: The pages generalised floating point addition and generalised floating point multiplication have code implementing arbitrary precision floating point balanced ternary.
| #Common_Lisp | Common Lisp | ;;; balanced ternary
;;; represented as a list of 0, 1 or -1s, with least significant digit first
;;; convert ternary to integer
(defun bt-integer (b)
(reduce (lambda (x y) (+ x (* 3 y))) b :from-end t :initial-value 0))
;;; convert integer to ternary
(defun integer-bt (n)
(if (zerop n) nil
(case (mod n 3)
(0 (cons 0 (integer-bt (/ n 3))))
(1 (cons 1 (integer-bt (floor n 3))))
(2 (cons -1 (integer-bt (floor (1+ n) 3)))))))
;;; convert string to ternary
(defun string-bt (s)
(loop with o = nil for c across s do
(setf o (cons (case c (#\+ 1) (#\- -1) (#\0 0)) o))
finally (return o)))
;;; convert ternary to string
(defun bt-string (bt)
(if (not bt) "0"
(let* ((l (length bt))
(s (make-array l :element-type 'character)))
(mapc (lambda (b)
(setf (aref s (decf l))
(case b (-1 #\-) (0 #\0) (1 #\+))))
bt)
s)))
;;; arithmetics
(defun bt-neg (a) (map 'list #'- a))
(defun bt-sub (a b) (bt-add a (bt-neg b)))
(let ((tbl #((0 -1) (1 -1) (-1 0) (0 0) (1 0) (-1 1) (0 1))))
(defun bt-add-digits (a b c)
(values-list (aref tbl (+ 3 a b c)))))
(defun bt-add (a b &optional (c 0))
(if (not (and a b))
(if (zerop c) (or a b)
(bt-add (list c) (or a b)))
(multiple-value-bind (d c)
(bt-add-digits (if a (car a) 0) (if b (car b) 0) c)
(let ((res (bt-add (cdr a) (cdr b) c)))
;; trim leading zeros
(if (or res (not (zerop d)))
(cons d res))))))
(defun bt-mul (a b)
(if (not (and a b))
nil
(bt-add (case (car a)
(-1 (bt-neg b))
( 0 nil)
( 1 b))
(cons 0 (bt-mul (cdr a) b)))))
;;; division with quotient/remainder, for completeness
(defun bt-truncate (a b)
(let ((n (- (length a) (length b)))
(d (car (last b))))
(if (minusp n)
(values nil a)
(labels ((recur (a b x)
(multiple-value-bind (quo rem)
(if (plusp x) (recur a (cons 0 b) (1- x))
(values nil a))
(loop with g = (car (last rem))
with quo = (cons 0 quo)
while (= (length rem) (length b)) do
(cond ((= g d) (setf rem (bt-sub rem b)
quo (bt-add '(1) quo)))
((= g (- d)) (setf rem (bt-add rem b)
quo (bt-add '(-1) quo))))
(setf x (car (last rem)))
finally (return (values quo rem))))))
(recur a b n)))))
;;; test case
(let* ((a (string-bt "+-0++0+"))
(b (integer-bt -436))
(c (string-bt "+-++-"))
(d (bt-mul a (bt-sub b c))))
(format t "a~5d~8t~a~%b~5d~8t~a~%c~5d~8t~a~%a × (b − c) = ~d ~a~%"
(bt-integer a) (bt-string a)
(bt-integer b) (bt-string b)
(bt-integer c) (bt-string c)
(bt-integer d) (bt-string d))) |
http://rosettacode.org/wiki/Babbage_problem | Babbage problem |
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.
For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].
Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.
| #Limbo | Limbo | implement Babbage;
include "sys.m";
sys: Sys;
print: import sys;
include "draw.m";
draw: Draw;
Babbage : module
{
init : fn(ctxt : ref Draw->Context, args : list of string);
};
init (ctxt: ref Draw->Context, args: list of string)
{
sys = load Sys Sys->PATH;
current := 0;
while ((current * current) % 1000000 != 269696)
current++;
print("%d", current);
}
|
http://rosettacode.org/wiki/Babbage_problem | Babbage problem |
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.
For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].
Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.
| #Lua | Lua | -- get smallest number <= sqrt(269696)
k = math.floor(math.sqrt(269696))
-- if root is odd -> make it even
if k % 2 == 1 then
k = k - 1
end
-- cycle through numbers
while not ((k * k) % 1000000 == 269696) do
k = k + 2
end
io.write(string.format("%d * %d = %d\n", k, k, k * k)) |
http://rosettacode.org/wiki/Balanced_brackets | Balanced brackets | Task:
Generate a string with N opening brackets [ and with N closing brackets ], in some arbitrary order.
Determine whether the generated string is balanced; that is, whether it consists entirely of pairs of opening/closing brackets (in that order), none of which mis-nest.
Examples
(empty) OK
[] OK
[][] OK
[[][]] OK
][ NOT OK
][][ NOT OK
[]][[] NOT OK
| #ARM_Assembly | ARM Assembly |
.data
balanced_message:
.ascii "OK\n"
unbalanced_message:
.ascii "NOT OK\n"
.text
.equ balanced_msg_len, 3
.equ unbalanced_msg_len, 7
BalancedBrackets:
mov r1, #0
mov r2, #0
mov r3, #0
process_bracket:
ldrb r2, [r0, r1]
cmp r2, #0
beq evaluate_balance
cmp r2, #'['
addeq r3, r3, #1
cmp r2, #']'
subeq r3, r3, #1
cmp r3, #0
blt unbalanced
add r1, r1, #1
b process_bracket
evaluate_balance:
cmp r3, #0
beq balanced
unbalanced:
ldr r1, =unbalanced_message
mov r2, #unbalanced_msg_len
b display_result
balanced:
ldr r1, =balanced_message
mov r2, #balanced_msg_len
display_result:
mov r7, #4
mov r0, #1
svc #0
mov pc, lr
|
http://rosettacode.org/wiki/Averages/Mode | Averages/Mode | Task[edit]
Write a program to find the mode value of a collection.
The case where the collection is empty may be ignored. Care must be taken to handle the case where the mode is non-unique.
If it is not appropriate or possible to support a general collection, use a vector (array), if possible. If it is not appropriate or possible to support an unspecified value type, use integers.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #E | E | pragma.enable("accumulator")
def mode(values) {
def counts := [].asMap().diverge()
var maxCount := 0
for v in values {
maxCount max= (counts[v] := counts.fetch(v, fn{0}) + 1)
}
return accum [].asSet() for v => ==maxCount in counts { _.with(v) }
} |
http://rosettacode.org/wiki/Averages/Simple_moving_average | Averages/Simple moving average | Computing the simple moving average of a series of numbers.
Task[edit]
Create a stateful function/class/instance that takes a period and returns a routine that takes a number as argument and returns a simple moving average of its arguments so far.
Description
A simple moving average is a method for computing an average of a stream of numbers by only averaging the last P numbers from the stream, where P is known as the period.
It can be implemented by calling an initialing routine with P as its argument, I(P), which should then return a routine that when called with individual, successive members of a stream of numbers, computes the mean of (up to), the last P of them, lets call this SMA().
The word stateful in the task description refers to the need for SMA() to remember certain information between calls to it:
The period, P
An ordered container of at least the last P numbers from each of its individual calls.
Stateful also means that successive calls to I(), the initializer, should return separate routines that do not share saved state so they could be used on two independent streams of data.
Pseudo-code for an implementation of SMA is:
function SMA(number: N):
stateful integer: P
stateful list: stream
number: average
stream.append_last(N)
if stream.length() > P:
# Only average the last P elements of the stream
stream.delete_first()
if stream.length() == 0:
average = 0
else:
average = sum( stream.values() ) / stream.length()
return average
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Oforth | Oforth | import: parallel
: createSMA(period)
| ch |
Channel new [ ] over send drop ->ch
#[ ch receive + left(period) dup avg swap ch send drop ] ; |
http://rosettacode.org/wiki/Averages/Mean_time_of_day | Averages/Mean time of day | Task[edit]
A particular activity of bats occurs at these times of the day:
23:00:17, 23:40:20, 00:12:45, 00:17:19
Using the idea that there are twenty-four hours in a day,
which is analogous to there being 360 degrees in a circle,
map times of day to and from angles;
and using the ideas of Averages/Mean angle
compute and show the average time of the nocturnal activity
to an accuracy of one second of time.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #C.2B.2B | C++ | #include <iomanip>
#include <iostream>
#include <vector>
#define _USE_MATH_DEFINES
#include <math.h>
struct Time {
int hour, minute, second;
friend std::ostream &operator<<(std::ostream &, const Time &);
};
std::ostream &operator<<(std::ostream &os, const Time &t) {
return os << std::setfill('0')
<< std::setw(2) << t.hour << ':'
<< std::setw(2) << t.minute << ':'
<< std::setw(2) << t.second;
}
double timeToDegrees(Time &&t) {
return 360.0 * t.hour / 24.0
+ 360.0 * t.minute / (24 * 60.0)
+ 360.0 * t.second / (24 * 3600.0);
}
Time degreesToTime(double angle) {
while (angle < 0.0) {
angle += 360.0;
}
while (angle > 360.0) {
angle -= 360.0;
}
double totalSeconds = 24.0 * 60 * 60 * angle / 360;
Time t;
t.second = (int)totalSeconds % 60;
t.minute = ((int)totalSeconds % 3600 - t.second) / 60;
t.hour = (int)totalSeconds / 3600;
return t;
}
double meanAngle(const std::vector<double> &angles) {
double yPart = 0.0, xPart = 0.0;
for (auto a : angles) {
xPart += cos(a * M_PI / 180);
yPart += sin(a * M_PI / 180);
}
return atan2(yPart / angles.size(), xPart / angles.size()) * 180 / M_PI;
}
int main() {
std::vector<double> tv;
tv.push_back(timeToDegrees({ 23, 0, 17 }));
tv.push_back(timeToDegrees({ 23, 40, 20 }));
tv.push_back(timeToDegrees({ 0, 12, 45 }));
tv.push_back(timeToDegrees({ 0, 17, 19 }));
double ma = meanAngle(tv);
auto mt = degreesToTime(ma);
std::cout << mt << '\n';
return 0;
} |
http://rosettacode.org/wiki/AVL_tree | AVL tree |
This page uses content from Wikipedia. The original article was at AVL tree. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
In computer science, an AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; at no time do they differ by more than one because rebalancing is done ensure this is the case. Lookup, insertion, and deletion all take O(log n) time in both the average and worst cases, where n is the number of nodes in the tree prior to the operation. Insertions and deletions may require the tree to be rebalanced by one or more tree rotations. Note the tree of nodes comprise a set, so duplicate node keys are not allowed.
AVL trees are often compared with red-black trees because they support the same set of operations and because red-black trees also take O(log n) time for the basic operations. Because AVL trees are more rigidly balanced, they are faster than red-black trees for lookup-intensive applications. Similar to red-black trees, AVL trees are height-balanced, but in general not weight-balanced nor μ-balanced; that is, sibling nodes can have hugely differing numbers of descendants.
Task
Implement an AVL tree in the language of choice, and provide at least basic operations.
| #ARM_Assembly | ARM Assembly |
/* ARM assembly Raspberry PI */
/* program avltree2.s */
/* REMARK 1 : this program use routines in a include file
see task Include a file language arm assembly
for the routine affichageMess conversion10
see at end of this program the instruction include */
/*******************************************/
/* Constantes */
/*******************************************/
.equ STDOUT, 1 @ Linux output console
.equ EXIT, 1 @ Linux syscall
.equ WRITE, 4 @ Linux syscall
.equ BRK, 0x2d @ Linux syscall
.equ CHARPOS, '@'
.equ NBVAL, 12
/*******************************************/
/* Structures */
/********************************************/
/* structure tree */
.struct 0
tree_root: @ root pointer (or node right)
.struct tree_root + 4
tree_size: @ number of element of tree
.struct tree_size + 4
tree_suite:
.struct tree_suite + 12 @ for alignement to node
tree_fin:
/* structure node tree */
.struct 0
node_right: @ right pointer
.struct node_right + 4
node_left: @ left pointer
.struct node_left + 4
node_value: @ element value
.struct node_value + 4
node_height: @ element value
.struct node_height + 4
node_parent: @ element value
.struct node_parent + 4
node_fin:
/* structure queue*/
.struct 0
queue_begin: @ next pointer
.struct queue_begin + 4
queue_end: @ element value
.struct queue_end + 4
queue_fin:
/* structure node queue */
.struct 0
queue_node_next: @ next pointer
.struct queue_node_next + 4
queue_node_value: @ element value
.struct queue_node_value + 4
queue_node_fin:
/*******************************************/
/* Initialized data */
/*******************************************/
.data
szMessPreOrder: .asciz "PreOrder :\n"
szCarriageReturn: .asciz "\n"
/* datas error display */
szMessErreur: .asciz "Error detected.\n"
szMessKeyDbl: .asciz "Key exists in tree.\n"
szMessInsInv: .asciz "Insertion in inverse order.\n"
/* datas message display */
szMessResult: .asciz "Ele: @ G: @ D: @ val @ h @ pere @\n"
sValue: .space 12,' '
.asciz "\n"
/*******************************************/
/* UnInitialized data */
/*******************************************/
.bss
sZoneConv: .skip 24
stTree: .skip tree_fin @ place to structure tree
stTree1: .skip tree_fin @ place to structure tree
stQueue: .skip queue_fin @ place to structure queue
/*******************************************/
/* code section */
/*******************************************/
.text
.global main
main:
mov r8,#1 @ node tree value
1: @ loop insertion in order
ldr r0,iAdrstTree @ structure tree address
mov r1,r8
bl insertElement @ add element value r1
cmp r0,#-1
beq 99f
//ldr r3,iAdrstTree @ tree root address (begin structure)
//ldr r0,[r3,#tree_root]
//ldr r1,iAdrdisplayElement @ function to execute
//bl preOrder
add r8,#1 @ increment value
cmp r8,#NBVAL @ end ?
ble 1b @ no -> loop
ldr r0,iAdrstTree @ structure tree address
mov r1,#11 @ verif key dobble
bl insertElement @ add element value r1
cmp r0,#-1
bne 2f
ldr r0,iAdrszMessErreur
bl affichageMess
2:
ldr r0,iAdrszMessPreOrder @ load verification
bl affichageMess
ldr r3,iAdrstTree @ tree root address (begin structure)
ldr r0,[r3,#tree_root]
ldr r1,iAdrdisplayElement @ function to execute
bl preOrder
ldr r0,iAdrszMessInsInv
bl affichageMess
mov r8,#NBVAL @ node tree value
3: @ loop insertion inverse order
ldr r0,iAdrstTree1 @ structure tree address
mov r1,r8
bl insertElement @ add element value r1
cmp r0,#-1
beq 99f
sub r8,#1 @ increment value
cmp r8,#0 @ end ?
bgt 3b @ no -> loop
ldr r0,iAdrszMessPreOrder @ load verification
bl affichageMess
ldr r3,iAdrstTree1 @ tree root address (begin structure)
ldr r0,[r3,#tree_root]
ldr r1,iAdrdisplayElement @ function to execute
bl preOrder
@ search value
ldr r0,iAdrstTree1 @ tree root address (begin structure)
mov r1,#11 @ value to search
bl searchTree
cmp r0,#-1
beq 100f
mov r2,r0
ldr r0,iAdrszMessKeyDbl @ key exists
bl affichageMess
@ suppresssion previous value
mov r0,r2
ldr r1,iAdrstTree1
bl supprimer
ldr r0,iAdrszMessPreOrder @ verification
bl affichageMess
ldr r3,iAdrstTree1 @ tree root address (begin structure)
ldr r0,[r3,#tree_root]
ldr r1,iAdrdisplayElement @ function to execute
bl preOrder
b 100f
99: @ display error
ldr r0,iAdrszMessErreur
bl affichageMess
100: @ standard end of the program
mov r7, #EXIT @ request to exit program
svc 0 @ perform system call
iAdrszMessPreOrder: .int szMessPreOrder
iAdrszMessErreur: .int szMessErreur
iAdrszCarriageReturn: .int szCarriageReturn
iAdrstTree: .int stTree
iAdrstTree1: .int stTree1
iAdrstQueue: .int stQueue
iAdrdisplayElement: .int displayElement
iAdrszMessInsInv: .int szMessInsInv
/******************************************************************/
/* insert element in the tree */
/******************************************************************/
/* r0 contains the address of the tree structure */
/* r1 contains the value of element */
/* r0 returns address of element or - 1 if error */
insertElement: @ INFO: insertElement
push {r1-r8,lr} @ save registers
mov r7,r0 @ save head
mov r0,#node_fin @ reservation place one element
bl allocHeap
cmp r0,#-1 @ allocation error
beq 100f
mov r5,r0
str r1,[r5,#node_value] @ store value in address heap
mov r3,#0
str r3,[r5,#node_left] @ init left pointer with zero
str r3,[r5,#node_right] @ init right pointer with zero
str r3,[r5,#node_height] @ init balance with zero
ldr r2,[r7,#tree_size] @ load tree size
cmp r2,#0 @ 0 element ?
bne 1f
str r5,[r7,#tree_root] @ yes -> store in root
b 4f
1: @ else search free address in tree
ldr r3,[r7,#tree_root] @ start with address root
2: @ begin loop to insertion
ldr r4,[r3,#node_value] @ load key
cmp r1,r4
beq 6f @ key equal
blt 3f @ key <
@ key > insertion right
ldr r8,[r3,#node_right] @ node empty ?
cmp r8,#0
movne r3,r8 @ no -> next node
bne 2b @ and loop
str r5,[r3,#node_right] @ store node address in right pointer
b 4f
3: @ left
ldr r8,[r3,#node_left] @ left pointer empty ?
cmp r8,#0
movne r3,r8 @
bne 2b @ no -> loop
str r5,[r3,#node_left] @ store node address in left pointer
4:
str r3,[r5,#node_parent] @ store parent
mov r4,#1
str r4,[r5,#node_height] @ store height = 1
mov r0,r5 @ begin node to requilbrate
mov r1,r7 @ head address
bl equilibrer
5:
add r2,#1 @ increment tree size
str r2,[r7,#tree_size]
mov r0,#0
b 100f
6: @ key equal ?
ldr r0,iAdrszMessKeyDbl
bl affichageMess
mov r0,#-1
b 100f
100:
pop {r1-r8,lr} @ restaur registers
bx lr @ return
iAdrszMessKeyDbl: .int szMessKeyDbl
/******************************************************************/
/* equilibrer after insertion */
/******************************************************************/
/* r0 contains the address of the node */
/* r1 contains the address of head */
equilibrer: @ INFO: equilibrer
push {r1-r8,lr} @ save registers
mov r3,#0 @ balance factor
1: @ begin loop
ldr r5,[r0,#node_parent] @ load father
cmp r5,#0 @ end ?
beq 5f
cmp r3,#2 @ right tree too long
beq 5f
cmp r3,#-2 @ left tree too long
beq 5f
mov r6,r0 @ s = current
ldr r0,[r6,#node_parent] @ current = father
ldr r7,[r0,#node_left]
cmp r7,#0
ldrne r8,[r7,#node_height] @ height left tree
moveq r8,#0
ldr r7,[r0,#node_right]
cmp r7,#0
ldrne r9,[r7,#node_height] @ height right tree
moveq r9,#0
cmp r8,r9
addgt r8,#1
strgt r8,[r0,#node_height]
addle r9,#1
strle r9,[r0,#node_height]
//
ldr r7,[r0,#node_right]
cmp r7,#0
ldrne r8,[r7,#node_height]
moveq r8,#0
ldr r7,[r0,#node_left]
cmp r7,#0
ldrne r9,[r7,#node_height]
moveq r9,#0
sub r3,r8,r9 @ compute balance factor
b 1b
5:
cmp r3,#2
beq 6f
cmp r3,#-2
beq 6f
b 100f
6:
mov r3,r1
mov r4,r0
mov r1,r6
bl equiUnSommet
@ change head address ?
ldr r2,[r3,#tree_root]
cmp r2,r4
streq r6,[r3,#tree_root]
100:
pop {r1-r8,lr} @ restaur registers
bx lr @ return
/******************************************************************/
/* equilibre 1 sommet */
/******************************************************************/
/* r0 contains the address of the node */
/* r1 contains the address of the node */
equiUnSommet: @ INFO: equiUnSommet
push {r1-r9,lr} @ save registers
mov r5,r0 @ save p
mov r6,r1 // s
ldr r2,[r5,#node_left]
cmp r2,r6
bne 5f
ldr r7,[r5,#node_right]
cmp r7,#0
moveq r8,#0
ldrne r8,[r7,#node_height]
ldr r7,[r5,#node_left]
cmp r7,#0
moveq r9,#0
ldrne r9,[r7,#node_height]
sub r3,r8,r9
cmp r3,#-2
bne 100f
ldr r7,[r6,#node_right]
cmp r7,#0
moveq r8,#0
ldrne r8,[r7,#node_height]
ldr r7,[r6,#node_left]
cmp r7,#0
moveq r9,#0
ldrne r9,[r7,#node_height]
sub r3,r8,r9
cmp r3,#1
bge 2f
mov r0,r5
bl rotRight
b 100f
2:
mov r0,r6
bl rotLeft
mov r0,r5
bl rotRight
b 100f
5:
ldr r7,[r5,#node_right]
cmp r7,#0
moveq r8,#0
ldrne r8,[r7,#node_height]
ldr r7,[r5,#node_left]
cmp r7,#0
moveq r9,#0
ldrne r9,[r7,#node_height]
sub r3,r8,r9
cmp r3,#2
bne 100f
ldr r7,[r6,#node_right]
cmp r7,#0
moveq r8,#0
ldrne r8,[r7,#node_height]
ldr r7,[r6,#node_left]
cmp r7,#0
moveq r9,#0
ldrne r9,[r7,#node_height]
sub r3,r8,r9
cmp r3,#-1
ble 2f
mov r0,r5
bl rotLeft
b 100f
2:
mov r0,r6
bl rotRight
mov r0,r5
bl rotLeft
b 100f
100:
pop {r1-r9,lr} @ restaur registers
bx lr @ return
/******************************************************************/
/* right rotation */
/******************************************************************/
/* r0 contains the address of the node */
rotRight: @ INFO: rotRight
push {r1-r5,lr} @ save registers
// r2 r2
// r0 r1
// r1 r0
// r3 r3
ldr r1,[r0,#node_left] @ load left children
ldr r2,[r0,#node_parent] @ load father
cmp r2,#0 @ no father ???
beq 2f
ldr r3,[r2,#node_left] @ load left node father
cmp r3,r0 @ equal current node ?
streq r1,[r2,#node_left] @ yes store left children
strne r1,[r2,#node_right] @ no store right
2:
str r2,[r1,#node_parent] @ change parent
str r1,[r0,#node_parent]
ldr r3,[r1,#node_right]
str r3,[r0,#node_left]
cmp r3,#0
strne r0,[r3,#node_parent] @ change parent node left
str r0,[r1,#node_right]
ldr r3,[r0,#node_left] @ compute newbalance factor
cmp r3,#0
moveq r4,#0
ldrne r4,[r3,#node_height]
ldr r3,[r0,#node_right]
cmp r3,#0
moveq r5,#0
ldrne r5,[r3,#node_height]
cmp r4,r5
addgt r4,#1
strgt r4,[r0,#node_height]
addle r5,#1
strle r5,[r0,#node_height]
//
ldr r3,[r1,#node_left] @ compute new balance factor
cmp r3,#0
moveq r4,#0
ldrne r4,[r3,#node_height]
ldr r3,[r1,#node_right]
cmp r3,#0
moveq r5,#0
ldrne r5,[r3,#node_height]
cmp r4,r5
addgt r4,#1
strgt r4,[r1,#node_height]
addle r5,#1
strle r5,[r1,#node_height]
100:
pop {r1-r5,lr} @ restaur registers
bx lr
/******************************************************************/
/* left rotation */
/******************************************************************/
/* r0 contains the address of the node sommet */
rotLeft: @ INFO: rotLeft
push {r1-r5,lr} @ save registers
// r2 r2
// r0 r1
// r1 r0
// r3 r3
ldr r1,[r0,#node_right] @ load right children
ldr r2,[r0,#node_parent] @ load father (racine)
cmp r2,#0 @ no father ???
beq 2f
ldr r3,[r2,#node_left] @ load left node father
cmp r3,r0 @ equal current node ?
streq r1,[r2,#node_left] @ yes store left children
strne r1,[r2,#node_right] @ no store to right
2:
str r2,[r1,#node_parent] @ change parent of right children
str r1,[r0,#node_parent] @ change parent of sommet
ldr r3,[r1,#node_left] @ left children
str r3,[r0,#node_right] @ left children pivot exists ?
cmp r3,#0
strne r0,[r3,#node_parent] @ yes store in
str r0,[r1,#node_left]
//
ldr r3,[r0,#node_left] @ compute new height for old summit
cmp r3,#0
moveq r4,#0
ldrne r4,[r3,#node_height] @ left height
ldr r3,[r0,#node_right]
cmp r3,#0
moveq r5,#0
ldrne r5,[r3,#node_height] @ right height
cmp r4,r5
addgt r4,#1
strgt r4,[r0,#node_height] @ if right > left
addle r5,#1
strle r5,[r0,#node_height] @ if left > right
//
ldr r3,[r1,#node_left] @ compute new height for new
cmp r3,#0
moveq r4,#0
ldrne r4,[r3,#node_height]
ldr r3,[r1,#node_right]
cmp r3,#0
moveq r5,#0
ldrne r5,[r3,#node_height]
cmp r4,r5
addgt r4,#1
strgt r4,[r1,#node_height]
addle r5,#1
strle r5,[r1,#node_height]
100:
pop {r1-r5,lr} @ restaur registers
bx lr
/******************************************************************/
/* search value in tree */
/******************************************************************/
/* r0 contains the address of structure of tree */
/* r1 contains the value to search */
searchTree: @ INFO: searchTree
push {r1-r4,lr} @ save registers
ldr r2,[r0,#tree_root]
1: @ begin loop
ldr r4,[r2,#node_value] @ load key
cmp r1,r4
beq 3f @ key equal
blt 2f @ key <
@ key > insertion right
ldr r3,[r2,#node_right] @ node empty ?
cmp r3,#0
movne r2,r3 @ no -> next node
bne 1b @ and loop
mov r0,#-1 @ not find
b 100f
2: @ left
ldr r3,[r2,#node_left] @ left pointer empty ?
cmp r3,#0
movne r2,r3 @
bne 1b @ no -> loop
mov r0,#-1 @ not find
b 100f
3:
mov r0,r2 @ return node address
100:
pop {r1-r4,lr} @ restaur registers
bx lr
/******************************************************************/
/* suppression node */
/******************************************************************/
/* r0 contains the address of the node */
/* r1 contains structure tree address */
supprimer: @ INFO: supprimer
push {r1-r8,lr} @ save registers
ldr r1,[r0,#node_left]
cmp r1,#0
bne 5f
ldr r1,[r0,#node_right]
cmp r1,#0
bne 5f
@ is a leaf
mov r4,#0
ldr r3,[r0,#node_parent] @ father
cmp r3,#0
streq r4,[r1,#tree_root]
beq 100f
ldr r1,[r3,#node_left]
cmp r1,r0
bne 2f
str r4,[r3,#node_left] @ suppression left children
ldr r5,[r3,#node_right]
cmp r5,#0
moveq r6,#0
ldrne r6,[r5,#node_height]
add r6,#1
str r6,[r3,#node_height]
b 3f
2: @ suppression right children
str r4,[r3,#node_right]
ldr r5,[r3,#node_left]
cmp r5,#0
moveq r6,#0
ldrne r6,[r5,#node_height]
add r6,#1
str r6,[r3,#node_height]
3: @ new balance
mov r0,r3
bl equilibrerSupp
b 100f
5: @ is not à leaf
ldr r7,[r0,#node_right]
cmp r7,#0
beq 7f
mov r8,r0
mov r0,r7
6:
ldr r6,[r0,#node_left]
cmp r6,#0
movne r0,r6
bne 6b
b 9f
7:
ldr r7,[r0,#node_left] @ search the litle element
cmp r7,#0
beq 9f
mov r8,r0
mov r0,r7
8:
ldr r6,[r0,#node_right] @ search the great element
cmp r6,#0
movne r0,r6
bne 8b
9:
ldr r5,[r0,#node_value] @ copy value
str r5,[r8,#node_value]
bl supprimer @ suppression node r0
100:
pop {r1-r8,lr} @ restaur registers
bx lr
/******************************************************************/
/* equilibrer after suppression */
/******************************************************************/
/* r0 contains the address of the node */
/* r1 contains the address of head */
equilibrerSupp: @ INFO: equilibrerSupp
push {r1-r8,lr} @ save registers
mov r3,#1 @ balance factor
ldr r2,[r1,#tree_root]
1:
ldr r5,[r0,#node_parent] @ load father
cmp r5,#0 @ no father
beq 100f
cmp r3,#0 @ balance equilibred
beq 100f
mov r6,r0 @ save entry node
ldr r0,[r6,#node_parent] @ current = father
ldr r7,[r0,#node_left]
cmp r7,#0
ldrne r8,[r7,#node_height] @ height left tree
moveq r8,#0
ldr r7,[r0,#node_right]
cmp r7,#0
ldrne r9,[r7,#node_height] @ height right tree
moveq r9,#0
cmp r8,r9
addgt r8,#1
strgt r8,[r0,#node_height]
addle r9,#1
strle r9,[r0,#node_height]
//
ldr r7,[r0,#node_right]
cmp r7,#0
ldrne r8,[r7,#node_height]
moveq r8,#0
ldr r7,[r0,#node_left]
cmp r7,#0
ldrne r9,[r7,#node_height]
moveq r9,#0
sub r3,r8,r9 @ compute balance factor
mov r2,r1
mov r4,r0 @ save current
mov r1,r6
bl equiUnSommet
@ change head address ?
cmp r2,r4
streq r6,[r3,#tree_root]
mov r0,r4 @ restaur current
b 1b
100:
pop {r1-r8,lr} @ restaur registers
bx lr @ return
/******************************************************************/
/* preOrder */
/******************************************************************/
/* r0 contains the address of the node */
/* r1 function address */
preOrder: @ INFO: preOrder
push {r1-r2,lr} @ save registers
cmp r0,#0
beq 100f
mov r2,r0
blx r1 @ call function
ldr r0,[r2,#node_left]
bl preOrder
ldr r0,[r2,#node_right]
bl preOrder
100:
pop {r1-r2,lr} @ restaur registers
bx lr
/******************************************************************/
/* display node */
/******************************************************************/
/* r0 contains node address */
displayElement: @ INFO: displayElement
push {r1,r2,r3,lr} @ save registers
mov r2,r0
ldr r1,iAdrsZoneConv
bl conversion16
mov r4,#0
strb r4,[r1,r0]
ldr r0,iAdrszMessResult
ldr r1,iAdrsZoneConv
bl strInsertAtCharInc
mov r3,r0
ldr r0,[r2,#node_left]
ldr r1,iAdrsZoneConv
bl conversion16
mov r4,#0
strb r4,[r1,r0]
mov r0,r3
ldr r1,iAdrsZoneConv
bl strInsertAtCharInc
mov r3,r0
ldr r0,[r2,#node_right]
ldr r1,iAdrsZoneConv
bl conversion16
mov r4,#0
strb r4,[r1,r0]
mov r0,r3
ldr r1,iAdrsZoneConv
bl strInsertAtCharInc
mov r3,r0
ldr r0,[r2,#node_value]
ldr r1,iAdrsZoneConv
bl conversion10
mov r4,#0
strb r4,[r1,r0]
mov r0,r3
ldr r1,iAdrsZoneConv
bl strInsertAtCharInc
mov r3,r0
ldr r0,[r2,#node_height]
ldr r1,iAdrsZoneConv
bl conversion10
mov r4,#0
strb r4,[r1,r0]
mov r0,r3
ldr r1,iAdrsZoneConv
bl strInsertAtCharInc
mov r3,r0
ldr r0,[r2,#node_parent]
ldr r1,iAdrsZoneConv
bl conversion16
mov r4,#0
strb r4,[r1,r0]
mov r0,r3
ldr r1,iAdrsZoneConv
bl strInsertAtCharInc
bl affichageMess
100:
pop {r1,r2,r3,lr} @ restaur registers
bx lr @ return
iAdrszMessResult: .int szMessResult
iAdrsZoneConv: .int sZoneConv
iAdrsValue: .int sValue
/******************************************************************/
/* memory allocation on the heap */
/******************************************************************/
/* r0 contains the size to allocate */
/* r0 returns address of memory heap or - 1 if error */
/* CAUTION : The size of the allowance must be a multiple of 4 */
allocHeap:
push {r5-r7,lr} @ save registers
@ allocation
mov r6,r0 @ save size
mov r0,#0 @ read address start heap
mov r7,#0x2D @ call system 'brk'
svc #0
mov r5,r0 @ save address heap for return
add r0,r6 @ reservation place for size
mov r7,#0x2D @ call system 'brk'
svc #0
cmp r0,#-1 @ allocation error
movne r0,r5 @ return address memory heap
pop {r5-r7,lr} @ restaur registers
bx lr @ return
/***************************************************/
/* ROUTINES INCLUDE */
/***************************************************/
.include "../affichage.inc"
|
http://rosettacode.org/wiki/Averages/Mean_angle | Averages/Mean angle | When calculating the average or mean of an angle one has to take into account how angles wrap around so that any angle in degrees plus any integer multiple of 360 degrees is a measure of the same angle.
If one wanted an average direction of the wind over two readings where the first reading was of 350 degrees and the second was of 10 degrees then the average of the numbers is 180 degrees, whereas if you can note that 350 degrees is equivalent to -10 degrees and so you have two readings at 10 degrees either side of zero degrees leading to a more fitting mean angle of zero degrees.
To calculate the mean angle of several angles:
Assume all angles are on the unit circle and convert them to complex numbers expressed in real and imaginary form.
Compute the mean of the complex numbers.
Convert the complex mean to polar coordinates whereupon the phase of the complex mean is the required angular mean.
(Note that, since the mean is the sum divided by the number of numbers, and division by a positive real number does not affect the angle, you can also simply compute the sum for step 2.)
You can alternatively use this formula:
Given the angles
α
1
,
…
,
α
n
{\displaystyle \alpha _{1},\dots ,\alpha _{n}}
the mean is computed by
α
¯
=
atan2
(
1
n
⋅
∑
j
=
1
n
sin
α
j
,
1
n
⋅
∑
j
=
1
n
cos
α
j
)
{\displaystyle {\bar {\alpha }}=\operatorname {atan2} \left({\frac {1}{n}}\cdot \sum _{j=1}^{n}\sin \alpha _{j},{\frac {1}{n}}\cdot \sum _{j=1}^{n}\cos \alpha _{j}\right)}
Task[edit]
write a function/method/subroutine/... that given a list of angles in degrees returns their mean angle.
(You should use a built-in function if you have one that does this for degrees or radians).
Use the function to compute the means of these lists of angles (in degrees):
[350, 10]
[90, 180, 270, 360]
[10, 20, 30]
Show your output here.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #AutoHotkey | AutoHotkey | Angles := [[350, 10], [90, 180, 270, 360], [10, 20, 30]]
MsgBox, % MeanAngle(Angles[1]) "`n"
. MeanAngle(Angles[2]) "`n"
. MeanAngle(Angles[3])
MeanAngle(a, x=0, y=0) {
static c := ATan(1) / 45
for k, v in a {
x += Cos(v * c) / a.MaxIndex()
y += Sin(v * c) / a.MaxIndex()
}
return atan2(x, y) / c
}
atan2(x, y) {
return dllcall("msvcrt\atan2", "Double",y, "Double",x, "CDECL Double")
} |
http://rosettacode.org/wiki/Averages/Median | Averages/Median | Task[edit]
Write a program to find the median value of a vector of floating-point numbers.
The program need not handle the case where the vector is empty, but must handle the case where there are an even number of elements. In that case, return the average of the two middle values.
There are several approaches to this. One is to sort the elements, and then pick the element(s) in the middle.
Sorting would take at least O(n logn). Another approach would be to build a priority queue from the elements, and then extract half of the elements to get to the middle element(s). This would also take O(n logn). The best solution is to use the selection algorithm to find the median in O(n) time.
See also
Quickselect_algorithm
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #ALGOL_68 | ALGOL 68 | INT max_elements = 1000000;
# Return the k-th smallest item in array x of length len #
PROC quick_select = (INT k, REF[]REAL x) REAL:
BEGIN
PROC swap = (INT a, b) VOID:
BEGIN
REAL t = x[a];
x[a] := x[b]; x[b] := t
END;
INT left := 1, right := UPB x;
INT pos, i;
REAL pivot;
WHILE left < right DO
pivot := x[k];
swap (k, right);
pos := left;
FOR i FROM left TO right DO
IF x[i] < pivot THEN
swap (i, pos);
pos +:= 1
FI
OD;
swap (right, pos);
IF pos = k THEN break FI;
IF pos < k THEN left := pos + 1
ELSE right := pos - 1
FI
OD;
break:
SKIP;
x[k]
END;
# Initialize random length REAL array with random doubles #
INT length = ENTIER (next random * max_elements);
[length]REAL x;
FOR i TO length DO
x[i] := (next random * 1e6 - 0.5e6)
OD;
REAL median :=
IF NOT ODD length THEN
# Even number of elements, median is average of middle two #
(quick_select (length % 2, x) + quick_select(length % 2 - 1, x)) / 2
ELSE
# select middle element #
quick_select(length % 2, x)
FI;
# Sanity testing of median #
INT less := 0, more := 0, eq := 0;
FOR i TO length DO
IF x[i] < median THEN less +:= 1
ELIF x[i] > median THEN more +:= 1
ELSE eq +:= 1
FI
OD;
print (("length: ", whole (length,0), new line, "median: ", median, new line,
"<: ", whole (less,0), new line,
">: ", whole (more, 0), new line,
"=: ", whole (eq, 0), new line)) |
http://rosettacode.org/wiki/Averages/Pythagorean_means | Averages/Pythagorean means | Task[edit]
Compute all three of the Pythagorean means of the set of integers 1 through 10 (inclusive).
Show that
A
(
x
1
,
…
,
x
n
)
≥
G
(
x
1
,
…
,
x
n
)
≥
H
(
x
1
,
…
,
x
n
)
{\displaystyle A(x_{1},\ldots ,x_{n})\geq G(x_{1},\ldots ,x_{n})\geq H(x_{1},\ldots ,x_{n})}
for this set of positive integers.
The most common of the three means, the arithmetic mean, is the sum of the list divided by its length:
A
(
x
1
,
…
,
x
n
)
=
x
1
+
⋯
+
x
n
n
{\displaystyle A(x_{1},\ldots ,x_{n})={\frac {x_{1}+\cdots +x_{n}}{n}}}
The geometric mean is the
n
{\displaystyle n}
th root of the product of the list:
G
(
x
1
,
…
,
x
n
)
=
x
1
⋯
x
n
n
{\displaystyle G(x_{1},\ldots ,x_{n})={\sqrt[{n}]{x_{1}\cdots x_{n}}}}
The harmonic mean is
n
{\displaystyle n}
divided by the sum of the reciprocal of each item in the list:
H
(
x
1
,
…
,
x
n
)
=
n
1
x
1
+
⋯
+
1
x
n
{\displaystyle H(x_{1},\ldots ,x_{n})={\frac {n}{{\frac {1}{x_{1}}}+\cdots +{\frac {1}{x_{n}}}}}}
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Elixir | Elixir | defmodule Means do
def arithmetic(list) do
Enum.sum(list) / length(list)
end
def geometric(list) do
:math.pow(Enum.reduce(list, &(*/2)), 1 / length(list))
end
def harmonic(list) do
1 / arithmetic(Enum.map(list, &(1 / &1)))
end
end
list = Enum.to_list(1..10)
IO.puts "Arithmetic mean: #{am = Means.arithmetic(list)}"
IO.puts "Geometric mean: #{gm = Means.geometric(list)}"
IO.puts "Harmonic mean: #{hm = Means.harmonic(list)}"
IO.puts "(#{am} >= #{gm} >= #{hm}) is #{am >= gm and gm >= hm}" |
http://rosettacode.org/wiki/Balanced_ternary | Balanced ternary | Balanced ternary is a way of representing numbers. Unlike the prevailing binary representation, a balanced ternary integer is in base 3, and each digit can have the values 1, 0, or −1.
Examples
Decimal 11 = 32 + 31 − 30, thus it can be written as "++−"
Decimal 6 = 32 − 31 + 0 × 30, thus it can be written as "+−0"
Task
Implement balanced ternary representation of integers with the following:
Support arbitrarily large integers, both positive and negative;
Provide ways to convert to and from text strings, using digits '+', '-' and '0' (unless you are already using strings to represent balanced ternary; but see requirement 5).
Provide ways to convert to and from native integer type (unless, improbably, your platform's native integer type is balanced ternary). If your native integers can't support arbitrary length, overflows during conversion must be indicated.
Provide ways to perform addition, negation and multiplication directly on balanced ternary integers; do not convert to native integers first.
Make your implementation efficient, with a reasonable definition of "efficient" (and with a reasonable definition of "reasonable").
Test case With balanced ternaries a from string "+-0++0+", b from native integer -436, c "+-++-":
write out a, b and c in decimal notation;
calculate a × (b − c), write out the result in both ternary and decimal notations.
Note: The pages generalised floating point addition and generalised floating point multiplication have code implementing arbitrary precision floating point balanced ternary.
| #D | D | import std.stdio, std.bigint, std.range, std.algorithm;
struct BalancedTernary {
// Represented as a list of 0, 1 or -1s,
// with least significant digit first.
enum Dig : byte { N=-1, Z=0, P=+1 } // Digit.
const Dig[] digits;
// This could also be a BalancedTernary template argument.
static immutable string dig2str = "-0+";
immutable static Dig[dchar] str2dig; // = ['+': Dig.P, ...];
nothrow static this() {
str2dig = ['+': Dig.P, '-': Dig.N, '0': Dig.Z];
}
immutable pure nothrow static Dig[2][] table =
[[Dig.Z, Dig.N], [Dig.P, Dig.N], [Dig.N, Dig.Z],
[Dig.Z, Dig.Z], [Dig.P, Dig.Z], [Dig.N, Dig.P],
[Dig.Z, Dig.P]];
this(in string inp) const pure {
this.digits = inp.retro.map!(c => str2dig[c]).array;
}
this(in long inp) const pure nothrow {
this.digits = _bint2ternary(inp.BigInt);
}
this(in BigInt inp) const pure nothrow {
this.digits = _bint2ternary(inp);
}
this(in BalancedTernary inp) const pure nothrow {
// No need to dup, they are virtually immutable.
this.digits = inp.digits;
}
private this(in Dig[] inp) pure nothrow {
this.digits = inp;
}
static Dig[] _bint2ternary(in BigInt n) pure nothrow {
static py_div(T1, T2)(in T1 a, in T2 b) pure nothrow {
if (a < 0) {
return (b < 0) ?
-a / -b :
-(-a / b) - (-a % b != 0 ? 1 : 0);
} else {
return (b < 0) ?
-(a / -b) - (a % -b != 0 ? 1 : 0) :
a / b;
}
}
if (n == 0) return [];
// This final switch in D v.2.064 is fake, not enforced.
final switch (((n % 3) + 3) % 3) { // (n % 3) is the remainder.
case 0: return Dig.Z ~ _bint2ternary(py_div(n, 3));
case 1: return Dig.P ~ _bint2ternary(py_div(n, 3));
case 2: return Dig.N ~ _bint2ternary(py_div(n + 1, 3));
}
}
@property BigInt toBint() const pure nothrow {
return reduce!((y, x) => x + 3 * y)(0.BigInt, digits.retro);
}
string toString() const pure nothrow {
if (digits.empty) return "0";
return digits.retro.map!(d => dig2str[d + 1]).array;
}
static const(Dig)[] neg_(in Dig[] digs) pure nothrow {
return digs.map!(a => -a).array;
}
BalancedTernary opUnary(string op:"-")() const pure nothrow {
return BalancedTernary(neg_(this.digits));
}
static const(Dig)[] add_(in Dig[] a, in Dig[] b, in Dig c=Dig.Z)
pure nothrow {
const a_or_b = a.length ? a : b;
if (a.empty || b.empty) {
if (c == Dig.Z)
return a_or_b;
else
return BalancedTernary.add_([c], a_or_b);
} else {
// (const d, c) = table[...];
const dc = table[3 + (a.length ? a[0] : 0) +
(b.length ? b[0] : 0) + c];
const res = add_(a[1 .. $], b[1 .. $], dc[1]);
// Trim leading zeros.
if (res.length || dc[0] != Dig.Z)
return [dc[0]] ~ res;
else
return res;
}
}
BalancedTernary opBinary(string op:"+")(in BalancedTernary b)
const pure nothrow {
return BalancedTernary(add_(this.digits, b.digits));
}
BalancedTernary opBinary(string op:"-")(in BalancedTernary b)
const pure nothrow {
return this + (-b);
}
static const(Dig)[] mul_(in Dig[] a, in Dig[] b) pure nothrow {
if (a.empty || b.empty) {
return [];
} else {
const y = Dig.Z ~ mul_(a[1 .. $], b);
final switch (a[0]) {
case Dig.N: return add_(neg_(b), y);
case Dig.Z: return add_([], y);
case Dig.P: return add_(b, y);
}
}
}
BalancedTernary opBinary(string op:"*")(in BalancedTernary b)
const pure nothrow {
return BalancedTernary(mul_(this.digits, b.digits));
}
}
void main() {
immutable a = BalancedTernary("+-0++0+");
writeln("a: ", a.toBint, ' ', a);
immutable b = BalancedTernary(-436);
writeln("b: ", b.toBint, ' ', b);
immutable c = BalancedTernary("+-++-");
writeln("c: ", c.toBint, ' ', c);
const /*immutable*/ r = a * (b - c);
writeln("a * (b - c): ", r.toBint, ' ', r);
} |
http://rosettacode.org/wiki/Babbage_problem | Babbage problem |
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.
For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].
Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.
| #M2000_Interpreter | M2000 Interpreter | Def Long k=1000000, T=269696, n
n=Sqrt(269696)
For n=n to k {
If n^2 mod k = T Then Exit
}
Report format$("The smallest number whose square ends in {0} is {1}, Its square is {2}", T, n, n**2)
|
http://rosettacode.org/wiki/Babbage_problem | Babbage problem |
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.
For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].
Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.
| #Mathematica.2FWolfram_Language | Mathematica/Wolfram Language | Solve[Mod[x^2, 10^6] == 269696 && 0 <= x <= 99736, x, Integers] |
http://rosettacode.org/wiki/Balanced_brackets | Balanced brackets | Task:
Generate a string with N opening brackets [ and with N closing brackets ], in some arbitrary order.
Determine whether the generated string is balanced; that is, whether it consists entirely of pairs of opening/closing brackets (in that order), none of which mis-nest.
Examples
(empty) OK
[] OK
[][] OK
[[][]] OK
][ NOT OK
][][ NOT OK
[]][[] NOT OK
| #Arturo | Arturo | isBalanced: function [s][
cnt: 0
loop split s [ch][
if? ch="]" [
cnt: cnt-1
if cnt<0 -> return false
]
else [
if ch="[" -> cnt: cnt+1
]
]
cnt=0
]
loop 1..10 'i [
str: join map 0..(2*i)-1 [x][ sample ["[" "]"]]
prints str
if? isBalanced str -> print " OK"
else -> print " Not OK"
] |
http://rosettacode.org/wiki/Averages/Mode | Averages/Mode | Task[edit]
Write a program to find the mode value of a collection.
The case where the collection is empty may be ignored. Care must be taken to handle the case where the mode is non-unique.
If it is not appropriate or possible to support a general collection, use a vector (array), if possible. If it is not appropriate or possible to support an unspecified value type, use integers.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #EchoLisp | EchoLisp |
(define (modes L)
(define G (group* L)) ;; sorts and group equal items
(define cardmax (for/max [(g G)] (length g)))
(map first (filter (lambda(g) (= cardmax (length g))) G)))
(modes '( a b c a d e f))
→ (a)
(modes (iota 6))
→ (0 1 2 3 4 5)
(modes '(x))
→ (x)
(modes '(🎾 🏉 ☕️ 🎾 🎲 🎯 🎺 ☕️ 🎲 🎸 🎻 🏆 ☕️ 🏁 🎾 🎲 🎻 🏉 ))
→ (🎾 ☕️ 🎲)
(modes '())
😖️ error: group : expected list : null 🔎 'modes'
|
http://rosettacode.org/wiki/Averages/Simple_moving_average | Averages/Simple moving average | Computing the simple moving average of a series of numbers.
Task[edit]
Create a stateful function/class/instance that takes a period and returns a routine that takes a number as argument and returns a simple moving average of its arguments so far.
Description
A simple moving average is a method for computing an average of a stream of numbers by only averaging the last P numbers from the stream, where P is known as the period.
It can be implemented by calling an initialing routine with P as its argument, I(P), which should then return a routine that when called with individual, successive members of a stream of numbers, computes the mean of (up to), the last P of them, lets call this SMA().
The word stateful in the task description refers to the need for SMA() to remember certain information between calls to it:
The period, P
An ordered container of at least the last P numbers from each of its individual calls.
Stateful also means that successive calls to I(), the initializer, should return separate routines that do not share saved state so they could be used on two independent streams of data.
Pseudo-code for an implementation of SMA is:
function SMA(number: N):
stateful integer: P
stateful list: stream
number: average
stream.append_last(N)
if stream.length() > P:
# Only average the last P elements of the stream
stream.delete_first()
if stream.length() == 0:
average = 0
else:
average = sum( stream.values() ) / stream.length()
return average
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #ooRexx | ooRexx |
testdata = .array~of(1, 2, 3, 4, 5, 5, 4, 3, 2, 1)
-- run with different period sizes
loop period over .array~of(3, 5)
say "Period size =" period
say
movingaverage = .movingaverage~new(period)
loop number over testdata
average = movingaverage~addnumber(number)
say " Next number =" number", moving average =" average
end
say
end
::class movingaverage
::method init
expose period queue sum
use strict arg period
sum = 0
-- the circular queue makes this easy
queue = .circularqueue~new(period)
-- add a number to the average set
::method addNumber
expose queue sum
use strict arg number
sum += number
-- add this to the queue
old = queue~queue(number)
-- if we pushed an element off the end of the queue,
-- subtract this from our sum
if old \= .nil then sum -= old
-- and return the current item
return sum / queue~items
-- extra method to retrieve current average
::method average
expose queue sum
-- undefined really, but just return 0
if queue~isempty then return 0
-- return current queue
return sum / queue~items
|
http://rosettacode.org/wiki/Averages/Mean_time_of_day | Averages/Mean time of day | Task[edit]
A particular activity of bats occurs at these times of the day:
23:00:17, 23:40:20, 00:12:45, 00:17:19
Using the idea that there are twenty-four hours in a day,
which is analogous to there being 360 degrees in a circle,
map times of day to and from angles;
and using the ideas of Averages/Mean angle
compute and show the average time of the nocturnal activity
to an accuracy of one second of time.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Common_Lisp | Common Lisp | ;; * Loading the split-sequence library
(eval-when (:compile-toplevel :load-toplevel :execute)
(ql:quickload '("split-sequence")))
;; * The package definition
(defpackage :mean-time-of-day
(:use :common-lisp :iterate :split-sequence))
(in-package :mean-time-of-day)
;; * The data
(defparameter *time-values*
'("23:00:17" "23:40:20" "00:12:45" "00:17:19"))
(defun time->radian (time)
"Returns the radian value for TIME given as a STRING like HH:MM:SS. Assuming a
valid input value."
(destructuring-bind (h m s)
(mapcar #'parse-integer (split-sequence #\: time))
(+ (* h (/ PI 12)) (* m (/ PI 12 60)) (* s (/ PI 12 3600)))))
(defun radian->time (radian)
"Returns the corresponding time as a string like HH:MM:SS for RADIAN."
(let* ((time (if (plusp radian)
(round (/ (* 12 3600 radian) PI))
(round (/ (* 12 3600 (+ radian (* 2 PI))) PI))))
(h (floor time 3600))
(m (floor (- time (* h 3600)) 60))
(s (- time (* h 3600) (* m 60))))
(format nil "~2,'0D:~2,'0D:~2,'0D" h m s)))
(defun make-polar (rho theta)
"Returns a complex representing the polar coordinates."
(complex (* rho (cos theta)) (* rho (sin theta))))
(defun mean-time (times)
"Returns the mean time value within 24h of the list of TIMES given as strings
HH:MM:SS."
(radian->time (phase
(reduce #'+ (mapcar (lambda (time)
(make-polar 1 (time->radian time))) times)))))
|
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