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http://rosettacode.org/wiki/Empty_program | Empty program | Task
Create the simplest possible program that is still considered "correct."
| #ALGOL_W | ALGOL W | . |
http://rosettacode.org/wiki/Enforced_immutability | Enforced immutability | Task
Demonstrate any means your language has to prevent the modification of values, or to create objects that cannot be modified after they have been created.
| #Pascal | Pascal | use constant PI => 3.14159;
use constant MSG => "Hello World"; |
http://rosettacode.org/wiki/Enforced_immutability | Enforced immutability | Task
Demonstrate any means your language has to prevent the modification of values, or to create objects that cannot be modified after they have been created.
| #Perl | Perl | use constant PI => 3.14159;
use constant MSG => "Hello World"; |
http://rosettacode.org/wiki/Enforced_immutability | Enforced immutability | Task
Demonstrate any means your language has to prevent the modification of values, or to create objects that cannot be modified after they have been created.
| #Phix | Phix | with javascript_semantics
constant n = 1
constant s = {1,2,3}
constant str = "immutable string"
|
http://rosettacode.org/wiki/Enforced_immutability | Enforced immutability | Task
Demonstrate any means your language has to prevent the modification of values, or to create objects that cannot be modified after they have been created.
| #PHP | PHP | define("PI", 3.14159265358);
define("MSG", "Hello World"); |
http://rosettacode.org/wiki/Entropy | Entropy | Task
Calculate the Shannon entropy H of a given input string.
Given the discrete random variable
X
{\displaystyle X}
that is a string of
N
{\displaystyle N}
"symbols" (total characters) consisting of
n
{\displaystyle n}
different characters (n=2 for binary), the Shannon entropy of X in bits/symbol is :
H
2
(
X
)
=
−
∑
i
=
1
n
c
o
u
n
t
i
N
log
2
(
c
o
u
n
t
i
N
)
{\displaystyle H_{2}(X)=-\sum _{i=1}^{n}{\frac {count_{i}}{N}}\log _{2}\left({\frac {count_{i}}{N}}\right)}
where
c
o
u
n
t
i
{\displaystyle count_{i}}
is the count of character
n
i
{\displaystyle n_{i}}
.
For this task, use X="1223334444" as an example. The result should be 1.84644... bits/symbol. This assumes X was a random variable, which may not be the case, or it may depend on the observer.
This coding problem calculates the "specific" or "intensive" entropy that finds its parallel in physics with "specific entropy" S0 which is entropy per kg or per mole, not like physical entropy S and therefore not the "information" content of a file. It comes from Boltzmann's H-theorem where
S
=
k
B
N
H
{\displaystyle S=k_{B}NH}
where N=number of molecules. Boltzmann's H is the same equation as Shannon's H, and it gives the specific entropy H on a "per molecule" basis.
The "total", "absolute", or "extensive" information entropy is
S
=
H
2
N
{\displaystyle S=H_{2}N}
bits
This is not the entropy being coded here, but it is the closest to physical entropy and a measure of the information content of a string. But it does not look for any patterns that might be available for compression, so it is a very restricted, basic, and certain measure of "information". Every binary file with an equal number of 1's and 0's will have S=N bits. All hex files with equal symbol frequencies will have
S
=
N
log
2
(
16
)
{\displaystyle S=N\log _{2}(16)}
bits of entropy. The total entropy in bits of the example above is S= 10*18.4644 = 18.4644 bits.
The H function does not look for any patterns in data or check if X was a random variable. For example, X=000000111111 gives the same calculated entropy in all senses as Y=010011100101. For most purposes it is usually more relevant to divide the gzip length by the length of the original data to get an informal measure of how much "order" was in the data.
Two other "entropies" are useful:
Normalized specific entropy:
H
n
=
H
2
∗
log
(
2
)
log
(
n
)
{\displaystyle H_{n}={\frac {H_{2}*\log(2)}{\log(n)}}}
which varies from 0 to 1 and it has units of "entropy/symbol" or just 1/symbol. For this example, Hn<\sub>= 0.923.
Normalized total (extensive) entropy:
S
n
=
H
2
N
∗
log
(
2
)
log
(
n
)
{\displaystyle S_{n}={\frac {H_{2}N*\log(2)}{\log(n)}}}
which varies from 0 to N and does not have units. It is simply the "entropy", but it needs to be called "total normalized extensive entropy" so that it is not confused with Shannon's (specific) entropy or physical entropy. For this example, Sn<\sub>= 9.23.
Shannon himself is the reason his "entropy/symbol" H function is very confusingly called "entropy". That's like calling a function that returns a speed a "meter". See section 1.7 of his classic A Mathematical Theory of Communication and search on "per symbol" and "units" to see he always stated his entropy H has units of "bits/symbol" or "entropy/symbol" or "information/symbol". So it is legitimate to say entropy NH is "information".
In keeping with Landauer's limit, the physics entropy generated from erasing N bits is
S
=
H
2
N
k
B
ln
(
2
)
{\displaystyle S=H_{2}Nk_{B}\ln(2)}
if the bit storage device is perfectly efficient. This can be solved for H2*N to (arguably) get the number of bits of information that a physical entropy represents.
Related tasks
Fibonacci_word
Entropy/Narcissist
| #Clojure | Clojure | (defn entropy [s]
(let [len (count s), log-2 (Math/log 2)]
(->> (frequencies s)
(map (fn [[_ v]]
(let [rf (/ v len)]
(-> (Math/log rf) (/ log-2) (* rf) Math/abs))))
(reduce +)))) |
http://rosettacode.org/wiki/Ethiopian_multiplication | Ethiopian multiplication | Ethiopian multiplication is a method of multiplying integers using only addition, doubling, and halving.
Method:
Take two numbers to be multiplied and write them down at the top of two columns.
In the left-hand column repeatedly halve the last number, discarding any remainders, and write the result below the last in the same column, until you write a value of 1.
In the right-hand column repeatedly double the last number and write the result below. stop when you add a result in the same row as where the left hand column shows 1.
Examine the table produced and discard any row where the value in the left column is even.
Sum the values in the right-hand column that remain to produce the result of multiplying the original two numbers together
For example: 17 × 34
17 34
Halving the first column:
17 34
8
4
2
1
Doubling the second column:
17 34
8 68
4 136
2 272
1 544
Strike-out rows whose first cell is even:
17 34
8 68
4 136
2 272
1 544
Sum the remaining numbers in the right-hand column:
17 34
8 --
4 ---
2 ---
1 544
====
578
So 17 multiplied by 34, by the Ethiopian method is 578.
Task
The task is to define three named functions/methods/procedures/subroutines:
one to halve an integer,
one to double an integer, and
one to state if an integer is even.
Use these functions to create a function that does Ethiopian multiplication.
References
Ethiopian multiplication explained (BBC Video clip)
A Night Of Numbers - Go Forth And Multiply (Video)
Russian Peasant Multiplication
Programming Praxis: Russian Peasant Multiplication
| #Clojure | Clojure | (defn halve [n]
(bit-shift-right n 1))
(defn twice [n] ; 'double' is taken
(bit-shift-left n 1))
(defn even [n] ; 'even?' is the standard fn
(zero? (bit-and n 1)))
(defn emult [x y]
(reduce +
(map second
(filter #(not (even (first %))) ; a.k.a. 'odd?'
(take-while #(pos? (first %))
(map vector
(iterate halve x)
(iterate twice y)))))))
(defn emult2 [x y]
(loop [a x, b y, r 0]
(if (= a 1)
(+ r b)
(if (even a)
(recur (halve a) (twice b) r)
(recur (halve a) (twice b) (+ r b)))))) |
http://rosettacode.org/wiki/Equilibrium_index | Equilibrium index | An equilibrium index of a sequence is an index into the sequence such that the sum of elements at lower indices is equal to the sum of elements at higher indices.
For example, in a sequence
A
{\displaystyle A}
:
A
0
=
−
7
{\displaystyle A_{0}=-7}
A
1
=
1
{\displaystyle A_{1}=1}
A
2
=
5
{\displaystyle A_{2}=5}
A
3
=
2
{\displaystyle A_{3}=2}
A
4
=
−
4
{\displaystyle A_{4}=-4}
A
5
=
3
{\displaystyle A_{5}=3}
A
6
=
0
{\displaystyle A_{6}=0}
3 is an equilibrium index, because:
A
0
+
A
1
+
A
2
=
A
4
+
A
5
+
A
6
{\displaystyle A_{0}+A_{1}+A_{2}=A_{4}+A_{5}+A_{6}}
6 is also an equilibrium index, because:
A
0
+
A
1
+
A
2
+
A
3
+
A
4
+
A
5
=
0
{\displaystyle A_{0}+A_{1}+A_{2}+A_{3}+A_{4}+A_{5}=0}
(sum of zero elements is zero)
7 is not an equilibrium index, because it is not a valid index of sequence
A
{\displaystyle A}
.
Task;
Write a function that, given a sequence, returns its equilibrium indices (if any).
Assume that the sequence may be very long.
| #Icon_and_Unicon | Icon and Unicon | procedure main(arglist)
L := if *arglist > 0 then arglist else [-7, 1, 5, 2, -4, 3, 0] # command line args or default
every writes( "equilibrium indicies of [ " | (!L ||" ") | "] = " | (eqindex(L)||" ") | "\n" )
end
procedure eqindex(L) # generate equilibrium points in a list L or fail
local s,l,i
every (s := 0, i := !L) do
s +:= numeric(i) | fail # sum and validate
every (l := 0, i := 1 to *L) do {
if l = (s-L[i])/2 then suspend i
l +:= L[i] # sum of left side
}
end |
http://rosettacode.org/wiki/Environment_variables | Environment variables | Task
Show how to get one of your process's environment variables.
The available variables vary by system; some of the common ones available on Unix include:
PATH
HOME
USER
| #Maple | Maple | getenv("PATH"); |
http://rosettacode.org/wiki/Environment_variables | Environment variables | Task
Show how to get one of your process's environment variables.
The available variables vary by system; some of the common ones available on Unix include:
PATH
HOME
USER
| #Mathematica_.2F_Wolfram_Language | Mathematica / Wolfram Language | Environment["PATH"] |
http://rosettacode.org/wiki/Environment_variables | Environment variables | Task
Show how to get one of your process's environment variables.
The available variables vary by system; some of the common ones available on Unix include:
PATH
HOME
USER
| #MATLAB_.2F_Octave | MATLAB / Octave | getenv('HOME')
getenv('PATH')
getenv('USER') |
http://rosettacode.org/wiki/Environment_variables | Environment variables | Task
Show how to get one of your process's environment variables.
The available variables vary by system; some of the common ones available on Unix include:
PATH
HOME
USER
| #Mercury | Mercury | :- module env_var.
:- interface.
:- import_module io.
:- pred main(io::di, io::uo) is det.
:- implementation.
:- import_module maybe, string.
main(!IO) :-
io.get_environment_var("HOME", MaybeValue, !IO),
(
MaybeValue = yes(Value),
io.write_string("HOME is " ++ Value ++ "\n", !IO)
;
MaybeValue = no,
io.write_string("environment variable HOME not set\n", !IO)
). |
http://rosettacode.org/wiki/Esthetic_numbers | Esthetic numbers | An esthetic number is a positive integer where every adjacent digit differs from its neighbour by 1.
E.G.
12 is an esthetic number. One and two differ by 1.
5654 is an esthetic number. Each digit is exactly 1 away from its neighbour.
890 is not an esthetic number. Nine and zero differ by 9.
These examples are nominally in base 10 but the concept extends easily to numbers in other bases. Traditionally, single digit numbers are included in esthetic numbers; zero may or may not be. For our purposes, for this task, do not include zero (0) as an esthetic number. Do not include numbers with leading zeros.
Esthetic numbers are also sometimes referred to as stepping numbers.
Task
Write a routine (function, procedure, whatever) to find esthetic numbers in a given base.
Use that routine to find esthetic numbers in bases 2 through 16 and display, here on this page, the esthectic numbers from index (base × 4) through index (base × 6), inclusive. (E.G. for base 2: 8th through 12th, for base 6: 24th through 36th, etc.)
Find and display, here on this page, the base 10 esthetic numbers with a magnitude between 1000 and 9999.
Stretch: Find and display, here on this page, the base 10 esthetic numbers with a magnitude between 1.0e8 and 1.3e8.
Related task
numbers with equal rises and falls
See also
OEIS A033075 - Positive numbers n such that all pairs of consecutive decimal digits differ by 1
Numbers Aplenty - Esthetic numbers
Geeks for Geeks - Stepping numbers
| #Sidef | Sidef | func generate_esthetic(root, upto, callback, b=10) {
var v = root.digits2num(b)
return nil if (v > upto)
callback(v)
var t = root.head
__FUNC__([t+1, root...], upto, callback, b) if (t+1 < b)
__FUNC__([t-1, root...], upto, callback, b) if (t-1 >= 0)
}
func between_esthetic(from, upto, b=10) {
gather {
for k in (1..^b) {
generate_esthetic([k], upto, { take(_) if (_ >= from) }, b)
}
}.sort
}
func first_n_esthetic(n, b=10) {
for (var m = n**2; true ; m *= b) {
var list = between_esthetic(1, m, b)
return list.first(n) if (list.len >= n)
}
}
for b in (2..16) {
say "\n#{b}-esthetic numbers with indices #{4*b}..#{6*b}: "
say first_n_esthetic(6*b, b).last(6*b - 4*b + 1).map{.base(b)}.join(' ')
}
say "\nBase 10 esthetic numbers between 1,000 and 9,999:"
between_esthetic(1e3, 1e4).slices(20).each { .join(' ').say }
say "\nBase 10 esthetic numbers between 100,000,000 and 130,000,000:"
between_esthetic(1e8, 13e7).slices(9).each { .join(' ').say } |
http://rosettacode.org/wiki/Euler%27s_sum_of_powers_conjecture | Euler's sum of powers conjecture | There is a conjecture in mathematics that held for over two hundred years before it was disproved by the finding of a counterexample in 1966 by Lander and Parkin.
Euler's (disproved) sum of powers conjecture
At least k positive kth powers are required to sum to a kth power,
except for the trivial case of one kth power: yk = yk
In 1966, Leon J. Lander and Thomas R. Parkin used a brute-force search on a CDC 6600 computer restricting numbers to those less than 250.
Task
Write a program to search for an integer solution for:
x05 + x15 + x25 + x35 == y5
Where all xi's and y are distinct integers between 0 and 250 (exclusive).
Show an answer here.
Related tasks
Pythagorean quadruples.
Pythagorean triples.
| #FreeBASIC | FreeBASIC | ' version 14-09-2015
' compile with: fbc -s console
' some constants calculated when the program is compiled
Const As UInteger max = 250
Const As ULongInt pow5_max = CULngInt(max) * max * max * max * max
' limit x1, x2, x3
Const As UInteger limit_x1 = (pow5_max / 4) ^ 0.2
Const As UInteger limit_x2 = (pow5_max / 3) ^ 0.2
Const As UInteger limit_x3 = (pow5_max / 2) ^ 0.2
' ------=< MAIN >=------
Dim As ULongInt pow5(max), ans1, ans2, ans3
Dim As UInteger x1, x2, x3, x4, x5 , m1, m2
Cls : Print
For x1 = 1 To max
pow5(x1) = CULngInt(x1) * x1 * x1 * x1 * x1
Next x1
For x1 = 1 To limit_x1
For x2 = x1 +1 To limit_x2
m1 = x1 + x2
ans1 = pow5(x1) + pow5(x2)
If ans1 > pow5_max Then Exit For
For x3 = x2 +1 To limit_x3
ans2 = ans1 + pow5(x3)
If ans2 > pow5_max Then Exit For
m2 = (m1 + x3) Mod 30
If m2 = 0 Then m2 = 30
For x4 = x3 +1 To max -1
ans3 = ans2 + pow5(x4)
If ans3 > pow5_max Then Exit For
For x5 = x4 + m2 To max Step 30
If ans3 < pow5(x5) Then Exit For
If ans3 = pow5(x5) Then
Print x1; "^5 + "; x2; "^5 + "; x3; "^5 + "; _
x4; "^5 = "; x5; "^5"
Exit For, For
EndIf
Next x5
Next x4
Next x3
Next x2
Next x1
Print
Print "done"
' empty keyboard buffer
While Inkey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End |
http://rosettacode.org/wiki/Factorial | Factorial | Definitions
The factorial of 0 (zero) is defined as being 1 (unity).
The Factorial Function of a positive integer, n, is defined as the product of the sequence:
n, n-1, n-2, ... 1
Task
Write a function to return the factorial of a number.
Solutions can be iterative or recursive.
Support for trapping negative n errors is optional.
Related task
Primorial numbers
| #Nim | Nim |
import math
let i:int = fac(x)
|
http://rosettacode.org/wiki/Even_or_odd | Even or odd | Task
Test whether an integer is even or odd.
There is more than one way to solve this task:
Use the even and odd predicates, if the language provides them.
Check the least significant digit. With binary integers, i bitwise-and 1 equals 0 iff i is even, or equals 1 iff i is odd.
Divide i by 2. The remainder equals 0 iff i is even. The remainder equals +1 or -1 iff i is odd.
Use modular congruences:
i ≡ 0 (mod 2) iff i is even.
i ≡ 1 (mod 2) iff i is odd.
| #Clojure | Clojure | (if (even? some-var) (do-even-stuff))
(if (odd? some-var) (do-odd-stuff)) |
http://rosettacode.org/wiki/Euler_method | Euler method | Euler's method numerically approximates solutions of first-order ordinary differential equations (ODEs) with a given initial value. It is an explicit method for solving initial value problems (IVPs), as described in the wikipedia page.
The ODE has to be provided in the following form:
d
y
(
t
)
d
t
=
f
(
t
,
y
(
t
)
)
{\displaystyle {\frac {dy(t)}{dt}}=f(t,y(t))}
with an initial value
y
(
t
0
)
=
y
0
{\displaystyle y(t_{0})=y_{0}}
To get a numeric solution, we replace the derivative on the LHS with a finite difference approximation:
d
y
(
t
)
d
t
≈
y
(
t
+
h
)
−
y
(
t
)
h
{\displaystyle {\frac {dy(t)}{dt}}\approx {\frac {y(t+h)-y(t)}{h}}}
then solve for
y
(
t
+
h
)
{\displaystyle y(t+h)}
:
y
(
t
+
h
)
≈
y
(
t
)
+
h
d
y
(
t
)
d
t
{\displaystyle y(t+h)\approx y(t)+h\,{\frac {dy(t)}{dt}}}
which is the same as
y
(
t
+
h
)
≈
y
(
t
)
+
h
f
(
t
,
y
(
t
)
)
{\displaystyle y(t+h)\approx y(t)+h\,f(t,y(t))}
The iterative solution rule is then:
y
n
+
1
=
y
n
+
h
f
(
t
n
,
y
n
)
{\displaystyle y_{n+1}=y_{n}+h\,f(t_{n},y_{n})}
where
h
{\displaystyle h}
is the step size, the most relevant parameter for accuracy of the solution. A smaller step size increases accuracy but also the computation cost, so it has always has to be hand-picked according to the problem at hand.
Example: Newton's Cooling Law
Newton's cooling law describes how an object of initial temperature
T
(
t
0
)
=
T
0
{\displaystyle T(t_{0})=T_{0}}
cools down in an environment of temperature
T
R
{\displaystyle T_{R}}
:
d
T
(
t
)
d
t
=
−
k
Δ
T
{\displaystyle {\frac {dT(t)}{dt}}=-k\,\Delta T}
or
d
T
(
t
)
d
t
=
−
k
(
T
(
t
)
−
T
R
)
{\displaystyle {\frac {dT(t)}{dt}}=-k\,(T(t)-T_{R})}
It says that the cooling rate
d
T
(
t
)
d
t
{\displaystyle {\frac {dT(t)}{dt}}}
of the object is proportional to the current temperature difference
Δ
T
=
(
T
(
t
)
−
T
R
)
{\displaystyle \Delta T=(T(t)-T_{R})}
to the surrounding environment.
The analytical solution, which we will compare to the numerical approximation, is
T
(
t
)
=
T
R
+
(
T
0
−
T
R
)
e
−
k
t
{\displaystyle T(t)=T_{R}+(T_{0}-T_{R})\;e^{-kt}}
Task
Implement a routine of Euler's method and then to use it to solve the given example of Newton's cooling law with it for three different step sizes of:
2 s
5 s and
10 s
and to compare with the analytical solution.
Initial values
initial temperature
T
0
{\displaystyle T_{0}}
shall be 100 °C
room temperature
T
R
{\displaystyle T_{R}}
shall be 20 °C
cooling constant
k
{\displaystyle k}
shall be 0.07
time interval to calculate shall be from 0 s ──► 100 s
A reference solution (Common Lisp) can be seen below. We see that bigger step sizes lead to reduced approximation accuracy.
| #Ring | Ring |
decimals(3)
see euler("return -0.07*(y-20)", 100, 0, 100, 2) + nl
see euler("return -0.07*(y-20)", 100, 0, 100, 5) + nl
see euler("return -0.07*(y-20)", 100, 0, 100, 10) + nl
func euler df, y, a, b, s
t = a
while t <= b
see "" + t + " " + y + nl
y += s * eval(df)
t += s
end
return y |
http://rosettacode.org/wiki/Euler_method | Euler method | Euler's method numerically approximates solutions of first-order ordinary differential equations (ODEs) with a given initial value. It is an explicit method for solving initial value problems (IVPs), as described in the wikipedia page.
The ODE has to be provided in the following form:
d
y
(
t
)
d
t
=
f
(
t
,
y
(
t
)
)
{\displaystyle {\frac {dy(t)}{dt}}=f(t,y(t))}
with an initial value
y
(
t
0
)
=
y
0
{\displaystyle y(t_{0})=y_{0}}
To get a numeric solution, we replace the derivative on the LHS with a finite difference approximation:
d
y
(
t
)
d
t
≈
y
(
t
+
h
)
−
y
(
t
)
h
{\displaystyle {\frac {dy(t)}{dt}}\approx {\frac {y(t+h)-y(t)}{h}}}
then solve for
y
(
t
+
h
)
{\displaystyle y(t+h)}
:
y
(
t
+
h
)
≈
y
(
t
)
+
h
d
y
(
t
)
d
t
{\displaystyle y(t+h)\approx y(t)+h\,{\frac {dy(t)}{dt}}}
which is the same as
y
(
t
+
h
)
≈
y
(
t
)
+
h
f
(
t
,
y
(
t
)
)
{\displaystyle y(t+h)\approx y(t)+h\,f(t,y(t))}
The iterative solution rule is then:
y
n
+
1
=
y
n
+
h
f
(
t
n
,
y
n
)
{\displaystyle y_{n+1}=y_{n}+h\,f(t_{n},y_{n})}
where
h
{\displaystyle h}
is the step size, the most relevant parameter for accuracy of the solution. A smaller step size increases accuracy but also the computation cost, so it has always has to be hand-picked according to the problem at hand.
Example: Newton's Cooling Law
Newton's cooling law describes how an object of initial temperature
T
(
t
0
)
=
T
0
{\displaystyle T(t_{0})=T_{0}}
cools down in an environment of temperature
T
R
{\displaystyle T_{R}}
:
d
T
(
t
)
d
t
=
−
k
Δ
T
{\displaystyle {\frac {dT(t)}{dt}}=-k\,\Delta T}
or
d
T
(
t
)
d
t
=
−
k
(
T
(
t
)
−
T
R
)
{\displaystyle {\frac {dT(t)}{dt}}=-k\,(T(t)-T_{R})}
It says that the cooling rate
d
T
(
t
)
d
t
{\displaystyle {\frac {dT(t)}{dt}}}
of the object is proportional to the current temperature difference
Δ
T
=
(
T
(
t
)
−
T
R
)
{\displaystyle \Delta T=(T(t)-T_{R})}
to the surrounding environment.
The analytical solution, which we will compare to the numerical approximation, is
T
(
t
)
=
T
R
+
(
T
0
−
T
R
)
e
−
k
t
{\displaystyle T(t)=T_{R}+(T_{0}-T_{R})\;e^{-kt}}
Task
Implement a routine of Euler's method and then to use it to solve the given example of Newton's cooling law with it for three different step sizes of:
2 s
5 s and
10 s
and to compare with the analytical solution.
Initial values
initial temperature
T
0
{\displaystyle T_{0}}
shall be 100 °C
room temperature
T
R
{\displaystyle T_{R}}
shall be 20 °C
cooling constant
k
{\displaystyle k}
shall be 0.07
time interval to calculate shall be from 0 s ──► 100 s
A reference solution (Common Lisp) can be seen below. We see that bigger step sizes lead to reduced approximation accuracy.
| #Ruby | Ruby | def euler(y, a, b, h)
a.step(b,h) do |t|
puts "%7.3f %7.3f" % [t,y]
y += h * yield(t,y)
end
end
[10, 5, 2].each do |step|
puts "Step = #{step}"
euler(100,0,100,step) {|time, temp| -0.07 * (temp - 20) }
puts
end |
http://rosettacode.org/wiki/Evaluate_binomial_coefficients | Evaluate binomial coefficients | This programming task, is to calculate ANY binomial coefficient.
However, it has to be able to output
(
5
3
)
{\displaystyle {\binom {5}{3}}}
, which is 10.
This formula is recommended:
(
n
k
)
=
n
!
(
n
−
k
)
!
k
!
=
n
(
n
−
1
)
(
n
−
2
)
…
(
n
−
k
+
1
)
k
(
k
−
1
)
(
k
−
2
)
…
1
{\displaystyle {\binom {n}{k}}={\frac {n!}{(n-k)!k!}}={\frac {n(n-1)(n-2)\ldots (n-k+1)}{k(k-1)(k-2)\ldots 1}}}
See Also:
Combinations and permutations
Pascal's triangle
The number of samples of size k from n objects.
With combinations and permutations generation tasks.
Order Unimportant
Order Important
Without replacement
(
n
k
)
=
n
C
k
=
n
(
n
−
1
)
…
(
n
−
k
+
1
)
k
(
k
−
1
)
…
1
{\displaystyle {\binom {n}{k}}=^{n}\operatorname {C} _{k}={\frac {n(n-1)\ldots (n-k+1)}{k(k-1)\dots 1}}}
n
P
k
=
n
⋅
(
n
−
1
)
⋅
(
n
−
2
)
⋯
(
n
−
k
+
1
)
{\displaystyle ^{n}\operatorname {P} _{k}=n\cdot (n-1)\cdot (n-2)\cdots (n-k+1)}
Task: Combinations
Task: Permutations
With replacement
(
n
+
k
−
1
k
)
=
n
+
k
−
1
C
k
=
(
n
+
k
−
1
)
!
(
n
−
1
)
!
k
!
{\displaystyle {\binom {n+k-1}{k}}=^{n+k-1}\operatorname {C} _{k}={(n+k-1)! \over (n-1)!k!}}
n
k
{\displaystyle n^{k}}
Task: Combinations with repetitions
Task: Permutations with repetitions
| #Julia | Julia | @show binomial(5, 3) |
http://rosettacode.org/wiki/Evaluate_binomial_coefficients | Evaluate binomial coefficients | This programming task, is to calculate ANY binomial coefficient.
However, it has to be able to output
(
5
3
)
{\displaystyle {\binom {5}{3}}}
, which is 10.
This formula is recommended:
(
n
k
)
=
n
!
(
n
−
k
)
!
k
!
=
n
(
n
−
1
)
(
n
−
2
)
…
(
n
−
k
+
1
)
k
(
k
−
1
)
(
k
−
2
)
…
1
{\displaystyle {\binom {n}{k}}={\frac {n!}{(n-k)!k!}}={\frac {n(n-1)(n-2)\ldots (n-k+1)}{k(k-1)(k-2)\ldots 1}}}
See Also:
Combinations and permutations
Pascal's triangle
The number of samples of size k from n objects.
With combinations and permutations generation tasks.
Order Unimportant
Order Important
Without replacement
(
n
k
)
=
n
C
k
=
n
(
n
−
1
)
…
(
n
−
k
+
1
)
k
(
k
−
1
)
…
1
{\displaystyle {\binom {n}{k}}=^{n}\operatorname {C} _{k}={\frac {n(n-1)\ldots (n-k+1)}{k(k-1)\dots 1}}}
n
P
k
=
n
⋅
(
n
−
1
)
⋅
(
n
−
2
)
⋯
(
n
−
k
+
1
)
{\displaystyle ^{n}\operatorname {P} _{k}=n\cdot (n-1)\cdot (n-2)\cdots (n-k+1)}
Task: Combinations
Task: Permutations
With replacement
(
n
+
k
−
1
k
)
=
n
+
k
−
1
C
k
=
(
n
+
k
−
1
)
!
(
n
−
1
)
!
k
!
{\displaystyle {\binom {n+k-1}{k}}=^{n+k-1}\operatorname {C} _{k}={(n+k-1)! \over (n-1)!k!}}
n
k
{\displaystyle n^{k}}
Task: Combinations with repetitions
Task: Permutations with repetitions
| #K | K | {[n;k]_(*/(k-1)_1+!n)%(*/1+!k)} . 5 3
10 |
http://rosettacode.org/wiki/Emirp_primes | Emirp primes | An emirp (prime spelled backwards) are primes that when reversed (in their decimal representation) are a different prime.
(This rules out palindromic primes.)
Task
show the first twenty emirps
show all emirps between 7,700 and 8,000
show the 10,000th emirp
In each list, the numbers should be in order.
Invoke the (same) program once per task requirement, this will show what limit is used as the upper bound for calculating surplus (regular) primes.
The specific method of how to determine if a range or if specific values are to be shown will be left to the programmer.
See also
Wikipedia, Emirp.
The Prime Pages, emirp.
Wolfram MathWorld™, Emirp.
The On‑Line Encyclopedia of Integer Sequences, emirps (A6567).
| #AWK | AWK |
function is_prime(n, p)
{
if (!(n%2) || !(n%3)) {
return 0 }
p = 1
while(p*p < n)
if (n%(p += 4) == 0 || n%(p += 2) == 0) {
return 0 }
return 1
}
function reverse(n, r)
{
r = 0
for (r = 0; int(n) != 0; n /= 10)
r = r*10 + int(n%10);
return r
}
function is_emirp(n, r)
{
r = reverse(n)
return ((r != n) && is_prime(n) && is_prime(r)) ? 1 : 0
}
BEGIN {
c = 0
for (x = 11; c < 20; x += 2) {
if (is_emirp(x)) {
printf(" %i,", x); ++c }
}
printf("\n")
for (x = 7701; x < 8000; x += 2) {
if (is_emirp(x)) {
printf(" %i,", x); ++c }
}
printf("\n")
c = 0
for (x = 11; ; x += 2)
if (is_emirp(x) && ++c == 10000) {
printf(" %i", x);
break;
}
printf("\n")
}
|
http://rosettacode.org/wiki/Elliptic_curve_arithmetic | Elliptic curve arithmetic | Elliptic curves are sometimes used in cryptography as a way to perform digital signatures.
The purpose of this task is to implement a simplified (without modular arithmetic) version of the elliptic curve arithmetic which is required by the elliptic curve DSA protocol.
In a nutshell, an elliptic curve is a bi-dimensional curve defined by the following relation between the x and y coordinates of any point on the curve:
y
2
=
x
3
+
a
x
+
b
{\displaystyle y^{2}=x^{3}+ax+b}
a and b are arbitrary parameters that define the specific curve which is used.
For this particular task, we'll use the following parameters:
a=0, b=7
The most interesting thing about elliptic curves is the fact that it is possible to define a group structure on it.
To do so we define an internal composition rule with an additive notation +, such that for any three distinct points P, Q and R on the curve, whenever these points are aligned, we have:
P + Q + R = 0
Here 0 (zero) is the infinity point, for which the x and y values are not defined. It's basically the same kind of point which defines the horizon in projective geometry.
We'll also assume here that this infinity point is unique and defines the neutral element of the addition.
This was not the definition of the addition, but only its desired property. For a more accurate definition, we proceed as such:
Given any three aligned points P, Q and R, we define the sum S = P + Q as the point (possibly the infinity point) such that S, R and the infinity point are aligned.
Considering the symmetry of the curve around the x-axis, it's easy to convince oneself that two points S and R can be aligned with the infinity point if and only if S and R are symmetric of one another towards the x-axis (because in that case there is no other candidate than the infinity point to complete the alignment triplet).
S is thus defined as the symmetric of R towards the x axis.
The task consists in defining the addition which, for any two points of the curve, returns the sum of these two points. You will pick two random points on the curve, compute their sum and show that the symmetric of the sum is aligned with the two initial points.
You will use the a and b parameters of secp256k1, i.e. respectively zero and seven.
Hint: You might need to define a "doubling" function, that returns P+P for any given point P.
Extra credit: define the full elliptic curve arithmetic (still not modular, though) by defining a "multiply" function that returns,
for any point P and integer n, the point P + P + ... + P (n times).
| #Java | Java | import static java.lang.Math.*;
import java.util.Locale;
public class Test {
public static void main(String[] args) {
Pt a = Pt.fromY(1);
Pt b = Pt.fromY(2);
System.out.printf("a = %s%n", a);
System.out.printf("b = %s%n", b);
Pt c = a.plus(b);
System.out.printf("c = a + b = %s%n", c);
Pt d = c.neg();
System.out.printf("d = -c = %s%n", d);
System.out.printf("c + d = %s%n", c.plus(d));
System.out.printf("a + b + d = %s%n", a.plus(b).plus(d));
System.out.printf("a * 12345 = %s%n", a.mult(12345));
}
}
class Pt {
final static int bCoeff = 7;
double x, y;
Pt(double x, double y) {
this.x = x;
this.y = y;
}
static Pt zero() {
return new Pt(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY);
}
boolean isZero() {
return this.x > 1e20 || this.x < -1e20;
}
static Pt fromY(double y) {
return new Pt(cbrt(pow(y, 2) - bCoeff), y);
}
Pt dbl() {
if (isZero())
return this;
double L = (3 * this.x * this.x) / (2 * this.y);
double x2 = pow(L, 2) - 2 * this.x;
return new Pt(x2, L * (this.x - x2) - this.y);
}
Pt neg() {
return new Pt(this.x, -this.y);
}
Pt plus(Pt q) {
if (this.x == q.x && this.y == q.y)
return dbl();
if (isZero())
return q;
if (q.isZero())
return this;
double L = (q.y - this.y) / (q.x - this.x);
double xx = pow(L, 2) - this.x - q.x;
return new Pt(xx, L * (this.x - xx) - this.y);
}
Pt mult(int n) {
Pt r = Pt.zero();
Pt p = this;
for (int i = 1; i <= n; i <<= 1) {
if ((i & n) != 0)
r = r.plus(p);
p = p.dbl();
}
return r;
}
@Override
public String toString() {
if (isZero())
return "Zero";
return String.format(Locale.US, "(%.3f,%.3f)", this.x, this.y);
}
} |
http://rosettacode.org/wiki/Enumerations | Enumerations | Task
Create an enumeration of constants with and without explicit values.
| #JSON | JSON | {"fruits" : { "apple" : null, "banana" : null, "cherry" : null }
{"fruits" : { "apple" : 0, "banana" : 1, "cherry" : 2 } |
http://rosettacode.org/wiki/Enumerations | Enumerations | Task
Create an enumeration of constants with and without explicit values.
| #Julia | Julia |
@enum Fruits APPLE BANANA CHERRY
|
http://rosettacode.org/wiki/Enumerations | Enumerations | Task
Create an enumeration of constants with and without explicit values.
| #Kotlin | Kotlin | // version 1.0.5-2
enum class Animals {
CAT, DOG, ZEBRA
}
enum class Dogs(val id: Int) {
BULLDOG(1), TERRIER(2), WOLFHOUND(4)
}
fun main(args: Array<String>) {
for (value in Animals.values()) println("${value.name.padEnd(5)} : ${value.ordinal}")
println()
for (value in Dogs.values()) println("${value.name.padEnd(9)} : ${value.id}")
} |
http://rosettacode.org/wiki/Elementary_cellular_automaton/Random_Number_Generator | Elementary cellular automaton/Random Number Generator | Rule 30 is considered to be chaotic enough to generate good pseudo-random numbers. As a matter of fact, rule 30 is used by the Mathematica software for its default random number generator.
Steven Wolfram's recommendation for random number generation from rule 30 consists in extracting successive bits in a fixed position in the array of cells, as the automaton changes state.
The purpose of this task is to demonstrate this. With the code written in the parent task, which you don't need to re-write here, show the ten first bytes that emerge from this recommendation. To be precise, you will start with a state of all cells but one equal to zero, and you'll follow the evolution of the particular cell whose state was initially one. Then you'll regroup those bits by packets of eight, reconstituting bytes with the first bit being the most significant.
You can pick which ever length you want for the initial array but it should be visible in the code so that your output can be reproduced with an other language.
For extra-credits, you will make this algorithm run as fast as possible in your language, for instance with an extensive use of bitwise logic.
Reference
Cellular automata: Is Rule 30 random? (PDF).
| #Perl | Perl | package Automaton {
sub new {
my $class = shift;
my $rule = [ reverse split //, sprintf "%08b", shift ];
return bless { rule => $rule, cells => [ @_ ] }, $class;
}
sub next {
my $this = shift;
my @previous = @{$this->{cells}};
$this->{cells} = [
@{$this->{rule}}[
map {
4*$previous[($_ - 1) % @previous]
+ 2*$previous[$_]
+ $previous[($_ + 1) % @previous]
} 0 .. @previous - 1
]
];
return $this;
}
use overload
q{""} => sub {
my $this = shift;
join '', map { $_ ? '#' : ' ' } @{$this->{cells}}
};
}
my $a = Automaton->new(30, 1, map 0, 1 .. 100);
for my $n (1 .. 10) {
my $sum = 0;
for my $b (1 .. 8) {
$sum = $sum * 2 + $a->{cells}[0];
$a->next;
}
print $sum, $n == 10 ? "\n" : " ";
} |
http://rosettacode.org/wiki/Empty_string | Empty string | Languages may have features for dealing specifically with empty strings
(those containing no characters).
Task
Demonstrate how to assign an empty string to a variable.
Demonstrate how to check that a string is empty.
Demonstrate how to check that a string is not empty.
Other tasks related to string operations:
Metrics
Array length
String length
Copy a string
Empty string (assignment)
Counting
Word frequency
Letter frequency
Jewels and stones
I before E except after C
Bioinformatics/base count
Count occurrences of a substring
Count how many vowels and consonants occur in a string
Remove/replace
XXXX redacted
Conjugate a Latin verb
Remove vowels from a string
String interpolation (included)
Strip block comments
Strip comments from a string
Strip a set of characters from a string
Strip whitespace from a string -- top and tail
Strip control codes and extended characters from a string
Anagrams/Derangements/shuffling
Word wheel
ABC problem
Sattolo cycle
Knuth shuffle
Ordered words
Superpermutation minimisation
Textonyms (using a phone text pad)
Anagrams
Anagrams/Deranged anagrams
Permutations/Derangements
Find/Search/Determine
ABC words
Odd words
Word ladder
Semordnilap
Word search
Wordiff (game)
String matching
Tea cup rim text
Alternade words
Changeable words
State name puzzle
String comparison
Unique characters
Unique characters in each string
Extract file extension
Levenshtein distance
Palindrome detection
Common list elements
Longest common suffix
Longest common prefix
Compare a list of strings
Longest common substring
Find common directory path
Words from neighbour ones
Change e letters to i in words
Non-continuous subsequences
Longest common subsequence
Longest palindromic substrings
Longest increasing subsequence
Words containing "the" substring
Sum of the digits of n is substring of n
Determine if a string is numeric
Determine if a string is collapsible
Determine if a string is squeezable
Determine if a string has all unique characters
Determine if a string has all the same characters
Longest substrings without repeating characters
Find words which contains all the vowels
Find words which contains most consonants
Find words which contains more than 3 vowels
Find words which first and last three letters are equals
Find words which odd letters are consonants and even letters are vowels or vice_versa
Formatting
Substring
Rep-string
Word wrap
String case
Align columns
Literals/String
Repeat a string
Brace expansion
Brace expansion using ranges
Reverse a string
Phrase reversals
Comma quibbling
Special characters
String concatenation
Substring/Top and tail
Commatizing numbers
Reverse words in a string
Suffixation of decimal numbers
Long literals, with continuations
Numerical and alphabetical suffixes
Abbreviations, easy
Abbreviations, simple
Abbreviations, automatic
Song lyrics/poems/Mad Libs/phrases
Mad Libs
Magic 8-ball
99 Bottles of Beer
The Name Game (a song)
The Old lady swallowed a fly
The Twelve Days of Christmas
Tokenize
Text between
Tokenize a string
Word break problem
Tokenize a string with escaping
Split a character string based on change of character
Sequences
Show ASCII table
De Bruijn sequences
Self-referential sequences
Generate lower case ASCII alphabet
| #Arturo | Arturo | s: ""
if empty? s -> print "the string is empty"
if 0 = size s -> print "yes, the string is empty"
s: "hello world"
if not? empty? s -> print "the string is not empty"
if 0 < size s -> print "no, the string is not empty" |
http://rosettacode.org/wiki/Empty_string | Empty string | Languages may have features for dealing specifically with empty strings
(those containing no characters).
Task
Demonstrate how to assign an empty string to a variable.
Demonstrate how to check that a string is empty.
Demonstrate how to check that a string is not empty.
Other tasks related to string operations:
Metrics
Array length
String length
Copy a string
Empty string (assignment)
Counting
Word frequency
Letter frequency
Jewels and stones
I before E except after C
Bioinformatics/base count
Count occurrences of a substring
Count how many vowels and consonants occur in a string
Remove/replace
XXXX redacted
Conjugate a Latin verb
Remove vowels from a string
String interpolation (included)
Strip block comments
Strip comments from a string
Strip a set of characters from a string
Strip whitespace from a string -- top and tail
Strip control codes and extended characters from a string
Anagrams/Derangements/shuffling
Word wheel
ABC problem
Sattolo cycle
Knuth shuffle
Ordered words
Superpermutation minimisation
Textonyms (using a phone text pad)
Anagrams
Anagrams/Deranged anagrams
Permutations/Derangements
Find/Search/Determine
ABC words
Odd words
Word ladder
Semordnilap
Word search
Wordiff (game)
String matching
Tea cup rim text
Alternade words
Changeable words
State name puzzle
String comparison
Unique characters
Unique characters in each string
Extract file extension
Levenshtein distance
Palindrome detection
Common list elements
Longest common suffix
Longest common prefix
Compare a list of strings
Longest common substring
Find common directory path
Words from neighbour ones
Change e letters to i in words
Non-continuous subsequences
Longest common subsequence
Longest palindromic substrings
Longest increasing subsequence
Words containing "the" substring
Sum of the digits of n is substring of n
Determine if a string is numeric
Determine if a string is collapsible
Determine if a string is squeezable
Determine if a string has all unique characters
Determine if a string has all the same characters
Longest substrings without repeating characters
Find words which contains all the vowels
Find words which contains most consonants
Find words which contains more than 3 vowels
Find words which first and last three letters are equals
Find words which odd letters are consonants and even letters are vowels or vice_versa
Formatting
Substring
Rep-string
Word wrap
String case
Align columns
Literals/String
Repeat a string
Brace expansion
Brace expansion using ranges
Reverse a string
Phrase reversals
Comma quibbling
Special characters
String concatenation
Substring/Top and tail
Commatizing numbers
Reverse words in a string
Suffixation of decimal numbers
Long literals, with continuations
Numerical and alphabetical suffixes
Abbreviations, easy
Abbreviations, simple
Abbreviations, automatic
Song lyrics/poems/Mad Libs/phrases
Mad Libs
Magic 8-ball
99 Bottles of Beer
The Name Game (a song)
The Old lady swallowed a fly
The Twelve Days of Christmas
Tokenize
Text between
Tokenize a string
Word break problem
Tokenize a string with escaping
Split a character string based on change of character
Sequences
Show ASCII table
De Bruijn sequences
Self-referential sequences
Generate lower case ASCII alphabet
| #Asymptote | Asymptote | string c; //implicitly assigned an empty string
if (length(c) == 0) {
write("Empty string");
} else {
write("Non empty string");
}
string s = ""; //explicitly assigned an empty string
if (s == "") {
write("Empty string");
}
if (s != "") {
write("Non empty string");
}
string t = "not empty";
if (t != "") {
write("Non empty string");
} else {
write("Empty string");
} |
http://rosettacode.org/wiki/Elliptic_Curve_Digital_Signature_Algorithm | Elliptic Curve Digital Signature Algorithm | Elliptic curves.
An elliptic curve E over ℤp (p ≥ 5) is defined by an equation of the form
y^2 = x^3 + ax + b, where a, b ∈ ℤp and the discriminant ≢ 0 (mod p),
together with a special point 𝒪 called the point at infinity.
The set E(ℤp) consists of all points (x, y), with x, y ∈ ℤp,
which satisfy the above defining equation, together with 𝒪.
There is a rule for adding two points on an elliptic curve to give a third point.
This addition operation and the set of points E(ℤp) form a group with identity 𝒪.
It is this group that is used in the construction of elliptic curve cryptosystems.
The addition rule — which can be explained geometrically — is summarized as follows:
1. P + 𝒪 = 𝒪 + P = P for all P ∈ E(ℤp).
2. If P = (x, y) ∈ E(ℤp), then inverse -P = (x,-y), and P + (-P) = 𝒪.
3. Let P = (xP, yP) and Q = (xQ, yQ), both ∈ E(ℤp), where P ≠ -Q.
Then R = P + Q = (xR, yR), where
xR = λ^2 - xP - xQ
yR = λ·(xP - xR) - yP,
with
λ = (yP - yQ) / (xP - xQ) if P ≠ Q,
(3·xP·xP + a) / 2·yP if P = Q (point doubling).
Remark: there already is a task page requesting “a simplified (without modular arithmetic)
version of the elliptic curve arithmetic”.
Here we do add modulo operations. If also the domain is changed from reals to rationals,
the elliptic curves are no longer continuous but break up into a finite number of distinct points.
In that form we use them to implement ECDSA:
Elliptic curve digital signature algorithm.
A digital signature is the electronic analogue of a hand-written signature
that convinces the recipient that a message has been sent intact by the presumed sender.
Anyone with access to the public key of the signer may verify this signature.
Changing even a single bit of a signed message will cause the verification procedure to fail.
ECDSA key generation. Party A does the following:
1. Select an elliptic curve E defined over ℤp.
The number of points in E(ℤp) should be divisible by a large prime r.
2. Select a base point G ∈ E(ℤp) of order r (which means that rG = 𝒪).
3. Select a random integer s in the interval [1, r - 1].
4. Compute W = sG.
The public key is (E, G, r, W), the private key is s.
ECDSA signature computation. To sign a message m, A does the following:
1. Compute message representative f = H(m), using a
cryptographic hash function.
Note that f can be greater than r but not longer (measuring bits).
2. Select a random integer u in the interval [1, r - 1].
3. Compute V = uG = (xV, yV) and c ≡ xV mod r (goto (2) if c = 0).
4. Compute d ≡ u^-1·(f + s·c) mod r (goto (2) if d = 0).
The signature for the message m is the pair of integers (c, d).
ECDSA signature verification. To verify A's signature, B should do the following:
1. Obtain an authentic copy of A's public key (E, G, r, W).
Verify that c and d are integers in the interval [1, r - 1].
2. Compute f = H(m) and h ≡ d^-1 mod r.
3. Compute h1 ≡ f·h mod r and h2 ≡ c·h mod r.
4. Compute h1G + h2W = (x1, y1) and c1 ≡ x1 mod r.
Accept the signature if and only if c1 = c.
To be cryptographically useful, the parameter r should have at least 250 bits.
The basis for the security of elliptic curve cryptosystems
is the intractability of the elliptic curve discrete logarithm problem (ECDLP) in a group of this size:
given two points G, W ∈ E(ℤp), where W lies in the subgroup of order r generated by G,
determine an integer k such that W = kG and 0 ≤ k < r.
Task.
The task is to write a toy version of the ECDSA, quasi the equal of a real-world
implementation, but utilizing parameters that fit into standard arithmetic types.
To keep things simple there's no need for key export or a hash function (just a sample
hash value and a way to tamper with it). The program should be lenient where possible
(for example: if it accepts a composite modulus N it will either function as expected,
or demonstrate the principle of elliptic curve factorization)
— but strict where required (a point G that is not on E will always cause failure).
Toy ECDSA is of course completely useless for its cryptographic purpose.
If this bothers you, please add a multiple-precision version.
Reference.
Elliptic curves are in the IEEE Std 1363-2000 (Standard Specifications for Public-Key Cryptography), see:
7. Primitives based on the elliptic curve discrete logarithm problem (p. 27ff.)
7.1 The EC setting
7.1.2 EC domain parameters
7.1.3 EC key pairs
7.2 Primitives
7.2.7 ECSP-DSA (p. 35)
7.2.8 ECVP-DSA (p. 36)
Annex A. Number-theoretic background
A.9 Elliptic curves: overview (p. 115)
A.10 Elliptic curves: algorithms (p. 121)
| #Wren | Wren | import "/dynamic" for Struct
import "/big" for BigInt
import "/fmt" for Fmt
import "/math" for Boolean
import "random" for Random
var rand = Random.new()
// rational ec point: x and y are BigInts
var Epnt = Struct.create("Epnt", ["x", "y"])
// elliptic curve parameters: N is a BigInt, G is an Epnt, rest are integral Nums
var Curve = Struct.create("Curve", ["a", "b", "N", "G", "r"])
// signature pair: a and b are integral Nums
var Pair = Struct.create("Pair", ["a", "b"])
// maximum modulus
var mxN = 1073741789
// max order G = mxN + 65536
var mxr = 1073807325
// symbolic infinity
var inf = BigInt.new(-2147483647)
// single global curve
var e = Curve.new(0, 0, BigInt.zero, Epnt.new(inf, BigInt.zero), 0)
// impossible inverse mod N
var inverr = false
// return mod(v^-1, u)
var exgcd = Fn.new { |v, u|
var r = 0
var s = 1
if (v < 0) v = v + u
while (v != 0) {
var q = (u / v).truncate
var t = u - q * v
u = v
v = t
t = r - q * s
r = s
s = t
}
if (u != 1) {
System.print(" impossible inverse mod N, gcd = %(u)")
inverr = true
}
return r
}
// returns mod(a, N), a is a BigInt
var modn = Fn.new { |a|
var b = a.copy()
b = b % e.N
if (b < 0) b = b + e.N
return b
}
// returns mod(a, r), a is a BigInt
var modr = Fn.new { |a|
var b = a.copy()
b = b % e.r
if (b < 0) b = b + e.r
return b
}
// returns the discriminant of E
var disc = Fn.new {
var a = BigInt.new(e.a)
var b = BigInt.new(e.b)
var c = modn.call(a * modn.call(a * a)) * 4
return modn.call((c + modn.call(b * b) * 27) * (-16)).toSmall
}
// return true if P is 'zero' point (at inf, 0)
var isZero = Fn.new { |p| p.x == inf && p.y == 0 }
// return true if P is on curve E
var isOn = Fn.new { |p|
var r = 0
var s = 0
if (!isZero.call(p)) {
r = modn.call(p.x * modn.call(p.x * p.x + e.a) + e.b).toSmall
s = modn.call(p.y * p.y).toSmall
}
return r == s
}
// full ec point addition
var padd = Fn.new { |p, q|
var la = BigInt.zero
var t = BigInt.zero
if (isZero.call(p)) return Epnt.new(q.x, q.y)
if (isZero.call(q)) return Epnt.new(p.x, p.y)
if (p.x != q.x) { // R = P + Q
t = p.y - q.y
la = modn.call(t * exgcd.call((p.x - q.x).toSmall, e.N.toSmall))
} else { // P = Q, R = 2P
if (p.y == q.y && p.y != 0) {
t = modn.call(modn.call(p.x * p.x) * 3 + e.a)
la = modn.call(t * exgcd.call((p.y * 2).toSmall, e.N.toSmall))
} else {
return Epnt.new(inf, BigInt.zero) // P = -Q, R = O
}
}
if (inverr) return Epnt.new(inf, BigInt.zero)
t = modn.call(la * la - p.x - q.x)
return Epnt.new(t, modn.call(la * (p.x - t) - p.y))
}
// R = multiple kP
var pmul = Fn.new { |p, k|
var s = Epnt.new(inf, BigInt.zero)
var q = Epnt.new(p.x, p.y)
while (k != 0) {
if (k % 2 == 1) s = padd.call(s, q)
if (inverr) {
s.x = inf
s.y = BigInt.zero
break
}
q = padd.call(q, q)
k = (k/2).floor
}
return s
}
// print point P with prefix f
var pprint = Fn.new { |f, p|
var y = p.y
if (isZero.call(p)) {
Fmt.print("$s (0)", f)
} else {
if (y > e.N - y) y = y - e.N
Fmt.print("$s ($i, $i)", f, p.x, y)
}
}
// initialize elliptic curve
var ellinit = Fn.new { |i|
var a = BigInt.new(i[0])
var b = BigInt.new(i[1])
e.N = BigInt.new(i[2])
inverr = false
if (e.N < 5 || e.N > mxN) return false
e.a = modn.call(a).toSmall
e.b = modn.call(b).toSmall
e.G.x = modn.call(BigInt.new(i[3]))
e.G.y = modn.call(BigInt.new(i[4]))
e.r = i[5]
if (e.r < 5 || e.r > mxr) return false
Fmt.write("\nE: y^2 = x^3 + $ix + $i", a, b)
Fmt.print(" (mod $i)", e.N)
pprint.call("base point G", e.G)
Fmt.print("order(G, E) = $d", e.r)
return true
}
// signature primitive
var signature = Fn.new { |s, f|
var c
var d
var u
var u1
var sg = Pair.new(0, 0)
var V
System.print("\nsignature computation")
while (true) {
while (true) {
u = 1 + (rand.float() * (e.r - 1)).truncate
V = pmul.call(e.G, u)
c = modr.call(V.x).toSmall
if (c != 0) break
}
u1 = exgcd.call(u, e.r)
d = modr.call((modr.call(s * c) + f) * u1).toSmall
if (d != 0) break
}
Fmt.print("one-time u = $d", u)
pprint.call("V = uG", V)
sg.a = c
sg.b = d
return sg
}
// verification primitive
var verify = Fn.new { |W, f, sg|
var c = sg.a
var d = sg.b
// domain check
var t = (c > 0) && (c < e.r)
t = Boolean.and(t, d > 0 && d < e.r)
if (!t) return false
System.print("\nsignature verification")
var h = BigInt.new(exgcd.call(d, e.r))
var h1 = modr.call(h * f).toSmall
var h2 = modr.call(h * c).toSmall
Fmt.print ("h1, h2 = $d, $d", h1, h2)
var V = pmul.call(e.G, h1)
var V2 = pmul.call(W, h2)
pprint.call("h1G", V)
pprint.call("h2W", V2)
V = padd.call(V, V2)
pprint.call("+ =", V)
if (isZero.call(V)) return false
var c1 = modr.call(V.x).toSmall
Fmt.print("c' = $d", c1)
return c1 == c
}
var errmsg = Fn.new {
System.print("invalid parameter set")
System.print("_____________________")
}
// digital signature on message hash f, error bit d
var ec_dsa = Fn.new { |f, d|
// parameter check
var t = disc.call() == 0
t = Boolean.or(t, isZero.call(e.G))
var W = pmul.call(e.G, e.r)
t = Boolean.or(t, !isZero.call(W))
t = Boolean.or(t, !isOn.call(e.G))
if (t) {
errmsg.call()
return
}
System.print("\nkey generation")
var s = 1 + (rand.float() * (e.r - 1)).truncate
W = pmul.call(e.G, s)
Fmt.print("private key s = $d\n", s)
pprint.call("public key W = sG", W)
// next highest power of 2 - 1
t = e.r
var i = 1
while (i < 32) {
t = t | (t >> i)
i = i << 1
}
while (f > t) f = f >> 1
Fmt.print("\naligned hash $x", f)
var sg = signature.call(BigInt.new(s), f)
if (inverr) {
errmsg.call()
return
}
Fmt.print("signature c, d = $d, $d", sg.a, sg.b)
if (d > 0) {
while (d > t) d = d >> 1
f = f ^ d
Fmt.print("\ncorrupted hash $x", f)
}
t = verify.call(W, f, sg)
if (inverr) {
errmsg.call()
return
}
if (t) {
System.print("Valid\n_____")
} else {
System.print("invalid\n_______")
}
}
// Test vectors: elliptic curve domain parameters,
// short Weierstrass model y^2 = x^3 + ax + b (mod N)
var sets = [
// a, b, modulus N, base point G, order(G, E), cofactor
[355, 671, 1073741789, 13693, 10088, 1073807281],
[ 0, 7, 67096021, 6580, 779, 16769911], // 4
[ -3, 1, 877073, 0, 1, 878159],
[ 0, 14, 22651, 63, 30, 151], // 151
[ 3, 2, 5, 2, 1, 5],
// ecdsa may fail if...
// the base point is of composite order
[ 0, 7, 67096021, 2402, 6067, 33539822], // 2
// the given order is a multiple of the true order
[ 0, 7, 67096021, 6580, 779, 67079644], // 1
// the modulus is not prime (deceptive example)
[ 0, 7, 877069, 3, 97123, 877069],
// fails if the modulus divides the discriminant
[ 39, 387, 22651, 95, 27, 22651]
]
// Digital signature on message hash f,
// set d > 0 to simulate corrupted data
var f = 0x789abcde
var d = 0
for (s in sets) {
if (ellinit.call(s)) {
ec_dsa.call(f, d)
} else {
break
}
} |
http://rosettacode.org/wiki/Empty_directory | Empty directory | Starting with a path to some directory, determine whether the directory is empty.
An empty directory contains no files nor subdirectories.
With Unix or Windows systems, every directory contains an entry for “.” and almost every directory contains “..” (except for a root directory); an empty directory contains no other entries.
| #Elixir | Elixir | path = hd(System.argv)
IO.puts File.dir?(path) and Enum.empty?( File.ls!(path) ) |
http://rosettacode.org/wiki/Empty_directory | Empty directory | Starting with a path to some directory, determine whether the directory is empty.
An empty directory contains no files nor subdirectories.
With Unix or Windows systems, every directory contains an entry for “.” and almost every directory contains “..” (except for a root directory); an empty directory contains no other entries.
| #Erlang | Erlang | 3> {ok, []} = file:list_dir_all("/usr").
** exception error: no match of right hand side value
{ok,["X11R6","X11","standalone","share","sbin","local",
"libexec","lib","bin"]}
4> {ok, []} = file:list_dir_all("/asd").
** exception error: no match of right hand side value {error,enoent}
5> {ok, []} = file:list_dir_all("./empty").
{ok,[]}
|
http://rosettacode.org/wiki/Empty_directory | Empty directory | Starting with a path to some directory, determine whether the directory is empty.
An empty directory contains no files nor subdirectories.
With Unix or Windows systems, every directory contains an entry for “.” and almost every directory contains “..” (except for a root directory); an empty directory contains no other entries.
| #F.23 | F# | open System.IO
let isEmptyDirectory x = (Directory.GetFiles x).Length = 0 && (Directory.GetDirectories x).Length = 0 |
http://rosettacode.org/wiki/Empty_directory | Empty directory | Starting with a path to some directory, determine whether the directory is empty.
An empty directory contains no files nor subdirectories.
With Unix or Windows systems, every directory contains an entry for “.” and almost every directory contains “..” (except for a root directory); an empty directory contains no other entries.
| #Factor | Factor | USE: io.directories
: empty-directory? ( path -- ? ) directory-entries empty? ; |
http://rosettacode.org/wiki/Empty_program | Empty program | Task
Create the simplest possible program that is still considered "correct."
| #AmigaE | AmigaE | PROC main()
ENDPROC |
http://rosettacode.org/wiki/Empty_program | Empty program | Task
Create the simplest possible program that is still considered "correct."
| #AppleScript | AppleScript | return |
http://rosettacode.org/wiki/Enforced_immutability | Enforced immutability | Task
Demonstrate any means your language has to prevent the modification of values, or to create objects that cannot be modified after they have been created.
| #PicoLisp | PicoLisp | : (de pi () 4)
-> pi
: (pi)
-> 4 |
http://rosettacode.org/wiki/Enforced_immutability | Enforced immutability | Task
Demonstrate any means your language has to prevent the modification of values, or to create objects that cannot be modified after they have been created.
| #PL.2FI | PL/I | *process source attributes xref;
constants: Proc Options(main);
Dcl three Bin Fixed(15) Value(3);
Put Skip List(1/three);
Put Skip List(1/3);
End; |
http://rosettacode.org/wiki/Enforced_immutability | Enforced immutability | Task
Demonstrate any means your language has to prevent the modification of values, or to create objects that cannot be modified after they have been created.
| #PowerBASIC | PowerBASIC | $me = "myname"
%age = 35 |
http://rosettacode.org/wiki/Enforced_immutability | Enforced immutability | Task
Demonstrate any means your language has to prevent the modification of values, or to create objects that cannot be modified after they have been created.
| #PureBasic | PureBasic | #i_Const1 = 11
#i_Const2 = 3.1415
#i_Const3 = "A'm a string" |
http://rosettacode.org/wiki/Entropy | Entropy | Task
Calculate the Shannon entropy H of a given input string.
Given the discrete random variable
X
{\displaystyle X}
that is a string of
N
{\displaystyle N}
"symbols" (total characters) consisting of
n
{\displaystyle n}
different characters (n=2 for binary), the Shannon entropy of X in bits/symbol is :
H
2
(
X
)
=
−
∑
i
=
1
n
c
o
u
n
t
i
N
log
2
(
c
o
u
n
t
i
N
)
{\displaystyle H_{2}(X)=-\sum _{i=1}^{n}{\frac {count_{i}}{N}}\log _{2}\left({\frac {count_{i}}{N}}\right)}
where
c
o
u
n
t
i
{\displaystyle count_{i}}
is the count of character
n
i
{\displaystyle n_{i}}
.
For this task, use X="1223334444" as an example. The result should be 1.84644... bits/symbol. This assumes X was a random variable, which may not be the case, or it may depend on the observer.
This coding problem calculates the "specific" or "intensive" entropy that finds its parallel in physics with "specific entropy" S0 which is entropy per kg or per mole, not like physical entropy S and therefore not the "information" content of a file. It comes from Boltzmann's H-theorem where
S
=
k
B
N
H
{\displaystyle S=k_{B}NH}
where N=number of molecules. Boltzmann's H is the same equation as Shannon's H, and it gives the specific entropy H on a "per molecule" basis.
The "total", "absolute", or "extensive" information entropy is
S
=
H
2
N
{\displaystyle S=H_{2}N}
bits
This is not the entropy being coded here, but it is the closest to physical entropy and a measure of the information content of a string. But it does not look for any patterns that might be available for compression, so it is a very restricted, basic, and certain measure of "information". Every binary file with an equal number of 1's and 0's will have S=N bits. All hex files with equal symbol frequencies will have
S
=
N
log
2
(
16
)
{\displaystyle S=N\log _{2}(16)}
bits of entropy. The total entropy in bits of the example above is S= 10*18.4644 = 18.4644 bits.
The H function does not look for any patterns in data or check if X was a random variable. For example, X=000000111111 gives the same calculated entropy in all senses as Y=010011100101. For most purposes it is usually more relevant to divide the gzip length by the length of the original data to get an informal measure of how much "order" was in the data.
Two other "entropies" are useful:
Normalized specific entropy:
H
n
=
H
2
∗
log
(
2
)
log
(
n
)
{\displaystyle H_{n}={\frac {H_{2}*\log(2)}{\log(n)}}}
which varies from 0 to 1 and it has units of "entropy/symbol" or just 1/symbol. For this example, Hn<\sub>= 0.923.
Normalized total (extensive) entropy:
S
n
=
H
2
N
∗
log
(
2
)
log
(
n
)
{\displaystyle S_{n}={\frac {H_{2}N*\log(2)}{\log(n)}}}
which varies from 0 to N and does not have units. It is simply the "entropy", but it needs to be called "total normalized extensive entropy" so that it is not confused with Shannon's (specific) entropy or physical entropy. For this example, Sn<\sub>= 9.23.
Shannon himself is the reason his "entropy/symbol" H function is very confusingly called "entropy". That's like calling a function that returns a speed a "meter". See section 1.7 of his classic A Mathematical Theory of Communication and search on "per symbol" and "units" to see he always stated his entropy H has units of "bits/symbol" or "entropy/symbol" or "information/symbol". So it is legitimate to say entropy NH is "information".
In keeping with Landauer's limit, the physics entropy generated from erasing N bits is
S
=
H
2
N
k
B
ln
(
2
)
{\displaystyle S=H_{2}Nk_{B}\ln(2)}
if the bit storage device is perfectly efficient. This can be solved for H2*N to (arguably) get the number of bits of information that a physical entropy represents.
Related tasks
Fibonacci_word
Entropy/Narcissist
| #CLU | CLU | % NOTE: when compiling with Portable CLU,
% this program needs to be merged with 'useful.lib' to get log()
%
% pclu -merge $CLUHOME/lib/useful.lib -compile entropy.clu
shannon = proc (s: string) returns (real)
% find the frequency of each character
freq: array[int] := array[int]$fill(0, 256, 0)
for c: char in string$chars(s) do
i: int := char$c2i(c)
freq[i] := freq[i] + 1
end
% calculate the component for each character
h: real := 0.0
rlen: real := real$i2r(string$size(s))
for i: int in array[int]$indexes(freq) do
if freq[i] ~= 0 then
f: real := real$i2r(freq[i]) / rlen
h := h - f * log(f) / log(2.0)
end
end
return (h)
end shannon
start_up = proc ()
po: stream := stream$primary_output()
stream$putl(po, f_form(shannon("1223334444"), 1, 6))
end start_up |
http://rosettacode.org/wiki/Entropy | Entropy | Task
Calculate the Shannon entropy H of a given input string.
Given the discrete random variable
X
{\displaystyle X}
that is a string of
N
{\displaystyle N}
"symbols" (total characters) consisting of
n
{\displaystyle n}
different characters (n=2 for binary), the Shannon entropy of X in bits/symbol is :
H
2
(
X
)
=
−
∑
i
=
1
n
c
o
u
n
t
i
N
log
2
(
c
o
u
n
t
i
N
)
{\displaystyle H_{2}(X)=-\sum _{i=1}^{n}{\frac {count_{i}}{N}}\log _{2}\left({\frac {count_{i}}{N}}\right)}
where
c
o
u
n
t
i
{\displaystyle count_{i}}
is the count of character
n
i
{\displaystyle n_{i}}
.
For this task, use X="1223334444" as an example. The result should be 1.84644... bits/symbol. This assumes X was a random variable, which may not be the case, or it may depend on the observer.
This coding problem calculates the "specific" or "intensive" entropy that finds its parallel in physics with "specific entropy" S0 which is entropy per kg or per mole, not like physical entropy S and therefore not the "information" content of a file. It comes from Boltzmann's H-theorem where
S
=
k
B
N
H
{\displaystyle S=k_{B}NH}
where N=number of molecules. Boltzmann's H is the same equation as Shannon's H, and it gives the specific entropy H on a "per molecule" basis.
The "total", "absolute", or "extensive" information entropy is
S
=
H
2
N
{\displaystyle S=H_{2}N}
bits
This is not the entropy being coded here, but it is the closest to physical entropy and a measure of the information content of a string. But it does not look for any patterns that might be available for compression, so it is a very restricted, basic, and certain measure of "information". Every binary file with an equal number of 1's and 0's will have S=N bits. All hex files with equal symbol frequencies will have
S
=
N
log
2
(
16
)
{\displaystyle S=N\log _{2}(16)}
bits of entropy. The total entropy in bits of the example above is S= 10*18.4644 = 18.4644 bits.
The H function does not look for any patterns in data or check if X was a random variable. For example, X=000000111111 gives the same calculated entropy in all senses as Y=010011100101. For most purposes it is usually more relevant to divide the gzip length by the length of the original data to get an informal measure of how much "order" was in the data.
Two other "entropies" are useful:
Normalized specific entropy:
H
n
=
H
2
∗
log
(
2
)
log
(
n
)
{\displaystyle H_{n}={\frac {H_{2}*\log(2)}{\log(n)}}}
which varies from 0 to 1 and it has units of "entropy/symbol" or just 1/symbol. For this example, Hn<\sub>= 0.923.
Normalized total (extensive) entropy:
S
n
=
H
2
N
∗
log
(
2
)
log
(
n
)
{\displaystyle S_{n}={\frac {H_{2}N*\log(2)}{\log(n)}}}
which varies from 0 to N and does not have units. It is simply the "entropy", but it needs to be called "total normalized extensive entropy" so that it is not confused with Shannon's (specific) entropy or physical entropy. For this example, Sn<\sub>= 9.23.
Shannon himself is the reason his "entropy/symbol" H function is very confusingly called "entropy". That's like calling a function that returns a speed a "meter". See section 1.7 of his classic A Mathematical Theory of Communication and search on "per symbol" and "units" to see he always stated his entropy H has units of "bits/symbol" or "entropy/symbol" or "information/symbol". So it is legitimate to say entropy NH is "information".
In keeping with Landauer's limit, the physics entropy generated from erasing N bits is
S
=
H
2
N
k
B
ln
(
2
)
{\displaystyle S=H_{2}Nk_{B}\ln(2)}
if the bit storage device is perfectly efficient. This can be solved for H2*N to (arguably) get the number of bits of information that a physical entropy represents.
Related tasks
Fibonacci_word
Entropy/Narcissist
| #CoffeeScript | CoffeeScript | entropy = (s) ->
freq = (s) ->
result = {}
for ch in s.split ""
result[ch] ?= 0
result[ch]++
return result
frq = freq s
n = s.length
((frq[f]/n for f of frq).reduce ((e, p) -> e - p * Math.log(p)), 0) * Math.LOG2E
console.log "The entropy of the string '1223334444' is #{entropy '1223334444'}" |
http://rosettacode.org/wiki/Ethiopian_multiplication | Ethiopian multiplication | Ethiopian multiplication is a method of multiplying integers using only addition, doubling, and halving.
Method:
Take two numbers to be multiplied and write them down at the top of two columns.
In the left-hand column repeatedly halve the last number, discarding any remainders, and write the result below the last in the same column, until you write a value of 1.
In the right-hand column repeatedly double the last number and write the result below. stop when you add a result in the same row as where the left hand column shows 1.
Examine the table produced and discard any row where the value in the left column is even.
Sum the values in the right-hand column that remain to produce the result of multiplying the original two numbers together
For example: 17 × 34
17 34
Halving the first column:
17 34
8
4
2
1
Doubling the second column:
17 34
8 68
4 136
2 272
1 544
Strike-out rows whose first cell is even:
17 34
8 68
4 136
2 272
1 544
Sum the remaining numbers in the right-hand column:
17 34
8 --
4 ---
2 ---
1 544
====
578
So 17 multiplied by 34, by the Ethiopian method is 578.
Task
The task is to define three named functions/methods/procedures/subroutines:
one to halve an integer,
one to double an integer, and
one to state if an integer is even.
Use these functions to create a function that does Ethiopian multiplication.
References
Ethiopian multiplication explained (BBC Video clip)
A Night Of Numbers - Go Forth And Multiply (Video)
Russian Peasant Multiplication
Programming Praxis: Russian Peasant Multiplication
| #CLU | CLU | halve = proc (n: int) returns (int)
return(n/2)
end halve
double = proc (n: int) returns (int)
return(n*2)
end double
even = proc (n: int) returns (bool)
return(n//2 = 0)
end even
e_mul = proc (a, b: int) returns (int)
total: int := 0
while (a > 0) do
if ~even(a) then total := total + b end
a := halve(a)
b := double(b)
end
return(total)
end e_mul
start_up = proc ()
po: stream := stream$primary_output()
stream$putl(po, int$unparse(e_mul(17, 34)))
end start_up |
http://rosettacode.org/wiki/Equilibrium_index | Equilibrium index | An equilibrium index of a sequence is an index into the sequence such that the sum of elements at lower indices is equal to the sum of elements at higher indices.
For example, in a sequence
A
{\displaystyle A}
:
A
0
=
−
7
{\displaystyle A_{0}=-7}
A
1
=
1
{\displaystyle A_{1}=1}
A
2
=
5
{\displaystyle A_{2}=5}
A
3
=
2
{\displaystyle A_{3}=2}
A
4
=
−
4
{\displaystyle A_{4}=-4}
A
5
=
3
{\displaystyle A_{5}=3}
A
6
=
0
{\displaystyle A_{6}=0}
3 is an equilibrium index, because:
A
0
+
A
1
+
A
2
=
A
4
+
A
5
+
A
6
{\displaystyle A_{0}+A_{1}+A_{2}=A_{4}+A_{5}+A_{6}}
6 is also an equilibrium index, because:
A
0
+
A
1
+
A
2
+
A
3
+
A
4
+
A
5
=
0
{\displaystyle A_{0}+A_{1}+A_{2}+A_{3}+A_{4}+A_{5}=0}
(sum of zero elements is zero)
7 is not an equilibrium index, because it is not a valid index of sequence
A
{\displaystyle A}
.
Task;
Write a function that, given a sequence, returns its equilibrium indices (if any).
Assume that the sequence may be very long.
| #J | J | equilidx=: +/\ I.@:= +/\. |
http://rosettacode.org/wiki/Equilibrium_index | Equilibrium index | An equilibrium index of a sequence is an index into the sequence such that the sum of elements at lower indices is equal to the sum of elements at higher indices.
For example, in a sequence
A
{\displaystyle A}
:
A
0
=
−
7
{\displaystyle A_{0}=-7}
A
1
=
1
{\displaystyle A_{1}=1}
A
2
=
5
{\displaystyle A_{2}=5}
A
3
=
2
{\displaystyle A_{3}=2}
A
4
=
−
4
{\displaystyle A_{4}=-4}
A
5
=
3
{\displaystyle A_{5}=3}
A
6
=
0
{\displaystyle A_{6}=0}
3 is an equilibrium index, because:
A
0
+
A
1
+
A
2
=
A
4
+
A
5
+
A
6
{\displaystyle A_{0}+A_{1}+A_{2}=A_{4}+A_{5}+A_{6}}
6 is also an equilibrium index, because:
A
0
+
A
1
+
A
2
+
A
3
+
A
4
+
A
5
=
0
{\displaystyle A_{0}+A_{1}+A_{2}+A_{3}+A_{4}+A_{5}=0}
(sum of zero elements is zero)
7 is not an equilibrium index, because it is not a valid index of sequence
A
{\displaystyle A}
.
Task;
Write a function that, given a sequence, returns its equilibrium indices (if any).
Assume that the sequence may be very long.
| #Java | Java |
public class Equlibrium {
public static void main(String[] args) {
int[] sequence = {-7, 1, 5, 2, -4, 3, 0};
equlibrium_indices(sequence);
}
public static void equlibrium_indices(int[] sequence){
//find total sum
int totalSum = 0;
for (int n : sequence) {
totalSum += n;
}
//compare running sum to remaining sum to find equlibrium indices
int runningSum = 0;
for (int i = 0; i < sequence.length; i++) {
int n = sequence[i];
if (totalSum - runningSum - n == runningSum) {
System.out.println(i);
}
runningSum += n;
}
}
}
|
http://rosettacode.org/wiki/Environment_variables | Environment variables | Task
Show how to get one of your process's environment variables.
The available variables vary by system; some of the common ones available on Unix include:
PATH
HOME
USER
| #min | min | $PATH |
http://rosettacode.org/wiki/Environment_variables | Environment variables | Task
Show how to get one of your process's environment variables.
The available variables vary by system; some of the common ones available on Unix include:
PATH
HOME
USER
| #Modula-3 | Modula-3 | MODULE EnvVars EXPORTS Main;
IMPORT IO, Env;
VAR
k, v: TEXT;
BEGIN
IO.Put(Env.Get("HOME") & "\n");
FOR i := 0 TO Env.Count - 1 DO
Env.GetNth(i, k, v);
IO.Put(k & " = " & v & "\n")
END
END EnvVars. |
http://rosettacode.org/wiki/Environment_variables | Environment variables | Task
Show how to get one of your process's environment variables.
The available variables vary by system; some of the common ones available on Unix include:
PATH
HOME
USER
| #MUMPS | MUMPS | Set X=$ZF(-1,"show logical")
Set X=$ZF(-1,"show symbol") |
http://rosettacode.org/wiki/Environment_variables | Environment variables | Task
Show how to get one of your process's environment variables.
The available variables vary by system; some of the common ones available on Unix include:
PATH
HOME
USER
| #NetRexx | NetRexx | /* NetRexx */
options replace format comments java crossref symbols nobinary
runSample(arg)
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method sysEnvironment(vn = '') public static
if vn.length > 0 then do
envName = vn
envValu = System.getenv(envName)
if envValu = null then envValu = ''
say envName '=' envValu
end
else do
envVars = System.getenv()
key = String
loop key over envVars.keySet()
envName = key
envValu = String envVars.get(key)
say envName '=' envValu
end key
end
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method sysProperties(vn = '') public static
if vn.length > 0 then do
propName = vn
propValu = System.getProperty(propName)
if propValu = null then propValu = ''
say propName '=' propValu
end
else do
sysProps = System.getProperties()
key = String
loop key over sysProps.keySet()
propName = key
propValu = sysProps.getProperty(key)
say propName '=' propValu
end key
end
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method runSample(arg) public static
parse arg ev pv .
if ev = '' then ev = 'CLASSPATH'
if pv = '' then pv = 'java.class.path'
say '-'.left(80, '-').overlay(' Environment "'ev'" ', 5)
sysEnvironment(ev)
say '-'.left(80, '-').overlay(' Properties "'pv'" ', 5)
sysProperties(pv)
say
say '-'.left(80, '-').overlay(' Environment ', 5)
sysEnvironment()
say '-'.left(80, '-').overlay(' Properties ', 5)
sysProperties()
say
return
|
http://rosettacode.org/wiki/Esthetic_numbers | Esthetic numbers | An esthetic number is a positive integer where every adjacent digit differs from its neighbour by 1.
E.G.
12 is an esthetic number. One and two differ by 1.
5654 is an esthetic number. Each digit is exactly 1 away from its neighbour.
890 is not an esthetic number. Nine and zero differ by 9.
These examples are nominally in base 10 but the concept extends easily to numbers in other bases. Traditionally, single digit numbers are included in esthetic numbers; zero may or may not be. For our purposes, for this task, do not include zero (0) as an esthetic number. Do not include numbers with leading zeros.
Esthetic numbers are also sometimes referred to as stepping numbers.
Task
Write a routine (function, procedure, whatever) to find esthetic numbers in a given base.
Use that routine to find esthetic numbers in bases 2 through 16 and display, here on this page, the esthectic numbers from index (base × 4) through index (base × 6), inclusive. (E.G. for base 2: 8th through 12th, for base 6: 24th through 36th, etc.)
Find and display, here on this page, the base 10 esthetic numbers with a magnitude between 1000 and 9999.
Stretch: Find and display, here on this page, the base 10 esthetic numbers with a magnitude between 1.0e8 and 1.3e8.
Related task
numbers with equal rises and falls
See also
OEIS A033075 - Positive numbers n such that all pairs of consecutive decimal digits differ by 1
Numbers Aplenty - Esthetic numbers
Geeks for Geeks - Stepping numbers
| #Swift | Swift | extension Sequence {
func take(_ n: Int) -> [Element] {
var res = [Element]()
for el in self {
guard res.count != n else {
return res
}
res.append(el)
}
return res
}
}
extension String {
func isEsthetic(base: Int = 10) -> Bool {
zip(dropFirst(0), dropFirst())
.lazy
.allSatisfy({ abs(Int(String($0.0), radix: base)! - Int(String($0.1), radix: base)!) == 1 })
}
}
func getEsthetics(from: Int, to: Int, base: Int = 10) -> [String] {
guard base >= 2, to >= from else {
return []
}
var start = ""
var end = ""
repeat {
if start.count & 1 == 1 {
start += "0"
} else {
start += "1"
}
} while Int(start, radix: base)! < from
let digiMax = String(base - 1, radix: base)
let lessThanDigiMax = String(base - 2, radix: base)
var count = 0
repeat {
if count != base - 1 {
end += String(count + 1, radix: base)
count += 1
} else {
if String(end.last!) == digiMax {
end += lessThanDigiMax
} else {
end += digiMax
}
}
} while Int(end, radix: base)! < to
if Int(start, radix: base)! >= Int(end, radix: base)! {
return []
}
var esthetics = [Int]()
func shimmer(_ n: Int, _ m: Int, _ i: Int) {
if (n...m).contains(i) {
esthetics.append(i)
} else if i == 0 || i > m {
return
}
let d = i % base
let i1 = i &* base &+ d &- 1
let i2 = i1 &+ 2
if (i1 < i || i2 < i) {
// overflow
return
}
switch d {
case 0: shimmer(n, m, i2)
case base-1: shimmer(n, m, i1)
case _:
shimmer(n, m, i1)
shimmer(n, m, i2)
}
}
for digit in 0..<base {
shimmer(Int(start, radix: base)!, Int(end, radix: base)!, digit)
}
return esthetics.filter({ $0 <= to }).map({ String($0, radix: base) })
}
for base in 2...16 {
let esthetics = (0...)
.lazy
.map({ String($0, radix: base) })
.filter({ $0.isEsthetic(base: base) })
.dropFirst(base * 4)
.take((base * 6) - (base * 4) + 1)
print("Base \(base) esthetics from \(base * 4) to \(base * 6)")
print(esthetics)
print()
}
let base10Esthetics = (1000...9999).filter({ String($0).isEsthetic() })
print("\(base10Esthetics.count) esthetics between 1000 and 9999:")
print(base10Esthetics)
print()
func printSlice(of array: [String]) {
print(array.take(5))
print("...")
print(Array(array.lazy.reversed().take(5).reversed()))
print("\(array.count) total\n")
}
print("Esthetics between \(Int(1e8)) and \(13 * Int(1e7)):")
printSlice(of: getEsthetics(from: Int(1e8), to: 13 * Int(1e7)))
print("Esthetics between \(Int(1e11)) and \(13 * Int(1e10))")
printSlice(of: getEsthetics(from: Int(1e11), to: 13 * Int(1e10)))
print("Esthetics between \(Int(1e14)) and \(13 * Int(1e13)):")
printSlice(of: getEsthetics(from: Int(1e14), to: 13 * Int(1e13)))
print("Esthetics between \(Int(1e17)) and \(13 * Int(1e16)):")
printSlice(of: getEsthetics(from: Int(1e17), to: 13 * Int(1e16))) |
http://rosettacode.org/wiki/Euler%27s_sum_of_powers_conjecture | Euler's sum of powers conjecture | There is a conjecture in mathematics that held for over two hundred years before it was disproved by the finding of a counterexample in 1966 by Lander and Parkin.
Euler's (disproved) sum of powers conjecture
At least k positive kth powers are required to sum to a kth power,
except for the trivial case of one kth power: yk = yk
In 1966, Leon J. Lander and Thomas R. Parkin used a brute-force search on a CDC 6600 computer restricting numbers to those less than 250.
Task
Write a program to search for an integer solution for:
x05 + x15 + x25 + x35 == y5
Where all xi's and y are distinct integers between 0 and 250 (exclusive).
Show an answer here.
Related tasks
Pythagorean quadruples.
Pythagorean triples.
| #Go | Go | package main
import (
"fmt"
"log"
)
func main() {
fmt.Println(eulerSum())
}
func eulerSum() (x0, x1, x2, x3, y int) {
var pow5 [250]int
for i := range pow5 {
pow5[i] = i * i * i * i * i
}
for x0 = 4; x0 < len(pow5); x0++ {
for x1 = 3; x1 < x0; x1++ {
for x2 = 2; x2 < x1; x2++ {
for x3 = 1; x3 < x2; x3++ {
sum := pow5[x0] +
pow5[x1] +
pow5[x2] +
pow5[x3]
for y = x0 + 1; y < len(pow5); y++ {
if sum == pow5[y] {
return
}
}
}
}
}
}
log.Fatal("no solution")
return
} |
http://rosettacode.org/wiki/Factorial | Factorial | Definitions
The factorial of 0 (zero) is defined as being 1 (unity).
The Factorial Function of a positive integer, n, is defined as the product of the sequence:
n, n-1, n-2, ... 1
Task
Write a function to return the factorial of a number.
Solutions can be iterative or recursive.
Support for trapping negative n errors is optional.
Related task
Primorial numbers
| #Niue | Niue | [ dup 1 > [ dup 1 - factorial * ] when ] 'factorial ;
( test )
4 factorial . ( => 24 )
10 factorial . ( => 3628800 ) |
http://rosettacode.org/wiki/Even_or_odd | Even or odd | Task
Test whether an integer is even or odd.
There is more than one way to solve this task:
Use the even and odd predicates, if the language provides them.
Check the least significant digit. With binary integers, i bitwise-and 1 equals 0 iff i is even, or equals 1 iff i is odd.
Divide i by 2. The remainder equals 0 iff i is even. The remainder equals +1 or -1 iff i is odd.
Use modular congruences:
i ≡ 0 (mod 2) iff i is even.
i ≡ 1 (mod 2) iff i is odd.
| #COBOL | COBOL | IF FUNCTION REM(Num, 2) = 0
DISPLAY Num " is even."
ELSE
DISPLAY Num " is odd."
END-IF |
http://rosettacode.org/wiki/Even_or_odd | Even or odd | Task
Test whether an integer is even or odd.
There is more than one way to solve this task:
Use the even and odd predicates, if the language provides them.
Check the least significant digit. With binary integers, i bitwise-and 1 equals 0 iff i is even, or equals 1 iff i is odd.
Divide i by 2. The remainder equals 0 iff i is even. The remainder equals +1 or -1 iff i is odd.
Use modular congruences:
i ≡ 0 (mod 2) iff i is even.
i ≡ 1 (mod 2) iff i is odd.
| #CoffeeScript | CoffeeScript | isEven = (x) -> !(x%2) |
http://rosettacode.org/wiki/Euler_method | Euler method | Euler's method numerically approximates solutions of first-order ordinary differential equations (ODEs) with a given initial value. It is an explicit method for solving initial value problems (IVPs), as described in the wikipedia page.
The ODE has to be provided in the following form:
d
y
(
t
)
d
t
=
f
(
t
,
y
(
t
)
)
{\displaystyle {\frac {dy(t)}{dt}}=f(t,y(t))}
with an initial value
y
(
t
0
)
=
y
0
{\displaystyle y(t_{0})=y_{0}}
To get a numeric solution, we replace the derivative on the LHS with a finite difference approximation:
d
y
(
t
)
d
t
≈
y
(
t
+
h
)
−
y
(
t
)
h
{\displaystyle {\frac {dy(t)}{dt}}\approx {\frac {y(t+h)-y(t)}{h}}}
then solve for
y
(
t
+
h
)
{\displaystyle y(t+h)}
:
y
(
t
+
h
)
≈
y
(
t
)
+
h
d
y
(
t
)
d
t
{\displaystyle y(t+h)\approx y(t)+h\,{\frac {dy(t)}{dt}}}
which is the same as
y
(
t
+
h
)
≈
y
(
t
)
+
h
f
(
t
,
y
(
t
)
)
{\displaystyle y(t+h)\approx y(t)+h\,f(t,y(t))}
The iterative solution rule is then:
y
n
+
1
=
y
n
+
h
f
(
t
n
,
y
n
)
{\displaystyle y_{n+1}=y_{n}+h\,f(t_{n},y_{n})}
where
h
{\displaystyle h}
is the step size, the most relevant parameter for accuracy of the solution. A smaller step size increases accuracy but also the computation cost, so it has always has to be hand-picked according to the problem at hand.
Example: Newton's Cooling Law
Newton's cooling law describes how an object of initial temperature
T
(
t
0
)
=
T
0
{\displaystyle T(t_{0})=T_{0}}
cools down in an environment of temperature
T
R
{\displaystyle T_{R}}
:
d
T
(
t
)
d
t
=
−
k
Δ
T
{\displaystyle {\frac {dT(t)}{dt}}=-k\,\Delta T}
or
d
T
(
t
)
d
t
=
−
k
(
T
(
t
)
−
T
R
)
{\displaystyle {\frac {dT(t)}{dt}}=-k\,(T(t)-T_{R})}
It says that the cooling rate
d
T
(
t
)
d
t
{\displaystyle {\frac {dT(t)}{dt}}}
of the object is proportional to the current temperature difference
Δ
T
=
(
T
(
t
)
−
T
R
)
{\displaystyle \Delta T=(T(t)-T_{R})}
to the surrounding environment.
The analytical solution, which we will compare to the numerical approximation, is
T
(
t
)
=
T
R
+
(
T
0
−
T
R
)
e
−
k
t
{\displaystyle T(t)=T_{R}+(T_{0}-T_{R})\;e^{-kt}}
Task
Implement a routine of Euler's method and then to use it to solve the given example of Newton's cooling law with it for three different step sizes of:
2 s
5 s and
10 s
and to compare with the analytical solution.
Initial values
initial temperature
T
0
{\displaystyle T_{0}}
shall be 100 °C
room temperature
T
R
{\displaystyle T_{R}}
shall be 20 °C
cooling constant
k
{\displaystyle k}
shall be 0.07
time interval to calculate shall be from 0 s ──► 100 s
A reference solution (Common Lisp) can be seen below. We see that bigger step sizes lead to reduced approximation accuracy.
| #Rust | Rust | fn header() {
print!(" Time: ");
for t in (0..100).step_by(10) {
print!(" {:7}", t);
}
println!();
}
fn analytic() {
print!("Analytic: ");
for t in (0..=100).step_by(10) {
print!(" {:7.3}", 20.0 + 80.0 * (-0.07 * f64::from(t)).exp());
}
println!();
}
fn euler<F: Fn(f64) -> f64>(f: F, mut y: f64, step: usize, end: usize) {
print!(" Step {:2}: ", step);
for t in (0..=end).step_by(step) {
if t % 10 == 0 {
print!(" {:7.3}", y);
}
y += step as f64 * f(y);
}
println!();
}
fn main() {
header();
analytic();
for &i in &[2, 5, 10] {
euler(|temp| -0.07 * (temp - 20.0), 100.0, i, 100);
}
} |
http://rosettacode.org/wiki/Euler_method | Euler method | Euler's method numerically approximates solutions of first-order ordinary differential equations (ODEs) with a given initial value. It is an explicit method for solving initial value problems (IVPs), as described in the wikipedia page.
The ODE has to be provided in the following form:
d
y
(
t
)
d
t
=
f
(
t
,
y
(
t
)
)
{\displaystyle {\frac {dy(t)}{dt}}=f(t,y(t))}
with an initial value
y
(
t
0
)
=
y
0
{\displaystyle y(t_{0})=y_{0}}
To get a numeric solution, we replace the derivative on the LHS with a finite difference approximation:
d
y
(
t
)
d
t
≈
y
(
t
+
h
)
−
y
(
t
)
h
{\displaystyle {\frac {dy(t)}{dt}}\approx {\frac {y(t+h)-y(t)}{h}}}
then solve for
y
(
t
+
h
)
{\displaystyle y(t+h)}
:
y
(
t
+
h
)
≈
y
(
t
)
+
h
d
y
(
t
)
d
t
{\displaystyle y(t+h)\approx y(t)+h\,{\frac {dy(t)}{dt}}}
which is the same as
y
(
t
+
h
)
≈
y
(
t
)
+
h
f
(
t
,
y
(
t
)
)
{\displaystyle y(t+h)\approx y(t)+h\,f(t,y(t))}
The iterative solution rule is then:
y
n
+
1
=
y
n
+
h
f
(
t
n
,
y
n
)
{\displaystyle y_{n+1}=y_{n}+h\,f(t_{n},y_{n})}
where
h
{\displaystyle h}
is the step size, the most relevant parameter for accuracy of the solution. A smaller step size increases accuracy but also the computation cost, so it has always has to be hand-picked according to the problem at hand.
Example: Newton's Cooling Law
Newton's cooling law describes how an object of initial temperature
T
(
t
0
)
=
T
0
{\displaystyle T(t_{0})=T_{0}}
cools down in an environment of temperature
T
R
{\displaystyle T_{R}}
:
d
T
(
t
)
d
t
=
−
k
Δ
T
{\displaystyle {\frac {dT(t)}{dt}}=-k\,\Delta T}
or
d
T
(
t
)
d
t
=
−
k
(
T
(
t
)
−
T
R
)
{\displaystyle {\frac {dT(t)}{dt}}=-k\,(T(t)-T_{R})}
It says that the cooling rate
d
T
(
t
)
d
t
{\displaystyle {\frac {dT(t)}{dt}}}
of the object is proportional to the current temperature difference
Δ
T
=
(
T
(
t
)
−
T
R
)
{\displaystyle \Delta T=(T(t)-T_{R})}
to the surrounding environment.
The analytical solution, which we will compare to the numerical approximation, is
T
(
t
)
=
T
R
+
(
T
0
−
T
R
)
e
−
k
t
{\displaystyle T(t)=T_{R}+(T_{0}-T_{R})\;e^{-kt}}
Task
Implement a routine of Euler's method and then to use it to solve the given example of Newton's cooling law with it for three different step sizes of:
2 s
5 s and
10 s
and to compare with the analytical solution.
Initial values
initial temperature
T
0
{\displaystyle T_{0}}
shall be 100 °C
room temperature
T
R
{\displaystyle T_{R}}
shall be 20 °C
cooling constant
k
{\displaystyle k}
shall be 0.07
time interval to calculate shall be from 0 s ──► 100 s
A reference solution (Common Lisp) can be seen below. We see that bigger step sizes lead to reduced approximation accuracy.
| #Scala | Scala |
object App{
def main(args : Array[String]) = {
def cooling( step : Int ) = {
eulerStep( (step , y) => {-0.07 * (y - 20)} ,
100.0,0,100,step)
}
cooling(10)
cooling(5)
cooling(2)
}
def eulerStep( func : (Int,Double) => Double,y0 : Double,
begin : Int, end : Int , step : Int) = {
println("Step size: %s".format(step))
var current : Int = begin
var y : Double = y0
while( current <= end){
println( "%d %.5f".format(current,y))
current += step
y += step * func(current,y)
}
println("DONE")
}
}
|
http://rosettacode.org/wiki/Evaluate_binomial_coefficients | Evaluate binomial coefficients | This programming task, is to calculate ANY binomial coefficient.
However, it has to be able to output
(
5
3
)
{\displaystyle {\binom {5}{3}}}
, which is 10.
This formula is recommended:
(
n
k
)
=
n
!
(
n
−
k
)
!
k
!
=
n
(
n
−
1
)
(
n
−
2
)
…
(
n
−
k
+
1
)
k
(
k
−
1
)
(
k
−
2
)
…
1
{\displaystyle {\binom {n}{k}}={\frac {n!}{(n-k)!k!}}={\frac {n(n-1)(n-2)\ldots (n-k+1)}{k(k-1)(k-2)\ldots 1}}}
See Also:
Combinations and permutations
Pascal's triangle
The number of samples of size k from n objects.
With combinations and permutations generation tasks.
Order Unimportant
Order Important
Without replacement
(
n
k
)
=
n
C
k
=
n
(
n
−
1
)
…
(
n
−
k
+
1
)
k
(
k
−
1
)
…
1
{\displaystyle {\binom {n}{k}}=^{n}\operatorname {C} _{k}={\frac {n(n-1)\ldots (n-k+1)}{k(k-1)\dots 1}}}
n
P
k
=
n
⋅
(
n
−
1
)
⋅
(
n
−
2
)
⋯
(
n
−
k
+
1
)
{\displaystyle ^{n}\operatorname {P} _{k}=n\cdot (n-1)\cdot (n-2)\cdots (n-k+1)}
Task: Combinations
Task: Permutations
With replacement
(
n
+
k
−
1
k
)
=
n
+
k
−
1
C
k
=
(
n
+
k
−
1
)
!
(
n
−
1
)
!
k
!
{\displaystyle {\binom {n+k-1}{k}}=^{n+k-1}\operatorname {C} _{k}={(n+k-1)! \over (n-1)!k!}}
n
k
{\displaystyle n^{k}}
Task: Combinations with repetitions
Task: Permutations with repetitions
| #Kotlin | Kotlin | // version 2.0
fun binomial(n: Int, k: Int) = when {
n < 0 || k < 0 -> throw IllegalArgumentException("negative numbers not allowed")
n == k -> 1L
else -> {
val kReduced = min(k, n - k) // minimize number of steps
var result = 1L
var numerator = n
var denominator = 1
while (denominator <= kReduced)
result = result * numerator-- / denominator++
result
}
}
fun main(args: Array<String>) {
for (n in 0..14) {
for (k in 0..n)
print("%4d ".format(binomial(n, k)))
println()
}
} |
http://rosettacode.org/wiki/Emirp_primes | Emirp primes | An emirp (prime spelled backwards) are primes that when reversed (in their decimal representation) are a different prime.
(This rules out palindromic primes.)
Task
show the first twenty emirps
show all emirps between 7,700 and 8,000
show the 10,000th emirp
In each list, the numbers should be in order.
Invoke the (same) program once per task requirement, this will show what limit is used as the upper bound for calculating surplus (regular) primes.
The specific method of how to determine if a range or if specific values are to be shown will be left to the programmer.
See also
Wikipedia, Emirp.
The Prime Pages, emirp.
Wolfram MathWorld™, Emirp.
The On‑Line Encyclopedia of Integer Sequences, emirps (A6567).
| #C | C | #include <stdio.h>
typedef unsigned uint;
int is_prime(uint n)
{
if (!(n%2) || !(n%3)) return 0;
uint p = 1;
while(p*p < n)
if (n%(p += 4) == 0 || n%(p += 2) == 0)
return 0;
return 1;
}
uint reverse(uint n)
{
uint r;
for (r = 0; n; n /= 10)
r = r*10 + (n%10);
return r;
}
int is_emirp(uint n)
{
uint r = reverse(n);
return r != n && is_prime(n) && is_prime(r);
}
int main(int argc, char **argv)
{
uint x, c = 0;
switch(argc) { // advanced args parsing
case 1: for (x = 11; c < 20; x += 2)
if (is_emirp(x))
printf(" %u", x), ++c;
break;
case 2: for (x = 7701; x < 8000; x += 2)
if (is_emirp(x))
printf(" %u", x);
break;
default:
for (x = 11; ; x += 2)
if (is_emirp(x) && ++c == 10000) {
printf("%u", x);
break;
}
}
putchar('\n');
return 0;
} |
http://rosettacode.org/wiki/Elliptic_curve_arithmetic | Elliptic curve arithmetic | Elliptic curves are sometimes used in cryptography as a way to perform digital signatures.
The purpose of this task is to implement a simplified (without modular arithmetic) version of the elliptic curve arithmetic which is required by the elliptic curve DSA protocol.
In a nutshell, an elliptic curve is a bi-dimensional curve defined by the following relation between the x and y coordinates of any point on the curve:
y
2
=
x
3
+
a
x
+
b
{\displaystyle y^{2}=x^{3}+ax+b}
a and b are arbitrary parameters that define the specific curve which is used.
For this particular task, we'll use the following parameters:
a=0, b=7
The most interesting thing about elliptic curves is the fact that it is possible to define a group structure on it.
To do so we define an internal composition rule with an additive notation +, such that for any three distinct points P, Q and R on the curve, whenever these points are aligned, we have:
P + Q + R = 0
Here 0 (zero) is the infinity point, for which the x and y values are not defined. It's basically the same kind of point which defines the horizon in projective geometry.
We'll also assume here that this infinity point is unique and defines the neutral element of the addition.
This was not the definition of the addition, but only its desired property. For a more accurate definition, we proceed as such:
Given any three aligned points P, Q and R, we define the sum S = P + Q as the point (possibly the infinity point) such that S, R and the infinity point are aligned.
Considering the symmetry of the curve around the x-axis, it's easy to convince oneself that two points S and R can be aligned with the infinity point if and only if S and R are symmetric of one another towards the x-axis (because in that case there is no other candidate than the infinity point to complete the alignment triplet).
S is thus defined as the symmetric of R towards the x axis.
The task consists in defining the addition which, for any two points of the curve, returns the sum of these two points. You will pick two random points on the curve, compute their sum and show that the symmetric of the sum is aligned with the two initial points.
You will use the a and b parameters of secp256k1, i.e. respectively zero and seven.
Hint: You might need to define a "doubling" function, that returns P+P for any given point P.
Extra credit: define the full elliptic curve arithmetic (still not modular, though) by defining a "multiply" function that returns,
for any point P and integer n, the point P + P + ... + P (n times).
| #Julia | Julia | struct Point{T<:AbstractFloat}
x::T
y::T
end
Point{T}() where T<:AbstractFloat = Point{T}(Inf, Inf)
Point() = Point{Float64}()
Base.show(io::IO, p::Point{T}) where T = iszero(p) ? print(io, "Zero{$T}") : @printf(io, "{%s}(%.3f, %.3f)", T, p.x, p.y)
Base.copy(p::Point) = Point(p.x, p.y)
Base.iszero(p::Point{T}) where T = p.x in (-Inf, Inf)
Base.:-(p::Point) = Point(p.x, -p.y)
function dbl(p::Point{T}) where T
iszero(p) && return p
L = 3p.x ^ 2 / 2p.y
x = L ^ 2 - 2p.x
y = L * (p.x - x) - p.y
return Point{T}(x, y)
end
Base.:(==)(a::Point{T}, C::Point{T}) where T = a.x == C.x && a.y == C.y
function Base.:+(p::Point{T}, q::Point{T}) where T
p == q && return dbl(p)
iszero(p) && return q
iszero(q) && return p
L = (q.y - p.y) / (q.x - p.x)
x = L ^ 2 - p.x - q.x
y = L * (p.x - x) - p.y
return Point{T}(x, y)
end
function Base.:*(p::Point, n::Integer)
r = Point()
i = 1
while i ≤ n
if i & n != 0 r += p end
p = dbl(p)
i <<= 1
end
return r
end
Base.:*(n::Integer, p::Point) = p * n
const C = 7
function Point(y::AbstractFloat)
n = y ^ 2 - C
x = n ≥ 0 ? n ^ (1 / 3) : -((-n) ^ (1 / 3))
return Point{typeof(y)}(x, y)
end
a = Point(1.0)
b = Point(2.0)
@show a b
@show c = a + b
@show d = -c
@show c + d
@show a + b + d
@show 12345a |
http://rosettacode.org/wiki/Elliptic_curve_arithmetic | Elliptic curve arithmetic | Elliptic curves are sometimes used in cryptography as a way to perform digital signatures.
The purpose of this task is to implement a simplified (without modular arithmetic) version of the elliptic curve arithmetic which is required by the elliptic curve DSA protocol.
In a nutshell, an elliptic curve is a bi-dimensional curve defined by the following relation between the x and y coordinates of any point on the curve:
y
2
=
x
3
+
a
x
+
b
{\displaystyle y^{2}=x^{3}+ax+b}
a and b are arbitrary parameters that define the specific curve which is used.
For this particular task, we'll use the following parameters:
a=0, b=7
The most interesting thing about elliptic curves is the fact that it is possible to define a group structure on it.
To do so we define an internal composition rule with an additive notation +, such that for any three distinct points P, Q and R on the curve, whenever these points are aligned, we have:
P + Q + R = 0
Here 0 (zero) is the infinity point, for which the x and y values are not defined. It's basically the same kind of point which defines the horizon in projective geometry.
We'll also assume here that this infinity point is unique and defines the neutral element of the addition.
This was not the definition of the addition, but only its desired property. For a more accurate definition, we proceed as such:
Given any three aligned points P, Q and R, we define the sum S = P + Q as the point (possibly the infinity point) such that S, R and the infinity point are aligned.
Considering the symmetry of the curve around the x-axis, it's easy to convince oneself that two points S and R can be aligned with the infinity point if and only if S and R are symmetric of one another towards the x-axis (because in that case there is no other candidate than the infinity point to complete the alignment triplet).
S is thus defined as the symmetric of R towards the x axis.
The task consists in defining the addition which, for any two points of the curve, returns the sum of these two points. You will pick two random points on the curve, compute their sum and show that the symmetric of the sum is aligned with the two initial points.
You will use the a and b parameters of secp256k1, i.e. respectively zero and seven.
Hint: You might need to define a "doubling" function, that returns P+P for any given point P.
Extra credit: define the full elliptic curve arithmetic (still not modular, though) by defining a "multiply" function that returns,
for any point P and integer n, the point P + P + ... + P (n times).
| #Kotlin | Kotlin | // version 1.1.4
const val C = 7
class Pt(val x: Double, val y: Double) {
val zero get() = Pt(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY)
val isZero get() = x > 1e20 || x < -1e20
fun dbl(): Pt {
if (isZero) return this
val l = 3.0 * x * x / (2.0 * y)
val t = l * l - 2.0 * x
return Pt(t, l * (x - t) - y)
}
operator fun unaryMinus() = Pt(x, -y)
operator fun plus(other: Pt): Pt {
if (x == other.x && y == other.y) return dbl()
if (isZero) return other
if (other.isZero) return this
val l = (other.y - y) / (other.x - x)
val t = l * l - x - other.x
return Pt(t, l * (x - t) - y)
}
operator fun times(n: Int): Pt {
var r: Pt = zero
var p = this
var i = 1
while (i <= n) {
if ((i and n) != 0) r += p
p = p.dbl()
i = i shl 1
}
return r
}
override fun toString() =
if (isZero) "Zero" else "(${"%.3f".format(x)}, ${"%.3f".format(y)})"
}
fun Double.toPt() = Pt(Math.cbrt(this * this - C), this)
fun main(args: Array<String>) {
val a = 1.0.toPt()
val b = 2.0.toPt()
val c = a + b
val d = -c
println("a = $a")
println("b = $b")
println("c = a + b = $c")
println("d = -c = $d")
println("c + d = ${c + d}")
println("a + b + d = ${a + b + d}")
println("a * 12345 = ${a * 12345}")
} |
http://rosettacode.org/wiki/Enumerations | Enumerations | Task
Create an enumeration of constants with and without explicit values.
| #Lingo | Lingo | -- parent script "Enumeration"
property ancestor
on new (me)
data = [:]
repeat with i = 2 to the paramCount
data[param(i)] = i-1
end repeat
me.ancestor = data
return me
end
on setAt (me)
-- do nothing
end
on setProp (me)
-- do nothing
end
on deleteAt (me)
-- do nothing
end
on deleteProp (me)
-- do nothing
end
on addProp (me)
-- do nothing
end |
http://rosettacode.org/wiki/Enumerations | Enumerations | Task
Create an enumeration of constants with and without explicit values.
| #Lua | Lua |
local fruit = {apple = 0, banana = 1, cherry = 2}
|
http://rosettacode.org/wiki/Enumerations | Enumerations | Task
Create an enumeration of constants with and without explicit values.
| #M2000_Interpreter | M2000 Interpreter |
Module Checkit {
\\ need revision 15, version 9.4
Enum Fruit {apple, banana, cherry}
Enum Fruit2 {apple2=10, banana2=20, cherry2=30}
Print apple, banana, cherry
Print apple2, banana2, cherry2
Print Len(apple)=0
Print Len(banana)=1
Print Len(cherry)=2
Print Len(cherry2)=2, Cherry2=30, Type$(Cherry2)="Fruit2"
k=each(Fruit)
While k {
\\ name of variable, value, length from first (0, 1, 2)
Print Eval$(k), Eval(k), k^
}
m=apple
Print Eval$(m)="apple"
Print Eval(m)=m
m++
Print Eval$(m)="banana"
Try {
\\ error, m is an object
m=100
}
Try {
\\ error not the same type
m=apple2
}
Try {
\\ read only can't change
apple2++
}
m++
Print Eval$(m)="cherry", m
k=Each(Fruit2 end to start)
While k {
Print Eval$(k), Eval(k) , k^
CheckByValue(Eval(k))
}
m2=apple2
Print "-------------------------"
CheckByValue(m2)
CheckByReference(&m2)
Print m2
Sub CheckByValue(z as Fruit2)
Print Eval$(z), z
End Sub
Sub CheckByReference(&z as Fruit2)
z++
Print Eval$(z), z
End Sub
}
Checkit
|
http://rosettacode.org/wiki/Elementary_cellular_automaton/Random_Number_Generator | Elementary cellular automaton/Random Number Generator | Rule 30 is considered to be chaotic enough to generate good pseudo-random numbers. As a matter of fact, rule 30 is used by the Mathematica software for its default random number generator.
Steven Wolfram's recommendation for random number generation from rule 30 consists in extracting successive bits in a fixed position in the array of cells, as the automaton changes state.
The purpose of this task is to demonstrate this. With the code written in the parent task, which you don't need to re-write here, show the ten first bytes that emerge from this recommendation. To be precise, you will start with a state of all cells but one equal to zero, and you'll follow the evolution of the particular cell whose state was initially one. Then you'll regroup those bits by packets of eight, reconstituting bytes with the first bit being the most significant.
You can pick which ever length you want for the initial array but it should be visible in the code so that your output can be reproduced with an other language.
For extra-credits, you will make this algorithm run as fast as possible in your language, for instance with an extensive use of bitwise logic.
Reference
Cellular automata: Is Rule 30 random? (PDF).
| #Phix | Phix | with javascript_semantics
--string s = ".........#.........", --(original)
string s = "...............................#"&
"................................",
--string s = "#"&repeat('.',100), -- [2]
t=s, r = "........"
integer rule = 30, k, l = length(s), w = 0
for i=1 to 8 do
r[i] = iff(mod(rule,2)?'#':'.')
rule = floor(rule/2)
end for
sequence res = {}
for i=0 to 80 do
w = w*2 + (s[32]='#')
-- w = w*2 + (s[1]='#') -- [2]
if mod(i+1,8)=0 then res&=w w=0 end if
for j=1 to l do
k = (s[iff(j=1?l:j-1)]='#')*4
+ (s[ j ]='#')*2
+ (s[iff(j=l?1:j+1)]='#')+1
t[j] = r[k]
end for
s = t
end for
pp(res)
|
http://rosettacode.org/wiki/Elementary_cellular_automaton/Random_Number_Generator | Elementary cellular automaton/Random Number Generator | Rule 30 is considered to be chaotic enough to generate good pseudo-random numbers. As a matter of fact, rule 30 is used by the Mathematica software for its default random number generator.
Steven Wolfram's recommendation for random number generation from rule 30 consists in extracting successive bits in a fixed position in the array of cells, as the automaton changes state.
The purpose of this task is to demonstrate this. With the code written in the parent task, which you don't need to re-write here, show the ten first bytes that emerge from this recommendation. To be precise, you will start with a state of all cells but one equal to zero, and you'll follow the evolution of the particular cell whose state was initially one. Then you'll regroup those bits by packets of eight, reconstituting bytes with the first bit being the most significant.
You can pick which ever length you want for the initial array but it should be visible in the code so that your output can be reproduced with an other language.
For extra-credits, you will make this algorithm run as fast as possible in your language, for instance with an extensive use of bitwise logic.
Reference
Cellular automata: Is Rule 30 random? (PDF).
| #Python | Python | from elementary_cellular_automaton import eca, eca_wrap
def rule30bytes(lencells=100):
cells = '1' + '0' * (lencells - 1)
gen = eca(cells, 30)
while True:
yield int(''.join(next(gen)[0] for i in range(8)), 2)
if __name__ == '__main__':
print([b for i,b in zip(range(10), rule30bytes())]) |
http://rosettacode.org/wiki/Empty_string | Empty string | Languages may have features for dealing specifically with empty strings
(those containing no characters).
Task
Demonstrate how to assign an empty string to a variable.
Demonstrate how to check that a string is empty.
Demonstrate how to check that a string is not empty.
Other tasks related to string operations:
Metrics
Array length
String length
Copy a string
Empty string (assignment)
Counting
Word frequency
Letter frequency
Jewels and stones
I before E except after C
Bioinformatics/base count
Count occurrences of a substring
Count how many vowels and consonants occur in a string
Remove/replace
XXXX redacted
Conjugate a Latin verb
Remove vowels from a string
String interpolation (included)
Strip block comments
Strip comments from a string
Strip a set of characters from a string
Strip whitespace from a string -- top and tail
Strip control codes and extended characters from a string
Anagrams/Derangements/shuffling
Word wheel
ABC problem
Sattolo cycle
Knuth shuffle
Ordered words
Superpermutation minimisation
Textonyms (using a phone text pad)
Anagrams
Anagrams/Deranged anagrams
Permutations/Derangements
Find/Search/Determine
ABC words
Odd words
Word ladder
Semordnilap
Word search
Wordiff (game)
String matching
Tea cup rim text
Alternade words
Changeable words
State name puzzle
String comparison
Unique characters
Unique characters in each string
Extract file extension
Levenshtein distance
Palindrome detection
Common list elements
Longest common suffix
Longest common prefix
Compare a list of strings
Longest common substring
Find common directory path
Words from neighbour ones
Change e letters to i in words
Non-continuous subsequences
Longest common subsequence
Longest palindromic substrings
Longest increasing subsequence
Words containing "the" substring
Sum of the digits of n is substring of n
Determine if a string is numeric
Determine if a string is collapsible
Determine if a string is squeezable
Determine if a string has all unique characters
Determine if a string has all the same characters
Longest substrings without repeating characters
Find words which contains all the vowels
Find words which contains most consonants
Find words which contains more than 3 vowels
Find words which first and last three letters are equals
Find words which odd letters are consonants and even letters are vowels or vice_versa
Formatting
Substring
Rep-string
Word wrap
String case
Align columns
Literals/String
Repeat a string
Brace expansion
Brace expansion using ranges
Reverse a string
Phrase reversals
Comma quibbling
Special characters
String concatenation
Substring/Top and tail
Commatizing numbers
Reverse words in a string
Suffixation of decimal numbers
Long literals, with continuations
Numerical and alphabetical suffixes
Abbreviations, easy
Abbreviations, simple
Abbreviations, automatic
Song lyrics/poems/Mad Libs/phrases
Mad Libs
Magic 8-ball
99 Bottles of Beer
The Name Game (a song)
The Old lady swallowed a fly
The Twelve Days of Christmas
Tokenize
Text between
Tokenize a string
Word break problem
Tokenize a string with escaping
Split a character string based on change of character
Sequences
Show ASCII table
De Bruijn sequences
Self-referential sequences
Generate lower case ASCII alphabet
| #AutoHotkey | AutoHotkey | ;; Traditional
; Assign an empty string:
var =
; Check that a string is empty:
If var =
MsgBox the var is empty
; Check that a string is not empty
If var !=
Msgbox the var is not empty
;; Expression mode:
; Assign an empty string:
var := ""
; Check that a string is empty:
If (var = "")
MsgBox the var is empty
; Check that a string is not empty
If (var != "")
Msgbox the var is not empty |
http://rosettacode.org/wiki/Empty_string | Empty string | Languages may have features for dealing specifically with empty strings
(those containing no characters).
Task
Demonstrate how to assign an empty string to a variable.
Demonstrate how to check that a string is empty.
Demonstrate how to check that a string is not empty.
Other tasks related to string operations:
Metrics
Array length
String length
Copy a string
Empty string (assignment)
Counting
Word frequency
Letter frequency
Jewels and stones
I before E except after C
Bioinformatics/base count
Count occurrences of a substring
Count how many vowels and consonants occur in a string
Remove/replace
XXXX redacted
Conjugate a Latin verb
Remove vowels from a string
String interpolation (included)
Strip block comments
Strip comments from a string
Strip a set of characters from a string
Strip whitespace from a string -- top and tail
Strip control codes and extended characters from a string
Anagrams/Derangements/shuffling
Word wheel
ABC problem
Sattolo cycle
Knuth shuffle
Ordered words
Superpermutation minimisation
Textonyms (using a phone text pad)
Anagrams
Anagrams/Deranged anagrams
Permutations/Derangements
Find/Search/Determine
ABC words
Odd words
Word ladder
Semordnilap
Word search
Wordiff (game)
String matching
Tea cup rim text
Alternade words
Changeable words
State name puzzle
String comparison
Unique characters
Unique characters in each string
Extract file extension
Levenshtein distance
Palindrome detection
Common list elements
Longest common suffix
Longest common prefix
Compare a list of strings
Longest common substring
Find common directory path
Words from neighbour ones
Change e letters to i in words
Non-continuous subsequences
Longest common subsequence
Longest palindromic substrings
Longest increasing subsequence
Words containing "the" substring
Sum of the digits of n is substring of n
Determine if a string is numeric
Determine if a string is collapsible
Determine if a string is squeezable
Determine if a string has all unique characters
Determine if a string has all the same characters
Longest substrings without repeating characters
Find words which contains all the vowels
Find words which contains most consonants
Find words which contains more than 3 vowels
Find words which first and last three letters are equals
Find words which odd letters are consonants and even letters are vowels or vice_versa
Formatting
Substring
Rep-string
Word wrap
String case
Align columns
Literals/String
Repeat a string
Brace expansion
Brace expansion using ranges
Reverse a string
Phrase reversals
Comma quibbling
Special characters
String concatenation
Substring/Top and tail
Commatizing numbers
Reverse words in a string
Suffixation of decimal numbers
Long literals, with continuations
Numerical and alphabetical suffixes
Abbreviations, easy
Abbreviations, simple
Abbreviations, automatic
Song lyrics/poems/Mad Libs/phrases
Mad Libs
Magic 8-ball
99 Bottles of Beer
The Name Game (a song)
The Old lady swallowed a fly
The Twelve Days of Christmas
Tokenize
Text between
Tokenize a string
Word break problem
Tokenize a string with escaping
Split a character string based on change of character
Sequences
Show ASCII table
De Bruijn sequences
Self-referential sequences
Generate lower case ASCII alphabet
| #Avail | Avail | emptyStringVar : string := "";
Assert: emptyStringVar = "";
Assert: emptyStringVar = <>;
Assert: emptyStringVar is empty;
Assert: |emptyStringVar| = 0; |
http://rosettacode.org/wiki/Empty_directory | Empty directory | Starting with a path to some directory, determine whether the directory is empty.
An empty directory contains no files nor subdirectories.
With Unix or Windows systems, every directory contains an entry for “.” and almost every directory contains “..” (except for a root directory); an empty directory contains no other entries.
| #FreeBASIC | FreeBASIC | ' FB 1.05.0 Win64
#Include "dir.bi"
Function IsDirEmpty(dirPath As String) As Boolean
Err = 0
' check dirPath is a valid directory
Dim As String fileName = Dir(dirPath, fbDirectory)
If Len(fileName) = 0 Then
Err = 1000 ' dirPath is not a valid path
Return False
End If
' now check if there are any files/subdirectories in it other than . and ..
Dim fileSpec As String = dirPath + "\*.*"
Const attribMask = fbNormal Or fbHidden Or fbSystem Or fbDirectory
Dim outAttrib As UInteger
fileName = Dir(fileSpec, attribMask, outAttrib) ' get first file
Do
If fileName <> ".." AndAlso fileName <> "." Then
If Len(fileName) = 0 Then Return True
Exit Do
End If
fileName = Dir ' get next file
Loop
Return False
End Function
Dim outAttrib As UInteger
Dim dirPath As String = "c:\freebasic\docs" ' known to be empty
Dim empty As Boolean = IsDirEmpty(dirPath)
Dim e As Long = Err
If e = 1000 Then
Print "'"; dirPath; "' is not a valid directory"
End
End If
If empty Then
Print "'"; dirPath; "' is empty"
Else
Print "'"; dirPath; "' is not empty"
End If
Print
Print "Press any key to quit"
Sleep |
http://rosettacode.org/wiki/Empty_directory | Empty directory | Starting with a path to some directory, determine whether the directory is empty.
An empty directory contains no files nor subdirectories.
With Unix or Windows systems, every directory contains an entry for “.” and almost every directory contains “..” (except for a root directory); an empty directory contains no other entries.
| #Gambas | Gambas | Public Sub Main()
Dim sFolder As String = User.home &/ "Rosetta"
Dim sDir As String[] = Dir(sFolder)
Dim sTemp As String
Dim sOutput As String = sfolder & " is NOT empty"
Try sTemp = sDir[0]
If Error Then sOutput = sfolder & " is empty"
Print sOutput
End |
http://rosettacode.org/wiki/Empty_program | Empty program | Task
Create the simplest possible program that is still considered "correct."
| #Argile | Argile | |
http://rosettacode.org/wiki/Empty_program | Empty program | Task
Create the simplest possible program that is still considered "correct."
| #ARM_Assembly | ARM Assembly | .text
.global _start
_start:
mov r0, #0
mov r7, #1
svc #0 |
http://rosettacode.org/wiki/Enforced_immutability | Enforced immutability | Task
Demonstrate any means your language has to prevent the modification of values, or to create objects that cannot be modified after they have been created.
| #Python | Python | >>> s = "Hello"
>>> s[0] = "h"
Traceback (most recent call last):
File "<pyshell#1>", line 1, in <module>
s[0] = "h"
TypeError: 'str' object does not support item assignment |
http://rosettacode.org/wiki/Enforced_immutability | Enforced immutability | Task
Demonstrate any means your language has to prevent the modification of values, or to create objects that cannot be modified after they have been created.
| #Racket | Racket | (struct coordinate (x y)) ; immutable struct |
http://rosettacode.org/wiki/Enforced_immutability | Enforced immutability | Task
Demonstrate any means your language has to prevent the modification of values, or to create objects that cannot be modified after they have been created.
| #Raku | Raku | constant $pi = 3.14159;
constant $msg = "Hello World";
constant @arr = (1, 2, 3, 4, 5); |
http://rosettacode.org/wiki/Enforced_immutability | Enforced immutability | Task
Demonstrate any means your language has to prevent the modification of values, or to create objects that cannot be modified after they have been created.
| #REXX | REXX | /*REXX program emulates immutable variables (as a post-computational check). */
call immutable '$=1' /* ◄─── assigns an immutable variable. */
call immutable ' pi = 3.14159' /* ◄─── " " " " */
call immutable 'radius= 2*pi/4 ' /* ◄─── " " " " */
call immutable ' r=13/2 ' /* ◄─── " " " " */
call immutable ' d=0002 * r' /* ◄─── " " " " */
call immutable ' f.1 = 12**2 ' /* ◄─── " " " " */
say ' $ =' $ /*show the variable, just to be sure. */
say ' pi =' pi /* " " " " " " " */
say ' radius =' radius /* " " " " " " " */
say ' r =' r /* " " " " " " " */
say ' d =' d /* " " " " " " " */
do radius=10 to -10 by -1 /*perform some faux important stuff. */
circum=$*pi*2*radius /*some kind of impressive calculation. */
end /*k*/ /* [↑] that should do it, by gum. */
call immutable /* ◄═══ see if immutable variables OK. */
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
immutable: if symbol('immutable.0')=='LIT' then immutable.0= /*1st time see immutable? */
if arg()==0 then do /* [↓] chk all immutables*/
do __=1 for words(immutable.0); _=word(immutable.0,__)
if value(_)==value('IMMUTABLE.!'_) then iterate /*same?*/
call ser -12, 'immutable variable ' _ " compromised."
end /*__*/ /* [↑] Error? ERRmsg, exit*/
return 0 /*return and indicate A-OK.*/
end /* [↓] immutable must have =*/
if pos('=',arg(1))==0 then call ser -4, "no equal sign in assignment:" arg(1)
parse arg _ '=' __; upper _; _=space(_) /*purify variable name.*/
if symbol("_")=='BAD' then call ser -8,_ "isn't a valid variable symbol."
immutable.0=immutable.0 _ /*add immutable var to list.*/
interpret '__='__; call value _,__ /*assign value to a variable*/
call value 'IMMUTABLE.!'_,__ /*assign value to bkup var. */
return words(immutable.0) /*return number immutables. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
ser: say; say '***error***' arg(2); say; exit arg(1) /*error msg.*/ |
http://rosettacode.org/wiki/Entropy | Entropy | Task
Calculate the Shannon entropy H of a given input string.
Given the discrete random variable
X
{\displaystyle X}
that is a string of
N
{\displaystyle N}
"symbols" (total characters) consisting of
n
{\displaystyle n}
different characters (n=2 for binary), the Shannon entropy of X in bits/symbol is :
H
2
(
X
)
=
−
∑
i
=
1
n
c
o
u
n
t
i
N
log
2
(
c
o
u
n
t
i
N
)
{\displaystyle H_{2}(X)=-\sum _{i=1}^{n}{\frac {count_{i}}{N}}\log _{2}\left({\frac {count_{i}}{N}}\right)}
where
c
o
u
n
t
i
{\displaystyle count_{i}}
is the count of character
n
i
{\displaystyle n_{i}}
.
For this task, use X="1223334444" as an example. The result should be 1.84644... bits/symbol. This assumes X was a random variable, which may not be the case, or it may depend on the observer.
This coding problem calculates the "specific" or "intensive" entropy that finds its parallel in physics with "specific entropy" S0 which is entropy per kg or per mole, not like physical entropy S and therefore not the "information" content of a file. It comes from Boltzmann's H-theorem where
S
=
k
B
N
H
{\displaystyle S=k_{B}NH}
where N=number of molecules. Boltzmann's H is the same equation as Shannon's H, and it gives the specific entropy H on a "per molecule" basis.
The "total", "absolute", or "extensive" information entropy is
S
=
H
2
N
{\displaystyle S=H_{2}N}
bits
This is not the entropy being coded here, but it is the closest to physical entropy and a measure of the information content of a string. But it does not look for any patterns that might be available for compression, so it is a very restricted, basic, and certain measure of "information". Every binary file with an equal number of 1's and 0's will have S=N bits. All hex files with equal symbol frequencies will have
S
=
N
log
2
(
16
)
{\displaystyle S=N\log _{2}(16)}
bits of entropy. The total entropy in bits of the example above is S= 10*18.4644 = 18.4644 bits.
The H function does not look for any patterns in data or check if X was a random variable. For example, X=000000111111 gives the same calculated entropy in all senses as Y=010011100101. For most purposes it is usually more relevant to divide the gzip length by the length of the original data to get an informal measure of how much "order" was in the data.
Two other "entropies" are useful:
Normalized specific entropy:
H
n
=
H
2
∗
log
(
2
)
log
(
n
)
{\displaystyle H_{n}={\frac {H_{2}*\log(2)}{\log(n)}}}
which varies from 0 to 1 and it has units of "entropy/symbol" or just 1/symbol. For this example, Hn<\sub>= 0.923.
Normalized total (extensive) entropy:
S
n
=
H
2
N
∗
log
(
2
)
log
(
n
)
{\displaystyle S_{n}={\frac {H_{2}N*\log(2)}{\log(n)}}}
which varies from 0 to N and does not have units. It is simply the "entropy", but it needs to be called "total normalized extensive entropy" so that it is not confused with Shannon's (specific) entropy or physical entropy. For this example, Sn<\sub>= 9.23.
Shannon himself is the reason his "entropy/symbol" H function is very confusingly called "entropy". That's like calling a function that returns a speed a "meter". See section 1.7 of his classic A Mathematical Theory of Communication and search on "per symbol" and "units" to see he always stated his entropy H has units of "bits/symbol" or "entropy/symbol" or "information/symbol". So it is legitimate to say entropy NH is "information".
In keeping with Landauer's limit, the physics entropy generated from erasing N bits is
S
=
H
2
N
k
B
ln
(
2
)
{\displaystyle S=H_{2}Nk_{B}\ln(2)}
if the bit storage device is perfectly efficient. This can be solved for H2*N to (arguably) get the number of bits of information that a physical entropy represents.
Related tasks
Fibonacci_word
Entropy/Narcissist
| #Common_Lisp | Common Lisp | (defun entropy (string)
(let ((table (make-hash-table :test 'equal))
(entropy 0))
(mapc (lambda (c) (setf (gethash c table) (+ (gethash c table 0) 1)))
(coerce string 'list))
(maphash (lambda (k v)
(decf entropy (* (/ v (length input-string))
(log (/ v (length input-string)) 2))))
table)
entropy)) |
http://rosettacode.org/wiki/Ethiopian_multiplication | Ethiopian multiplication | Ethiopian multiplication is a method of multiplying integers using only addition, doubling, and halving.
Method:
Take two numbers to be multiplied and write them down at the top of two columns.
In the left-hand column repeatedly halve the last number, discarding any remainders, and write the result below the last in the same column, until you write a value of 1.
In the right-hand column repeatedly double the last number and write the result below. stop when you add a result in the same row as where the left hand column shows 1.
Examine the table produced and discard any row where the value in the left column is even.
Sum the values in the right-hand column that remain to produce the result of multiplying the original two numbers together
For example: 17 × 34
17 34
Halving the first column:
17 34
8
4
2
1
Doubling the second column:
17 34
8 68
4 136
2 272
1 544
Strike-out rows whose first cell is even:
17 34
8 68
4 136
2 272
1 544
Sum the remaining numbers in the right-hand column:
17 34
8 --
4 ---
2 ---
1 544
====
578
So 17 multiplied by 34, by the Ethiopian method is 578.
Task
The task is to define three named functions/methods/procedures/subroutines:
one to halve an integer,
one to double an integer, and
one to state if an integer is even.
Use these functions to create a function that does Ethiopian multiplication.
References
Ethiopian multiplication explained (BBC Video clip)
A Night Of Numbers - Go Forth And Multiply (Video)
Russian Peasant Multiplication
Programming Praxis: Russian Peasant Multiplication
| #COBOL | COBOL | *>* Ethiopian multiplication
IDENTIFICATION DIVISION.
PROGRAM-ID. ethiopian-multiplication.
DATA DIVISION.
LOCAL-STORAGE SECTION.
01 l PICTURE 9(10) VALUE 17.
01 r PICTURE 9(10) VALUE 34.
01 ethiopian-multiply PICTURE 9(20).
01 product PICTURE 9(20).
PROCEDURE DIVISION.
CALL "ethiopian-multiply" USING
BY CONTENT l, BY CONTENT r,
BY REFERENCE ethiopian-multiply
END-CALL
DISPLAY ethiopian-multiply END-DISPLAY
MULTIPLY l BY r GIVING product END-MULTIPLY
DISPLAY product END-DISPLAY
STOP RUN.
END PROGRAM ethiopian-multiplication.
IDENTIFICATION DIVISION.
PROGRAM-ID. ethiopian-multiply.
DATA DIVISION.
LOCAL-STORAGE SECTION.
01 evenp PICTURE 9.
88 even VALUE 1.
88 odd VALUE 0.
LINKAGE SECTION.
01 l PICTURE 9(10).
01 r PICTURE 9(10).
01 product PICTURE 9(20) VALUE ZERO.
PROCEDURE DIVISION using l, r, product.
MOVE ZEROES TO product
PERFORM UNTIL l EQUAL ZERO
CALL "evenp" USING
BY CONTENT l,
BY REFERENCE evenp
END-CALL
IF odd
ADD r TO product GIVING product END-ADD
END-IF
CALL "halve" USING
BY CONTENT l,
BY REFERENCE l
END-CALL
CALL "twice" USING
BY CONTENT r,
BY REFERENCE r
END-CALL
END-PERFORM
GOBACK.
END PROGRAM ethiopian-multiply.
IDENTIFICATION DIVISION.
PROGRAM-ID. halve.
DATA DIVISION.
LOCAL-STORAGE SECTION.
LINKAGE SECTION.
01 n PICTURE 9(10).
01 m PICTURE 9(10).
PROCEDURE DIVISION USING n, m.
DIVIDE n BY 2 GIVING m END-DIVIDE
GOBACK.
END PROGRAM halve.
IDENTIFICATION DIVISION.
PROGRAM-ID. twice.
DATA DIVISION.
LOCAL-STORAGE SECTION.
LINKAGE SECTION.
01 n PICTURE 9(10).
01 m PICTURE 9(10).
PROCEDURE DIVISION USING n, m.
MULTIPLY n by 2 GIVING m END-MULTIPLY
GOBACK.
END PROGRAM twice.
IDENTIFICATION DIVISION.
PROGRAM-ID. evenp.
DATA DIVISION.
LOCAL-STORAGE SECTION.
01 q PICTURE 9(10).
LINKAGE SECTION.
01 n PICTURE 9(10).
01 m PICTURE 9(1).
88 even VALUE 1.
88 odd VALUE 0.
PROCEDURE DIVISION USING n, m.
DIVIDE n BY 2 GIVING q REMAINDER m END-DIVIDE
SUBTRACT m FROM 1 GIVING m END-SUBTRACT
GOBACK.
END PROGRAM evenp. |
http://rosettacode.org/wiki/Equilibrium_index | Equilibrium index | An equilibrium index of a sequence is an index into the sequence such that the sum of elements at lower indices is equal to the sum of elements at higher indices.
For example, in a sequence
A
{\displaystyle A}
:
A
0
=
−
7
{\displaystyle A_{0}=-7}
A
1
=
1
{\displaystyle A_{1}=1}
A
2
=
5
{\displaystyle A_{2}=5}
A
3
=
2
{\displaystyle A_{3}=2}
A
4
=
−
4
{\displaystyle A_{4}=-4}
A
5
=
3
{\displaystyle A_{5}=3}
A
6
=
0
{\displaystyle A_{6}=0}
3 is an equilibrium index, because:
A
0
+
A
1
+
A
2
=
A
4
+
A
5
+
A
6
{\displaystyle A_{0}+A_{1}+A_{2}=A_{4}+A_{5}+A_{6}}
6 is also an equilibrium index, because:
A
0
+
A
1
+
A
2
+
A
3
+
A
4
+
A
5
=
0
{\displaystyle A_{0}+A_{1}+A_{2}+A_{3}+A_{4}+A_{5}=0}
(sum of zero elements is zero)
7 is not an equilibrium index, because it is not a valid index of sequence
A
{\displaystyle A}
.
Task;
Write a function that, given a sequence, returns its equilibrium indices (if any).
Assume that the sequence may be very long.
| #JavaScript | JavaScript | function equilibrium(a) {
var N = a.length, i, l = [], r = [], e = []
for (l[0] = a[0], r[N - 1] = a[N - 1], i = 1; i<N; i++)
l[i] = l[i - 1] + a[i], r[N - i - 1] = r[N - i] + a[N - i - 1]
for (i = 0; i < N; i++)
if (l[i] === r[i]) e.push(i)
return e
}
// test & output
[ [-7, 1, 5, 2, -4, 3, 0], // 3, 6
[2, 4, 6], // empty
[2, 9, 2], // 1
[1, -1, 1, -1, 1, -1, 1], // 0,1,2,3,4,5,6
[1], // 0
[] // empty
].forEach(function(x) {
console.log(equilibrium(x))
}); |
http://rosettacode.org/wiki/Environment_variables | Environment variables | Task
Show how to get one of your process's environment variables.
The available variables vary by system; some of the common ones available on Unix include:
PATH
HOME
USER
| #NewLISP | NewLISP | > (env "SHELL")
"/bin/zsh"
> (env "TERM")
"xterm" |
http://rosettacode.org/wiki/Environment_variables | Environment variables | Task
Show how to get one of your process's environment variables.
The available variables vary by system; some of the common ones available on Unix include:
PATH
HOME
USER
| #Nim | Nim | import os
echo getEnv("HOME") |
http://rosettacode.org/wiki/Environment_variables | Environment variables | Task
Show how to get one of your process's environment variables.
The available variables vary by system; some of the common ones available on Unix include:
PATH
HOME
USER
| #NSIS | NSIS | ExpandEnvStrings $0 "%PATH%" ; Retrieve PATH and place it in builtin register 0.
ExpandEnvStrings $1 "%USERPROFILE%" ; Retrieve the user's profile location and place it in builtin register 1.
ExpandEnvStrings $2 "%USERNAME%" ; Retrieve the user's account name and place it in builtin register 2. |
http://rosettacode.org/wiki/Environment_variables | Environment variables | Task
Show how to get one of your process's environment variables.
The available variables vary by system; some of the common ones available on Unix include:
PATH
HOME
USER
| #Objective-C | Objective-C | [[[NSProcessInfo processInfo] environment] objectForKey:@"HOME"] |
http://rosettacode.org/wiki/Esthetic_numbers | Esthetic numbers | An esthetic number is a positive integer where every adjacent digit differs from its neighbour by 1.
E.G.
12 is an esthetic number. One and two differ by 1.
5654 is an esthetic number. Each digit is exactly 1 away from its neighbour.
890 is not an esthetic number. Nine and zero differ by 9.
These examples are nominally in base 10 but the concept extends easily to numbers in other bases. Traditionally, single digit numbers are included in esthetic numbers; zero may or may not be. For our purposes, for this task, do not include zero (0) as an esthetic number. Do not include numbers with leading zeros.
Esthetic numbers are also sometimes referred to as stepping numbers.
Task
Write a routine (function, procedure, whatever) to find esthetic numbers in a given base.
Use that routine to find esthetic numbers in bases 2 through 16 and display, here on this page, the esthectic numbers from index (base × 4) through index (base × 6), inclusive. (E.G. for base 2: 8th through 12th, for base 6: 24th through 36th, etc.)
Find and display, here on this page, the base 10 esthetic numbers with a magnitude between 1000 and 9999.
Stretch: Find and display, here on this page, the base 10 esthetic numbers with a magnitude between 1.0e8 and 1.3e8.
Related task
numbers with equal rises and falls
See also
OEIS A033075 - Positive numbers n such that all pairs of consecutive decimal digits differ by 1
Numbers Aplenty - Esthetic numbers
Geeks for Geeks - Stepping numbers
| #Wren | Wren | import "./fmt" for Conv, Fmt
var isEsthetic = Fn.new { |n, b|
if (n == 0) return false
var i = n % b
n = (n/b).floor
while (n > 0) {
var j = n % b
if ((i - j).abs != 1) return false
n = (n/b).floor
i = j
}
return true
}
var esths = []
var dfs // recursive function
dfs = Fn.new { |n, m, i|
if (i >= n && i <= m) esths.add(i)
if (i == 0 || i > m) return
var d = i % 10
var i1 = i*10 + d - 1
var i2 = i1 + 2
if (d == 0) {
dfs.call(n, m, i2)
} else if (d == 9) {
dfs.call(n, m, i1)
} else {
dfs.call(n, m, i1)
dfs.call(n, m, i2)
}
}
var listEsths = Fn.new { |n, n2, m, m2, perLine, all|
esths.clear()
for (i in 0..9) dfs.call(n2, m2, i)
var le = esths.count
Fmt.print("Base 10: $,d esthetic numbers between $,d and $,d", le, n, m)
if (all) {
var c = 0
for (esth in esths) {
System.write("%(esth) ")
if ((c+1)%perLine == 0) System.print()
c = c + 1
}
} else {
for (i in 0...perLine) System.write("%(Conv.dec(esths[i])) ")
System.print("\n............\n")
for (i in le-perLine...le) System.write("%(Conv.dec(esths[i])) ")
}
System.print("\n")
}
for (b in 2..16) {
System.print("Base %(b): %(4*b)th to %(6*b)th esthetic numbers:")
var n = 1
var c = 0
while (c < 6*b) {
if (isEsthetic.call(n, b)) {
c = c + 1
if (c >= 4*b) System.write("%(Conv.itoa(n, b)) ")
}
n = n + 1
}
System.print("\n")
}
// the following all use the obvious range limitations for the numbers in question
listEsths.call(1000, 1010, 9999, 9898, 16, true)
listEsths.call(1e8, 101010101, 13*1e7, 123456789, 9, true)
listEsths.call(1e11, 101010101010, 13*1e10, 123456789898, 7, false)
listEsths.call(1e14, 101010101010101, 13*1e13, 123456789898989, 5, false) |
http://rosettacode.org/wiki/Euler%27s_sum_of_powers_conjecture | Euler's sum of powers conjecture | There is a conjecture in mathematics that held for over two hundred years before it was disproved by the finding of a counterexample in 1966 by Lander and Parkin.
Euler's (disproved) sum of powers conjecture
At least k positive kth powers are required to sum to a kth power,
except for the trivial case of one kth power: yk = yk
In 1966, Leon J. Lander and Thomas R. Parkin used a brute-force search on a CDC 6600 computer restricting numbers to those less than 250.
Task
Write a program to search for an integer solution for:
x05 + x15 + x25 + x35 == y5
Where all xi's and y are distinct integers between 0 and 250 (exclusive).
Show an answer here.
Related tasks
Pythagorean quadruples.
Pythagorean triples.
| #Groovy | Groovy | class EulerSumOfPowers {
static final int MAX_NUMBER = 250
static void main(String[] args) {
boolean found = false
long[] fifth = new long[MAX_NUMBER]
for (int i = 1; i <= MAX_NUMBER; i++) {
long i2 = i * i
fifth[i - 1] = i2 * i2 * i
}
for (int a = 0; a < MAX_NUMBER && !found; a++) {
for (int b = a; b < MAX_NUMBER && !found; b++) {
for (int c = b; c < MAX_NUMBER && !found; c++) {
for (int d = c; d < MAX_NUMBER && !found; d++) {
long sum = fifth[a] + fifth[b] + fifth[c] + fifth[d]
int e = Arrays.binarySearch(fifth, sum)
found = (e >= 0)
if (found) {
println("${a + 1}^5 + ${b + 1}^5 + ${c + 1}^5 + ${d + 1}^5 + ${e + 1}^5")
}
}
}
}
}
}
} |
http://rosettacode.org/wiki/Factorial | Factorial | Definitions
The factorial of 0 (zero) is defined as being 1 (unity).
The Factorial Function of a positive integer, n, is defined as the product of the sequence:
n, n-1, n-2, ... 1
Task
Write a function to return the factorial of a number.
Solutions can be iterative or recursive.
Support for trapping negative n errors is optional.
Related task
Primorial numbers
| #Nyquist | Nyquist | (defun factorial (n)
(do ((x n (* x n)))
((= n 1) x)
(setq n (1- n)))) |
http://rosettacode.org/wiki/Even_or_odd | Even or odd | Task
Test whether an integer is even or odd.
There is more than one way to solve this task:
Use the even and odd predicates, if the language provides them.
Check the least significant digit. With binary integers, i bitwise-and 1 equals 0 iff i is even, or equals 1 iff i is odd.
Divide i by 2. The remainder equals 0 iff i is even. The remainder equals +1 or -1 iff i is odd.
Use modular congruences:
i ≡ 0 (mod 2) iff i is even.
i ≡ 1 (mod 2) iff i is odd.
| #ColdFusion | ColdFusion |
function f(numeric n) {
return n mod 2?"odd":"even"
}
|
http://rosettacode.org/wiki/Even_or_odd | Even or odd | Task
Test whether an integer is even or odd.
There is more than one way to solve this task:
Use the even and odd predicates, if the language provides them.
Check the least significant digit. With binary integers, i bitwise-and 1 equals 0 iff i is even, or equals 1 iff i is odd.
Divide i by 2. The remainder equals 0 iff i is even. The remainder equals +1 or -1 iff i is odd.
Use modular congruences:
i ≡ 0 (mod 2) iff i is even.
i ≡ 1 (mod 2) iff i is odd.
| #Common_Lisp | Common Lisp | (if (evenp some-var) (do-even-stuff))
(if (oddp some-other-var) (do-odd-stuff)) |
http://rosettacode.org/wiki/Euler_method | Euler method | Euler's method numerically approximates solutions of first-order ordinary differential equations (ODEs) with a given initial value. It is an explicit method for solving initial value problems (IVPs), as described in the wikipedia page.
The ODE has to be provided in the following form:
d
y
(
t
)
d
t
=
f
(
t
,
y
(
t
)
)
{\displaystyle {\frac {dy(t)}{dt}}=f(t,y(t))}
with an initial value
y
(
t
0
)
=
y
0
{\displaystyle y(t_{0})=y_{0}}
To get a numeric solution, we replace the derivative on the LHS with a finite difference approximation:
d
y
(
t
)
d
t
≈
y
(
t
+
h
)
−
y
(
t
)
h
{\displaystyle {\frac {dy(t)}{dt}}\approx {\frac {y(t+h)-y(t)}{h}}}
then solve for
y
(
t
+
h
)
{\displaystyle y(t+h)}
:
y
(
t
+
h
)
≈
y
(
t
)
+
h
d
y
(
t
)
d
t
{\displaystyle y(t+h)\approx y(t)+h\,{\frac {dy(t)}{dt}}}
which is the same as
y
(
t
+
h
)
≈
y
(
t
)
+
h
f
(
t
,
y
(
t
)
)
{\displaystyle y(t+h)\approx y(t)+h\,f(t,y(t))}
The iterative solution rule is then:
y
n
+
1
=
y
n
+
h
f
(
t
n
,
y
n
)
{\displaystyle y_{n+1}=y_{n}+h\,f(t_{n},y_{n})}
where
h
{\displaystyle h}
is the step size, the most relevant parameter for accuracy of the solution. A smaller step size increases accuracy but also the computation cost, so it has always has to be hand-picked according to the problem at hand.
Example: Newton's Cooling Law
Newton's cooling law describes how an object of initial temperature
T
(
t
0
)
=
T
0
{\displaystyle T(t_{0})=T_{0}}
cools down in an environment of temperature
T
R
{\displaystyle T_{R}}
:
d
T
(
t
)
d
t
=
−
k
Δ
T
{\displaystyle {\frac {dT(t)}{dt}}=-k\,\Delta T}
or
d
T
(
t
)
d
t
=
−
k
(
T
(
t
)
−
T
R
)
{\displaystyle {\frac {dT(t)}{dt}}=-k\,(T(t)-T_{R})}
It says that the cooling rate
d
T
(
t
)
d
t
{\displaystyle {\frac {dT(t)}{dt}}}
of the object is proportional to the current temperature difference
Δ
T
=
(
T
(
t
)
−
T
R
)
{\displaystyle \Delta T=(T(t)-T_{R})}
to the surrounding environment.
The analytical solution, which we will compare to the numerical approximation, is
T
(
t
)
=
T
R
+
(
T
0
−
T
R
)
e
−
k
t
{\displaystyle T(t)=T_{R}+(T_{0}-T_{R})\;e^{-kt}}
Task
Implement a routine of Euler's method and then to use it to solve the given example of Newton's cooling law with it for three different step sizes of:
2 s
5 s and
10 s
and to compare with the analytical solution.
Initial values
initial temperature
T
0
{\displaystyle T_{0}}
shall be 100 °C
room temperature
T
R
{\displaystyle T_{R}}
shall be 20 °C
cooling constant
k
{\displaystyle k}
shall be 0.07
time interval to calculate shall be from 0 s ──► 100 s
A reference solution (Common Lisp) can be seen below. We see that bigger step sizes lead to reduced approximation accuracy.
| #SequenceL | SequenceL | import <Utilities/Conversion.sl>;
import <Utilities/Sequence.sl>;
T0 := 100.0;
TR := 20.0;
k := 0.07;
main(args(2)) :=
let
results[i] := euler(newtonCooling, T0, 100, stringToInt(args[i]), 0, "delta_t = " ++ args[i]);
in
delimit(results, '\n');
newtonCooling(t) := -k * (t - TR);
euler: (float -> float) * float * int * int * int * char(1) -> char(1);
euler(f, y, n, h, x, output(1)) :=
let
newOutput := output ++ "\n\t" ++ intToString(x) ++ "\t" ++ floatToString(y, 3);
newY := y + h * f(y);
newX := x + h;
in
output when x > n
else
euler(f, newY, n, h, newX, newOutput); |
http://rosettacode.org/wiki/Euler_method | Euler method | Euler's method numerically approximates solutions of first-order ordinary differential equations (ODEs) with a given initial value. It is an explicit method for solving initial value problems (IVPs), as described in the wikipedia page.
The ODE has to be provided in the following form:
d
y
(
t
)
d
t
=
f
(
t
,
y
(
t
)
)
{\displaystyle {\frac {dy(t)}{dt}}=f(t,y(t))}
with an initial value
y
(
t
0
)
=
y
0
{\displaystyle y(t_{0})=y_{0}}
To get a numeric solution, we replace the derivative on the LHS with a finite difference approximation:
d
y
(
t
)
d
t
≈
y
(
t
+
h
)
−
y
(
t
)
h
{\displaystyle {\frac {dy(t)}{dt}}\approx {\frac {y(t+h)-y(t)}{h}}}
then solve for
y
(
t
+
h
)
{\displaystyle y(t+h)}
:
y
(
t
+
h
)
≈
y
(
t
)
+
h
d
y
(
t
)
d
t
{\displaystyle y(t+h)\approx y(t)+h\,{\frac {dy(t)}{dt}}}
which is the same as
y
(
t
+
h
)
≈
y
(
t
)
+
h
f
(
t
,
y
(
t
)
)
{\displaystyle y(t+h)\approx y(t)+h\,f(t,y(t))}
The iterative solution rule is then:
y
n
+
1
=
y
n
+
h
f
(
t
n
,
y
n
)
{\displaystyle y_{n+1}=y_{n}+h\,f(t_{n},y_{n})}
where
h
{\displaystyle h}
is the step size, the most relevant parameter for accuracy of the solution. A smaller step size increases accuracy but also the computation cost, so it has always has to be hand-picked according to the problem at hand.
Example: Newton's Cooling Law
Newton's cooling law describes how an object of initial temperature
T
(
t
0
)
=
T
0
{\displaystyle T(t_{0})=T_{0}}
cools down in an environment of temperature
T
R
{\displaystyle T_{R}}
:
d
T
(
t
)
d
t
=
−
k
Δ
T
{\displaystyle {\frac {dT(t)}{dt}}=-k\,\Delta T}
or
d
T
(
t
)
d
t
=
−
k
(
T
(
t
)
−
T
R
)
{\displaystyle {\frac {dT(t)}{dt}}=-k\,(T(t)-T_{R})}
It says that the cooling rate
d
T
(
t
)
d
t
{\displaystyle {\frac {dT(t)}{dt}}}
of the object is proportional to the current temperature difference
Δ
T
=
(
T
(
t
)
−
T
R
)
{\displaystyle \Delta T=(T(t)-T_{R})}
to the surrounding environment.
The analytical solution, which we will compare to the numerical approximation, is
T
(
t
)
=
T
R
+
(
T
0
−
T
R
)
e
−
k
t
{\displaystyle T(t)=T_{R}+(T_{0}-T_{R})\;e^{-kt}}
Task
Implement a routine of Euler's method and then to use it to solve the given example of Newton's cooling law with it for three different step sizes of:
2 s
5 s and
10 s
and to compare with the analytical solution.
Initial values
initial temperature
T
0
{\displaystyle T_{0}}
shall be 100 °C
room temperature
T
R
{\displaystyle T_{R}}
shall be 20 °C
cooling constant
k
{\displaystyle k}
shall be 0.07
time interval to calculate shall be from 0 s ──► 100 s
A reference solution (Common Lisp) can be seen below. We see that bigger step sizes lead to reduced approximation accuracy.
| #Sidef | Sidef | func euler_method(t0, t1, k, step_size) {
var results = [[0, t0]]
for s in (step_size..100 -> by(step_size)) {
t0 -= ((t0 - t1) * k * step_size)
results << [s, t0]
}
return results;
}
func analytical(t0, t1, k, time) {
(t0 - t1) * exp(-time * k) + t1
}
var (T0, T1, k) = (100, 20, .07)
var r2 = euler_method(T0, T1, k, 2).grep { _[0] %% 10 }
var r5 = euler_method(T0, T1, k, 5).grep { _[0] %% 10 }
var r10 = euler_method(T0, T1, k, 10).grep { _[0] %% 10 }
say "Time\t 2 err(%) 5 err(%) 10 err(%) Analytic"
say "-"*76
r2.range.each { |i|
var an = analytical(T0, T1, k, r2[i][0])
printf("%4d\t#{'%9.3f' * 7}\n",
r2[i][0],
r2[i][1], ( r2[i][1] / an) * 100 - 100,
r5[i][1], ( r5[i][1] / an) * 100 - 100,
r10[i][1], (r10[i][1] / an) * 100 - 100,
an)
} |
http://rosettacode.org/wiki/Evaluate_binomial_coefficients | Evaluate binomial coefficients | This programming task, is to calculate ANY binomial coefficient.
However, it has to be able to output
(
5
3
)
{\displaystyle {\binom {5}{3}}}
, which is 10.
This formula is recommended:
(
n
k
)
=
n
!
(
n
−
k
)
!
k
!
=
n
(
n
−
1
)
(
n
−
2
)
…
(
n
−
k
+
1
)
k
(
k
−
1
)
(
k
−
2
)
…
1
{\displaystyle {\binom {n}{k}}={\frac {n!}{(n-k)!k!}}={\frac {n(n-1)(n-2)\ldots (n-k+1)}{k(k-1)(k-2)\ldots 1}}}
See Also:
Combinations and permutations
Pascal's triangle
The number of samples of size k from n objects.
With combinations and permutations generation tasks.
Order Unimportant
Order Important
Without replacement
(
n
k
)
=
n
C
k
=
n
(
n
−
1
)
…
(
n
−
k
+
1
)
k
(
k
−
1
)
…
1
{\displaystyle {\binom {n}{k}}=^{n}\operatorname {C} _{k}={\frac {n(n-1)\ldots (n-k+1)}{k(k-1)\dots 1}}}
n
P
k
=
n
⋅
(
n
−
1
)
⋅
(
n
−
2
)
⋯
(
n
−
k
+
1
)
{\displaystyle ^{n}\operatorname {P} _{k}=n\cdot (n-1)\cdot (n-2)\cdots (n-k+1)}
Task: Combinations
Task: Permutations
With replacement
(
n
+
k
−
1
k
)
=
n
+
k
−
1
C
k
=
(
n
+
k
−
1
)
!
(
n
−
1
)
!
k
!
{\displaystyle {\binom {n+k-1}{k}}=^{n+k-1}\operatorname {C} _{k}={(n+k-1)! \over (n-1)!k!}}
n
k
{\displaystyle n^{k}}
Task: Combinations with repetitions
Task: Permutations with repetitions
| #Lambdatalk | Lambdatalk |
{def C
{lambda {:n :p}
{/ {* {S.serie :n {- :n :p -1} -1}}
{* {S.serie :p 1 -1}}}}}
-> C
{C 16 8}
-> 12870
1{S.map {lambda {:n} {br}1
{S.map {C :n} {S.serie 1 {- :n 1}}} 1}
{S.serie 2 16}}
->
1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
1 10 45 120 210 252 210 120 45 10 1
1 11 55 165 330 462 462 330 165 55 11 1
1 12 66 220 495 792 924 792 495 220 66 12 1
1 13 78 286 715 1287 1716 1716 1287 715 286 78 13 1
1 14 91 364 1001 2002 3003 3432 3003 2002 1001 364 91 14 1
1 15 105 455 1365 3003 5005 6435 6435 5005 3003 1365 455 105 15 1
1 16 120 560 1820 4368 8008 11440 12870 11440 8008 4368 1820 560 120 16 1
|
http://rosettacode.org/wiki/Emirp_primes | Emirp primes | An emirp (prime spelled backwards) are primes that when reversed (in their decimal representation) are a different prime.
(This rules out palindromic primes.)
Task
show the first twenty emirps
show all emirps between 7,700 and 8,000
show the 10,000th emirp
In each list, the numbers should be in order.
Invoke the (same) program once per task requirement, this will show what limit is used as the upper bound for calculating surplus (regular) primes.
The specific method of how to determine if a range or if specific values are to be shown will be left to the programmer.
See also
Wikipedia, Emirp.
The Prime Pages, emirp.
Wolfram MathWorld™, Emirp.
The On‑Line Encyclopedia of Integer Sequences, emirps (A6567).
| #C.23 | C# | using static System.Console;
using System;
using System.Linq;
using System.Collections.Generic;
public class Program
{
public static void Main() {
const int limit = 1_000_000;
WriteLine("First 20:");
WriteLine(FindEmirpPrimes(limit).Take(20).Delimit());
WriteLine();
WriteLine("Between 7700 and 8000:");
WriteLine(FindEmirpPrimes(limit).SkipWhile(p => p < 7700).TakeWhile(p => p < 8000).Delimit());
WriteLine();
WriteLine("10000th:");
WriteLine(FindEmirpPrimes(limit).ElementAt(9999));
}
private static IEnumerable<int> FindEmirpPrimes(int limit)
{
var primes = Primes(limit).ToHashSet();
foreach (int prime in primes) {
int reverse = prime.Reverse();
if (reverse != prime && primes.Contains(reverse)) yield return prime;
}
}
private static IEnumerable<int> Primes(int bound) {
if (bound < 2) yield break;
yield return 2;
BitArray composite = new BitArray((bound - 1) / 2);
int limit = ((int)(Math.Sqrt(bound)) - 1) / 2;
for (int i = 0; i < limit; i++) {
if (composite[i]) continue;
int prime = 2 * i + 3;
yield return prime;
for (int j = (prime * prime - 2) / 2; j < composite.Count; j += prime)
composite[j] = true;
}
for (int i = limit; i < composite.Count; i++)
if (!composite[i]) yield return 2 * i + 3;
}
}
public static class Extensions
{
public static HashSet<T> ToHashSet<T>(this IEnumerable<T> source) => new HashSet<T>(source);
private const string defaultSeparator = " ";
public static string Delimit<T>(this IEnumerable<T> source, string separator = defaultSeparator) =>
string.Join(separator ?? defaultSeparator, source);
public static int Reverse(this int number)
{
if (number < 0) return -Reverse(-number);
if (number < 10) return number;
int reverse = 0;
while (number > 0) {
reverse = reverse * 10 + number % 10;
number /= 10;
}
return reverse;
}
} |
http://rosettacode.org/wiki/Elliptic_curve_arithmetic | Elliptic curve arithmetic | Elliptic curves are sometimes used in cryptography as a way to perform digital signatures.
The purpose of this task is to implement a simplified (without modular arithmetic) version of the elliptic curve arithmetic which is required by the elliptic curve DSA protocol.
In a nutshell, an elliptic curve is a bi-dimensional curve defined by the following relation between the x and y coordinates of any point on the curve:
y
2
=
x
3
+
a
x
+
b
{\displaystyle y^{2}=x^{3}+ax+b}
a and b are arbitrary parameters that define the specific curve which is used.
For this particular task, we'll use the following parameters:
a=0, b=7
The most interesting thing about elliptic curves is the fact that it is possible to define a group structure on it.
To do so we define an internal composition rule with an additive notation +, such that for any three distinct points P, Q and R on the curve, whenever these points are aligned, we have:
P + Q + R = 0
Here 0 (zero) is the infinity point, for which the x and y values are not defined. It's basically the same kind of point which defines the horizon in projective geometry.
We'll also assume here that this infinity point is unique and defines the neutral element of the addition.
This was not the definition of the addition, but only its desired property. For a more accurate definition, we proceed as such:
Given any three aligned points P, Q and R, we define the sum S = P + Q as the point (possibly the infinity point) such that S, R and the infinity point are aligned.
Considering the symmetry of the curve around the x-axis, it's easy to convince oneself that two points S and R can be aligned with the infinity point if and only if S and R are symmetric of one another towards the x-axis (because in that case there is no other candidate than the infinity point to complete the alignment triplet).
S is thus defined as the symmetric of R towards the x axis.
The task consists in defining the addition which, for any two points of the curve, returns the sum of these two points. You will pick two random points on the curve, compute their sum and show that the symmetric of the sum is aligned with the two initial points.
You will use the a and b parameters of secp256k1, i.e. respectively zero and seven.
Hint: You might need to define a "doubling" function, that returns P+P for any given point P.
Extra credit: define the full elliptic curve arithmetic (still not modular, though) by defining a "multiply" function that returns,
for any point P and integer n, the point P + P + ... + P (n times).
| #Nim | Nim | import math, strformat
const B = 7
type Point = tuple[x, y: float]
#---------------------------------------------------------------------------------------------------
template zero(): Point =
(Inf, Inf)
#---------------------------------------------------------------------------------------------------
func isZero(pt: Point): bool {.inline.} =
pt.x > 1e20 or pt.x < -1e20
#---------------------------------------------------------------------------------------------------
func `-`(pt: Point): Point {.inline.} =
(pt.x, -pt.y)
#---------------------------------------------------------------------------------------------------
func double(pt: Point): Point =
if pt.isZero: return pt
let t = (3 * pt.x * pt.x) / (2 * pt.y)
result.x = t * t - 2 * pt.x
result.y = t * (pt.x - result.x) - pt.y
#---------------------------------------------------------------------------------------------------
func `+`(pt1, pt2: Point): Point =
if pt1.x == pt2.x and pt1.y == pt2.y: return double(pt1)
if pt1.isZero: return pt2
if pt2.isZero: return pt1
let t = (pt2.y - pt1.y) / (pt2.x - pt1.x)
result.x = t * t - pt1.x - pt2.x
result.y = t * (pt1.x - result.x) - pt1.y
#---------------------------------------------------------------------------------------------------
func `*`(pt: Point; n: int): Point =
result = zero()
var pt = pt
var i = 1
while i <= n:
if (i and n) != 0:
result = result + pt
pt = double(pt)
i = i shl 1
#---------------------------------------------------------------------------------------------------
func `$`(pt: Point): string =
if pt.isZero: "Zero" else: fmt"({pt.x:.3f}, {pt.y:.3f})"
#---------------------------------------------------------------------------------------------------
func fromY(y: float): Point {.inline.} =
(cbrt(y * y - B), y)
#———————————————————————————————————————————————————————————————————————————————————————————————————
when isMainModule:
let a = fromY(1)
let b = fromY(2)
echo "a = ", a
echo "b = ", b
let c = a + b
echo "c = a + b = ", c
let d = -c
echo "d = -c = ", d
echo "c + d = ", c + d
echo "a + b + d = ", a + b + d
echo "a * 12345 = ", a * 12345 |
http://rosettacode.org/wiki/Elliptic_curve_arithmetic | Elliptic curve arithmetic | Elliptic curves are sometimes used in cryptography as a way to perform digital signatures.
The purpose of this task is to implement a simplified (without modular arithmetic) version of the elliptic curve arithmetic which is required by the elliptic curve DSA protocol.
In a nutshell, an elliptic curve is a bi-dimensional curve defined by the following relation between the x and y coordinates of any point on the curve:
y
2
=
x
3
+
a
x
+
b
{\displaystyle y^{2}=x^{3}+ax+b}
a and b are arbitrary parameters that define the specific curve which is used.
For this particular task, we'll use the following parameters:
a=0, b=7
The most interesting thing about elliptic curves is the fact that it is possible to define a group structure on it.
To do so we define an internal composition rule with an additive notation +, such that for any three distinct points P, Q and R on the curve, whenever these points are aligned, we have:
P + Q + R = 0
Here 0 (zero) is the infinity point, for which the x and y values are not defined. It's basically the same kind of point which defines the horizon in projective geometry.
We'll also assume here that this infinity point is unique and defines the neutral element of the addition.
This was not the definition of the addition, but only its desired property. For a more accurate definition, we proceed as such:
Given any three aligned points P, Q and R, we define the sum S = P + Q as the point (possibly the infinity point) such that S, R and the infinity point are aligned.
Considering the symmetry of the curve around the x-axis, it's easy to convince oneself that two points S and R can be aligned with the infinity point if and only if S and R are symmetric of one another towards the x-axis (because in that case there is no other candidate than the infinity point to complete the alignment triplet).
S is thus defined as the symmetric of R towards the x axis.
The task consists in defining the addition which, for any two points of the curve, returns the sum of these two points. You will pick two random points on the curve, compute their sum and show that the symmetric of the sum is aligned with the two initial points.
You will use the a and b parameters of secp256k1, i.e. respectively zero and seven.
Hint: You might need to define a "doubling" function, that returns P+P for any given point P.
Extra credit: define the full elliptic curve arithmetic (still not modular, though) by defining a "multiply" function that returns,
for any point P and integer n, the point P + P + ... + P (n times).
| #OCaml | OCaml |
(* Task : Elliptic_curve_arithmetic *)
(*
Using the secp256k1 elliptic curve (a=0, b=7),
define the addition operation on points on the curve.
Extra credit: define the full elliptic curve arithmetic
(still not modular, though) by defining a "multiply" function.
*)
(*** Helpers ***)
type ec_point = Point of float * float | Inf
type ec_curve = { a : float; b : float }
(* By default, cube root doesn't work for negative bases *)
let cube_root : float -> float =
let third = 1. /. 3. in
let f x =
if x > 0.
then x ** third
else ~-. (~-. x ** third)
in
f
(* Finds the left-most x on this curve *)
let ec_minx ({a; b} : ec_curve) : float =
let factor = ~-. b *. 0.5 in
let discr = (factor ** 2.) +. (a ** 3. /. 27.) in
if discr <= 0.
then failwith "Not a simple curve"
else
let root = sqrt discr in
cube_root (factor +. root) +. cube_root (factor -. root)
(* Negates the point by negating y coord *)
let ec_neg : ec_point -> ec_point = function
| Inf -> Inf
| Point (x, y) -> Point (x, ~-. y)
(*** Actual task at hand ***)
(* Generates a random point in the vicinity of x=0 *)
let ec_random ({a; b} as c : ec_curve) : ec_point =
let minx = ec_minx c in
let x = Random.float (~-. minx *. 2.) +. minx in
let rhs = x ** 3. +. a *. x +. b in
Point (x, sqrt rhs)
(* Verifies that the point is on curve.
Due to rounding errors, sometimes these calculations aren't perfect.
*)
let on_curve ?(debug : bool = false) ({a; b} : ec_curve) : ec_point -> bool = function
| Inf -> true
| Point (x, y) ->
let lhs = y *. y in
let rhs = x ** 3. +. a *. x +. b in
let delta = abs_float (lhs -. rhs) in
(
if debug then Printf.printf "Delta = %.8f" delta;
delta < 0.000001
)
(* Doubles a point on the curve (adds a point to itself) *)
let ec_double ({a; b} as c : ec_curve) : ec_point -> ec_point = function
| Inf -> Inf
| Point (x, y) as p ->
if not (on_curve c p)
then failwith "Point not on this curve."
else if y = 0.
then Inf
else
let s = (3. *. x *. x +. a) /. (2. *. y) in
let x' = s *. s -. 2. *. x in
let y' = y +. s *. (x' -. x) in
Point (x', -. y')
(* Adds any two points on the curve *)
let ec_add ({a; b} as c : ec_curve) (p : ec_point) (q : ec_point) : ec_point =
match p, q with
| Inf, x | x, Inf -> x
| Point (px, py), Point (qx, qy) ->
if not (on_curve c p) || not (on_curve c q)
then failwith "Point not on this curve."
else if abs_float (px -. qx) < 0.000001 then
begin
if abs_float (py +. qy) < 0.000001
then Inf
else
(* py must equal qy here, otherwise something goes real bad *)
ec_double c p |> ec_neg
end
else
let s = (py -. qy) /. (px -. qx) in
let rx = s *. s -. px -. qx in
let ry = py +. s *. (rx -. px) in
Point (rx, -. ry)
(* Extra credit : multiplies a point by a scalar *)
let ec_mul ({a; b} as c : ec_curve) (p : ec_point) (n : int) : ec_point =
let rec helper n curPow acc =
if n = 0 then acc
else
let doubled = ec_double c curPow in
if n mod 2 = 0
then helper (n / 2) doubled acc
else helper (n / 2) doubled (ec_add c acc curPow)
in
helper n p Inf
(*** Output ***)
let string_of_point : ec_point -> string = function
| Inf -> "Zero"
| Point (x, y) -> Printf.sprintf "(%.4f, %.4f)" x y
let print_output () =
let c = { a = 0.; b = 7. } in
let p = ec_random c in
let q = ec_random c in
let r = ec_add c p q in
let t = ec_neg r in
Printf.printf "p = %s\n" (string_of_point p);
Printf.printf "q = %s\n" (string_of_point q);
Printf.printf "r = p + q = %s\n" (string_of_point r);
Printf.printf "t = -r = %s\n" (string_of_point t);
Printf.printf "r + t = %s\n" (ec_add c r t |> string_of_point);
Printf.printf "p + (q + t) = %s\n" (ec_add c q t |> ec_add c p |> string_of_point);
Printf.printf "p * 12345 = %s\n" (ec_mul c p 12345 |> string_of_point)
let _ =
print_output ();
print_output ()
|
http://rosettacode.org/wiki/Enumerations | Enumerations | Task
Create an enumeration of constants with and without explicit values.
| #M4 | M4 | define(`enums',
`define(`$2',$1)`'ifelse(eval($#>2),1,`enums(incr($1),shift(shift($@)))')')
define(`enum',
`enums(1,$@)')
enum(a,b,c,d)
`c='c |
http://rosettacode.org/wiki/Enumerations | Enumerations | Task
Create an enumeration of constants with and without explicit values.
| #Mathematica.2FWolfram_Language | Mathematica/Wolfram Language | MapIndexed[Set, {A, B, F, G}]
->{{1}, {2}, {3}, {4}}
A
->{1}
B
->{2}
G
->{4} |
http://rosettacode.org/wiki/Enumerations | Enumerations | Task
Create an enumeration of constants with and without explicit values.
| #MATLAB_.2F_Octave | MATLAB / Octave | stuff = {'apple', [1 2 3], 'cherry',1+2i}
stuff =
'apple' [1x3 double] 'cherry' [1.000000000000000 + 2.000000000000000i] |
http://rosettacode.org/wiki/Elementary_cellular_automaton/Random_Number_Generator | Elementary cellular automaton/Random Number Generator | Rule 30 is considered to be chaotic enough to generate good pseudo-random numbers. As a matter of fact, rule 30 is used by the Mathematica software for its default random number generator.
Steven Wolfram's recommendation for random number generation from rule 30 consists in extracting successive bits in a fixed position in the array of cells, as the automaton changes state.
The purpose of this task is to demonstrate this. With the code written in the parent task, which you don't need to re-write here, show the ten first bytes that emerge from this recommendation. To be precise, you will start with a state of all cells but one equal to zero, and you'll follow the evolution of the particular cell whose state was initially one. Then you'll regroup those bits by packets of eight, reconstituting bytes with the first bit being the most significant.
You can pick which ever length you want for the initial array but it should be visible in the code so that your output can be reproduced with an other language.
For extra-credits, you will make this algorithm run as fast as possible in your language, for instance with an extensive use of bitwise logic.
Reference
Cellular automata: Is Rule 30 random? (PDF).
| #Racket | Racket | #lang racket
;; below is the code from the parent task
(require "Elementary_cellular_automata.rkt")
(require racket/fixnum)
;; This is the RNG automaton
(define (CA30-random-generator
#:rule [rule 30] ; rule 30 is random, maybe you're interested in using others
;; width of the CA... this is implemented as a number of words plus,
;; maybe, another word containing the spare bits
#:bits [bits 256])
(define-values [full-words more-bits]
(quotient/remainder bits usable-bits/fixnum))
(define wrap-rule
(and (positive? more-bits) (wrap-rule-truncate-left-word more-bits)))
(define next-gen (CA-next-generation 30 #:wrap-rule wrap-rule))
(define v (make-fxvector (+ full-words (if more-bits 1 0))))
(fxvector-set! v 0 1) ; this bit will always have significance
(define (next-word)
(define-values [v+ o] (next-gen v 0))
(begin0 (fxvector-ref v 0) (set! v v+)))
(lambda (bits)
(for/fold ([acc 0]) ([_ (in-range bits)])
;; the CA is fixnum, but this function returns integers of arbitrary width
(bitwise-ior (arithmetic-shift acc 1) (bitwise-and (next-word) 1)))))
(module+ main
;; To match the other examples on this page, the automaton is 30+30+4 bits long
;; (i.e. 64 bits)
(define C30-rand-64 (CA30-random-generator #:bits 64))
;; this should be the list from "C"
(for/list ([i 10]) (C30-rand-64 8))
; we also do big numbers...
(number->string (C30-rand-64 256) 16)
(number->string (C30-rand-64 256) 16)
(number->string (C30-rand-64 256) 16)
(number->string (C30-rand-64 256) 16)) |
http://rosettacode.org/wiki/Elementary_cellular_automaton/Random_Number_Generator | Elementary cellular automaton/Random Number Generator | Rule 30 is considered to be chaotic enough to generate good pseudo-random numbers. As a matter of fact, rule 30 is used by the Mathematica software for its default random number generator.
Steven Wolfram's recommendation for random number generation from rule 30 consists in extracting successive bits in a fixed position in the array of cells, as the automaton changes state.
The purpose of this task is to demonstrate this. With the code written in the parent task, which you don't need to re-write here, show the ten first bytes that emerge from this recommendation. To be precise, you will start with a state of all cells but one equal to zero, and you'll follow the evolution of the particular cell whose state was initially one. Then you'll regroup those bits by packets of eight, reconstituting bytes with the first bit being the most significant.
You can pick which ever length you want for the initial array but it should be visible in the code so that your output can be reproduced with an other language.
For extra-credits, you will make this algorithm run as fast as possible in your language, for instance with an extensive use of bitwise logic.
Reference
Cellular automata: Is Rule 30 random? (PDF).
| #Raku | Raku | class Automaton {
has $.rule;
has @.cells;
has @.code = $!rule.fmt('%08b').flip.comb».Int;
method gist { "|{ @!cells.map({+$_ ?? '#' !! ' '}).join }|" }
method succ {
self.new: :$!rule, :@!code, :cells(
@!code[
4 «*« @!cells.rotate(-1)
»+« 2 «*« @!cells
»+« @!cells.rotate(1)
]
)
}
}
my Automaton $a .= new: :rule(30), :cells( flat 1, 0 xx 100 );
say :2[$a++.cells[0] xx 8] xx 10; |
http://rosettacode.org/wiki/Empty_string | Empty string | Languages may have features for dealing specifically with empty strings
(those containing no characters).
Task
Demonstrate how to assign an empty string to a variable.
Demonstrate how to check that a string is empty.
Demonstrate how to check that a string is not empty.
Other tasks related to string operations:
Metrics
Array length
String length
Copy a string
Empty string (assignment)
Counting
Word frequency
Letter frequency
Jewels and stones
I before E except after C
Bioinformatics/base count
Count occurrences of a substring
Count how many vowels and consonants occur in a string
Remove/replace
XXXX redacted
Conjugate a Latin verb
Remove vowels from a string
String interpolation (included)
Strip block comments
Strip comments from a string
Strip a set of characters from a string
Strip whitespace from a string -- top and tail
Strip control codes and extended characters from a string
Anagrams/Derangements/shuffling
Word wheel
ABC problem
Sattolo cycle
Knuth shuffle
Ordered words
Superpermutation minimisation
Textonyms (using a phone text pad)
Anagrams
Anagrams/Deranged anagrams
Permutations/Derangements
Find/Search/Determine
ABC words
Odd words
Word ladder
Semordnilap
Word search
Wordiff (game)
String matching
Tea cup rim text
Alternade words
Changeable words
State name puzzle
String comparison
Unique characters
Unique characters in each string
Extract file extension
Levenshtein distance
Palindrome detection
Common list elements
Longest common suffix
Longest common prefix
Compare a list of strings
Longest common substring
Find common directory path
Words from neighbour ones
Change e letters to i in words
Non-continuous subsequences
Longest common subsequence
Longest palindromic substrings
Longest increasing subsequence
Words containing "the" substring
Sum of the digits of n is substring of n
Determine if a string is numeric
Determine if a string is collapsible
Determine if a string is squeezable
Determine if a string has all unique characters
Determine if a string has all the same characters
Longest substrings without repeating characters
Find words which contains all the vowels
Find words which contains most consonants
Find words which contains more than 3 vowels
Find words which first and last three letters are equals
Find words which odd letters are consonants and even letters are vowels or vice_versa
Formatting
Substring
Rep-string
Word wrap
String case
Align columns
Literals/String
Repeat a string
Brace expansion
Brace expansion using ranges
Reverse a string
Phrase reversals
Comma quibbling
Special characters
String concatenation
Substring/Top and tail
Commatizing numbers
Reverse words in a string
Suffixation of decimal numbers
Long literals, with continuations
Numerical and alphabetical suffixes
Abbreviations, easy
Abbreviations, simple
Abbreviations, automatic
Song lyrics/poems/Mad Libs/phrases
Mad Libs
Magic 8-ball
99 Bottles of Beer
The Name Game (a song)
The Old lady swallowed a fly
The Twelve Days of Christmas
Tokenize
Text between
Tokenize a string
Word break problem
Tokenize a string with escaping
Split a character string based on change of character
Sequences
Show ASCII table
De Bruijn sequences
Self-referential sequences
Generate lower case ASCII alphabet
| #AWK | AWK | #!/usr/bin/awk -f
BEGIN {
# Demonstrate how to assign an empty string to a variable.
a="";
b="XYZ";
print "a = ",a;
print "b = ",b;
print "length(a)=",length(a);
print "length(b)=",length(b);
# Demonstrate how to check that a string is empty.
print "Is a empty ?",length(a)==0;
print "Is a not empty ?",length(a)!=0;
# Demonstrate how to check that a string is not empty.
print "Is b empty ?",length(b)==0;
print "Is b not empty ?",length(b)!=0;
} |
http://rosettacode.org/wiki/Empty_string | Empty string | Languages may have features for dealing specifically with empty strings
(those containing no characters).
Task
Demonstrate how to assign an empty string to a variable.
Demonstrate how to check that a string is empty.
Demonstrate how to check that a string is not empty.
Other tasks related to string operations:
Metrics
Array length
String length
Copy a string
Empty string (assignment)
Counting
Word frequency
Letter frequency
Jewels and stones
I before E except after C
Bioinformatics/base count
Count occurrences of a substring
Count how many vowels and consonants occur in a string
Remove/replace
XXXX redacted
Conjugate a Latin verb
Remove vowels from a string
String interpolation (included)
Strip block comments
Strip comments from a string
Strip a set of characters from a string
Strip whitespace from a string -- top and tail
Strip control codes and extended characters from a string
Anagrams/Derangements/shuffling
Word wheel
ABC problem
Sattolo cycle
Knuth shuffle
Ordered words
Superpermutation minimisation
Textonyms (using a phone text pad)
Anagrams
Anagrams/Deranged anagrams
Permutations/Derangements
Find/Search/Determine
ABC words
Odd words
Word ladder
Semordnilap
Word search
Wordiff (game)
String matching
Tea cup rim text
Alternade words
Changeable words
State name puzzle
String comparison
Unique characters
Unique characters in each string
Extract file extension
Levenshtein distance
Palindrome detection
Common list elements
Longest common suffix
Longest common prefix
Compare a list of strings
Longest common substring
Find common directory path
Words from neighbour ones
Change e letters to i in words
Non-continuous subsequences
Longest common subsequence
Longest palindromic substrings
Longest increasing subsequence
Words containing "the" substring
Sum of the digits of n is substring of n
Determine if a string is numeric
Determine if a string is collapsible
Determine if a string is squeezable
Determine if a string has all unique characters
Determine if a string has all the same characters
Longest substrings without repeating characters
Find words which contains all the vowels
Find words which contains most consonants
Find words which contains more than 3 vowels
Find words which first and last three letters are equals
Find words which odd letters are consonants and even letters are vowels or vice_versa
Formatting
Substring
Rep-string
Word wrap
String case
Align columns
Literals/String
Repeat a string
Brace expansion
Brace expansion using ranges
Reverse a string
Phrase reversals
Comma quibbling
Special characters
String concatenation
Substring/Top and tail
Commatizing numbers
Reverse words in a string
Suffixation of decimal numbers
Long literals, with continuations
Numerical and alphabetical suffixes
Abbreviations, easy
Abbreviations, simple
Abbreviations, automatic
Song lyrics/poems/Mad Libs/phrases
Mad Libs
Magic 8-ball
99 Bottles of Beer
The Name Game (a song)
The Old lady swallowed a fly
The Twelve Days of Christmas
Tokenize
Text between
Tokenize a string
Word break problem
Tokenize a string with escaping
Split a character string based on change of character
Sequences
Show ASCII table
De Bruijn sequences
Self-referential sequences
Generate lower case ASCII alphabet
| #Axe | Axe | ""→Str1
!If length(Str1)
Disp "EMPTY",i
Else
Disp "NOT EMPTY",i
End |
http://rosettacode.org/wiki/Empty_directory | Empty directory | Starting with a path to some directory, determine whether the directory is empty.
An empty directory contains no files nor subdirectories.
With Unix or Windows systems, every directory contains an entry for “.” and almost every directory contains “..” (except for a root directory); an empty directory contains no other entries.
| #Go | Go | package main
import (
"fmt"
"io/ioutil"
"log"
)
func main() {
empty, err := IsEmptyDir("/tmp")
if err != nil {
log.Fatalln(err)
}
if empty {
fmt.Printf("/tmp is empty\n")
} else {
fmt.Printf("/tmp is not empty\n")
}
}
func IsEmptyDir(name string) (bool, error) {
entries, err := ioutil.ReadDir(name)
if err != nil {
return false, err
}
return len(entries) == 0, nil
}
|
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