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http://rosettacode.org/wiki/Apply_a_callback_to_an_array | Apply a callback to an array | Task
Take a combined set of elements and apply a function to each element.
| #Clean | Clean | square x = x * x
values :: {#Int}
values = {x \\ x <- [1 .. 10]} |
http://rosettacode.org/wiki/Averages/Mode | Averages/Mode | Task[edit]
Write a program to find the mode value of a collection.
The case where the collection is empty may be ignored. Care must be taken to handle the case where the mode is non-unique.
If it is not appropriate or possible to support a general collection, use a vector (array), if possible. If it is not appropriate or possible to support an unspecified value type, use integers.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Octave | Octave | function m = mode2(v)
sv = sort(v);
% build two vectors, vals and c, so that
% c(i) holds how many times vals(i) appears
i = 1; c = []; vals = [];
while (i <= numel(v) )
tc = sum(sv==sv(i)); % it would be faster to count
% them "by hand", since sv is sorted...
c = [c, tc];
vals = [vals, sv(i)];
i += tc;
endwhile
% stack vals and c building a 2-rows matrix x
x = cat(1,vals,c);
% sort the second row (frequencies) into t (most frequent
% first) and take the "original indices" i ...
[t, i] = sort(x(2,:), "descend");
% ... so that we can use them to sort columns according
% to frequencies
nv = x(1,i);
% at last, collect into m (the result) all the values
% having the same bigger frequency
r = t(1); i = 1;
m = [];
while ( t(i) == r )
m = [m, nv(i)];
i++;
endwhile
endfunction |
http://rosettacode.org/wiki/Associative_array/Iteration | Associative array/Iteration | Show how to iterate over the key-value pairs of an associative array, and print each pair out.
Also show how to iterate just over the keys, or the values, if there is a separate way to do that in your language.
See also
Array
Associative array: Creation, Iteration
Collections
Compound data type
Doubly-linked list: Definition, Element definition, Element insertion, List Traversal, Element Removal
Linked list
Queue: Definition, Usage
Set
Singly-linked list: Element definition, Element insertion, List Traversal, Element Removal
Stack
| #D | D | import std.stdio: writeln;
void main() {
// the associative array
auto aa = ["alice":2, "bob":97, "charlie":45];
// how to iterate key/value pairs:
foreach (key, value; aa)
writeln("1) Got key ", key, " with value ", value);
writeln();
// how to iterate the keys:
foreach (key, _; aa)
writeln("2) Got key ", key);
writeln();
// how to iterate the values:
foreach (value; aa)
writeln("3) Got value ", value);
writeln();
// how to extract the values, lazy:
foreach (value; aa.byValue())
writeln("4) Got value ", value);
writeln();
// how to extract the keys, lazy:
foreach (key; aa.byKey())
writeln("5) Got key ", key);
writeln();
// how to extract all the keys:
foreach (key; aa.keys)
writeln("6) Got key ", key);
writeln();
// how to extract all the values:
foreach (value; aa.values)
writeln("7) Got value ", value);
} |
http://rosettacode.org/wiki/Apply_a_digital_filter_(direct_form_II_transposed) | Apply a digital filter (direct form II transposed) | Digital filters are used to apply a mathematical operation to a sampled signal. One of the common formulations is the "direct form II transposed" which can represent both infinite impulse response (IIR) and finite impulse response (FIR) filters, as well as being more numerically stable than other forms. [1]
Task
Filter a signal using an order 3 low-pass Butterworth filter. The coefficients for the filter are a=[1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17] and b = [0.16666667, 0.5, 0.5, 0.16666667]
The signal that needs filtering is the following vector: [-0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412, -0.662370894973, -1.00700480494, -0.404707073677 ,0.800482325044, 0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195, 0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293, 0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589]
| #Mathematica.2FWolfram_Language | Mathematica/Wolfram Language | b = {0.16666667, 0.5, 0.5, 0.16666667};
a = {1.00000000, -2.77555756*^-16, 3.33333333*^-01, -1.85037171*^-17};
signal = {-0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412, -0.662370894973, -1.00700480494, -0.404707073677, 0.800482325044, 0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195, 0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293, 0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589};
RecurrenceFilter[{a, b}, signal] |
http://rosettacode.org/wiki/Apply_a_digital_filter_(direct_form_II_transposed) | Apply a digital filter (direct form II transposed) | Digital filters are used to apply a mathematical operation to a sampled signal. One of the common formulations is the "direct form II transposed" which can represent both infinite impulse response (IIR) and finite impulse response (FIR) filters, as well as being more numerically stable than other forms. [1]
Task
Filter a signal using an order 3 low-pass Butterworth filter. The coefficients for the filter are a=[1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17] and b = [0.16666667, 0.5, 0.5, 0.16666667]
The signal that needs filtering is the following vector: [-0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412, -0.662370894973, -1.00700480494, -0.404707073677 ,0.800482325044, 0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195, 0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293, 0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589]
| #MATLAB | MATLAB |
signal = [-0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412, -0.662370894973, -1.00700480494, -0.404707073677 ,0.800482325044, 0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195, 0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293, 0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589];
a = [1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17];
b = [0.16666667, 0.5, 0.5, 0.16666667];
out = filter(b,a,signal)
figure
subplot(1,2,1)
stem(0:19, signal)
xlabel('n')
title('Original Signal')
subplot(1,2,2)
stem(0:19, out)
xlabel('n')
title('Filtered Signal')
|
http://rosettacode.org/wiki/Averages/Arithmetic_mean | Averages/Arithmetic mean | Task[edit]
Write a program to find the mean (arithmetic average) of a numeric vector.
In case of a zero-length input, since the mean of an empty set of numbers is ill-defined, the program may choose to behave in any way it deems appropriate, though if the programming language has an established convention for conveying math errors or undefined values, it's preferable to follow it.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Dyalect | Dyalect | func avg(args...) {
var acc = .0
var len = 0
for x in args {
len += 1
acc += x
}
acc / len
}
avg(1, 2, 3, 4, 5, 6) |
http://rosettacode.org/wiki/Averages/Arithmetic_mean | Averages/Arithmetic mean | Task[edit]
Write a program to find the mean (arithmetic average) of a numeric vector.
In case of a zero-length input, since the mean of an empty set of numbers is ill-defined, the program may choose to behave in any way it deems appropriate, though if the programming language has an established convention for conveying math errors or undefined values, it's preferable to follow it.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #E | E | def meanOrZero(numbers) {
var count := 0
var sum := 0
for x in numbers {
sum += x
count += 1
}
return sum / 1.max(count)
} |
http://rosettacode.org/wiki/Associative_array/Merging | Associative array/Merging | Task
Define two associative arrays, where one represents the following "base" data:
Key
Value
"name"
"Rocket Skates"
"price"
12.75
"color"
"yellow"
And the other represents "update" data:
Key
Value
"price"
15.25
"color"
"red"
"year"
1974
Merge these into a new associative array that contains every key found in either of the source ones. Each key should map to the value in the second (update) table if that exists, or else to the value in the first (base) table. If possible, do this in a way that does not mutate the original two associative arrays. Obviously this should be done in a way that would work for any data, not just the specific data given here, but in this example the result should be:
Key
Value
"name"
"Rocket Skates"
"price"
15.25
"color"
"red"
"year"
1974
| #Tcl | Tcl | set dict1 [dict create name "Rocket Skates" price 12.75 color yellow]
set dict2 [dict create price 15.25 color red year 1974]
dict for {key val} [dict merge $dict1 $dict2] {
puts "$key: $val"
} |
http://rosettacode.org/wiki/Associative_array/Merging | Associative array/Merging | Task
Define two associative arrays, where one represents the following "base" data:
Key
Value
"name"
"Rocket Skates"
"price"
12.75
"color"
"yellow"
And the other represents "update" data:
Key
Value
"price"
15.25
"color"
"red"
"year"
1974
Merge these into a new associative array that contains every key found in either of the source ones. Each key should map to the value in the second (update) table if that exists, or else to the value in the first (base) table. If possible, do this in a way that does not mutate the original two associative arrays. Obviously this should be done in a way that would work for any data, not just the specific data given here, but in this example the result should be:
Key
Value
"name"
"Rocket Skates"
"price"
15.25
"color"
"red"
"year"
1974
| #VBA | VBA |
Private Type Associative
Key As String
Value As Variant
End Type
Sub Main_Array_Associative()
Dim BaseArray(2) As Associative, UpdateArray(2) As Associative
FillArrays BaseArray, UpdateArray
ReDim Result(UBound(BaseArray)) As Associative
MergeArray Result, BaseArray, UpdateArray
PrintOut Result
End Sub
Private Sub MergeArray(Res() As Associative, Base() As Associative, Update() As Associative)
Dim i As Long, Respons As Long
Res = Base
For i = LBound(Update) To UBound(Update)
If Exist(Respons, Base, Update(i).Key) Then
Res(Respons).Value = Update(i).Value
Else
ReDim Preserve Res(UBound(Res) + 1)
Res(UBound(Res)).Key = Update(i).Key
Res(UBound(Res)).Value = Update(i).Value
End If
Next
End Sub
Private Function Exist(R As Long, B() As Associative, K As String) As Boolean
Dim i As Long
Do
If B(i).Key = K Then
Exist = True
R = i
End If
i = i + 1
Loop While i <= UBound(B) And Not Exist
End Function
Private Sub FillArrays(B() As Associative, U() As Associative)
B(0).Key = "name"
B(0).Value = "Rocket Skates"
B(1).Key = "price"
B(1).Value = 12.75
B(2).Key = "color"
B(2).Value = "yellow"
U(0).Key = "price"
U(0).Value = 15.25
U(1).Key = "color"
U(1).Value = "red"
U(2).Key = "year"
U(2).Value = 1974
End Sub
Private Sub PrintOut(A() As Associative)
Dim i As Long
Debug.Print "Key", "Value"
For i = LBound(A) To UBound(A)
Debug.Print A(i).Key, A(i).Value
Next i
Debug.Print "-----------------------------"
End Sub |
http://rosettacode.org/wiki/Average_loop_length | Average loop length | Let f be a uniformly-randomly chosen mapping from the numbers 1..N to the numbers 1..N (note: not necessarily a permutation of 1..N; the mapping could produce a number in more than one way or not at all). At some point, the sequence 1, f(1), f(f(1))... will contain a repetition, a number that occurring for the second time in the sequence.
Task
Write a program or a script that estimates, for each N, the average length until the first such repetition.
Also calculate this expected length using an analytical formula, and optionally compare the simulated result with the theoretical one.
This problem comes from the end of Donald Knuth's Christmas tree lecture 2011.
Example of expected output:
N average analytical (error)
=== ========= ============ =========
1 1.0000 1.0000 ( 0.00%)
2 1.4992 1.5000 ( 0.05%)
3 1.8784 1.8889 ( 0.56%)
4 2.2316 2.2188 ( 0.58%)
5 2.4982 2.5104 ( 0.49%)
6 2.7897 2.7747 ( 0.54%)
7 3.0153 3.0181 ( 0.09%)
8 3.2429 3.2450 ( 0.07%)
9 3.4536 3.4583 ( 0.14%)
10 3.6649 3.6602 ( 0.13%)
11 3.8091 3.8524 ( 1.12%)
12 3.9986 4.0361 ( 0.93%)
13 4.2074 4.2123 ( 0.12%)
14 4.3711 4.3820 ( 0.25%)
15 4.5275 4.5458 ( 0.40%)
16 4.6755 4.7043 ( 0.61%)
17 4.8877 4.8579 ( 0.61%)
18 4.9951 5.0071 ( 0.24%)
19 5.1312 5.1522 ( 0.41%)
20 5.2699 5.2936 ( 0.45%)
| #Ruby | Ruby | class Integer
def factorial
self == 0 ? 1 : (1..self).inject(:*)
end
end
def rand_until_rep(n)
rands = {}
loop do
r = rand(1..n)
return rands.size if rands[r]
rands[r] = true
end
end
runs = 1_000_000
puts " N average exp. diff ",
"=== ======== ======== ==========="
(1..20).each do |n|
sum_of_runs = runs.times.inject(0){|sum, _| sum += rand_until_rep(n)}
avg = sum_of_runs / runs.to_f
analytical = (1..n).inject(0){|sum, i| sum += (n.factorial / (n**i).to_f / (n-i).factorial)}
puts "%3d %8.4f %8.4f (%8.4f%%)" % [n, avg, analytical, (avg/analytical - 1)*100]
end |
http://rosettacode.org/wiki/Average_loop_length | Average loop length | Let f be a uniformly-randomly chosen mapping from the numbers 1..N to the numbers 1..N (note: not necessarily a permutation of 1..N; the mapping could produce a number in more than one way or not at all). At some point, the sequence 1, f(1), f(f(1))... will contain a repetition, a number that occurring for the second time in the sequence.
Task
Write a program or a script that estimates, for each N, the average length until the first such repetition.
Also calculate this expected length using an analytical formula, and optionally compare the simulated result with the theoretical one.
This problem comes from the end of Donald Knuth's Christmas tree lecture 2011.
Example of expected output:
N average analytical (error)
=== ========= ============ =========
1 1.0000 1.0000 ( 0.00%)
2 1.4992 1.5000 ( 0.05%)
3 1.8784 1.8889 ( 0.56%)
4 2.2316 2.2188 ( 0.58%)
5 2.4982 2.5104 ( 0.49%)
6 2.7897 2.7747 ( 0.54%)
7 3.0153 3.0181 ( 0.09%)
8 3.2429 3.2450 ( 0.07%)
9 3.4536 3.4583 ( 0.14%)
10 3.6649 3.6602 ( 0.13%)
11 3.8091 3.8524 ( 1.12%)
12 3.9986 4.0361 ( 0.93%)
13 4.2074 4.2123 ( 0.12%)
14 4.3711 4.3820 ( 0.25%)
15 4.5275 4.5458 ( 0.40%)
16 4.6755 4.7043 ( 0.61%)
17 4.8877 4.8579 ( 0.61%)
18 4.9951 5.0071 ( 0.24%)
19 5.1312 5.1522 ( 0.41%)
20 5.2699 5.2936 ( 0.45%)
| #Rust | Rust | extern crate rand;
use rand::{ThreadRng, thread_rng};
use rand::distributions::{IndependentSample, Range};
use std::collections::HashSet;
use std::env;
use std::process;
fn help() {
println!("usage: average_loop_length <max_N> <trials>");
}
fn main() {
let args: Vec<String> = env::args().collect();
let mut max_n: u32 = 20;
let mut trials: u32 = 1000;
match args.len() {
1 => {}
3 => {
max_n = args[1].parse::<u32>().unwrap();
trials = args[2].parse::<u32>().unwrap();
}
_ => {
help();
process::exit(0);
}
}
let mut rng = thread_rng();
println!(" N average analytical (error)");
println!("=== ========= ============ =========");
for n in 1..(max_n + 1) {
let the_analytical = analytical(n);
let the_empirical = empirical(n, trials, &mut rng);
println!(" {:>2} {:3.4} {:3.4} ( {:>+1.2}%)",
n,
the_empirical,
the_analytical,
100f64 * (the_empirical / the_analytical - 1f64));
}
}
fn factorial(n: u32) -> f64 {
(1..n + 1).fold(1f64, |p, n| p * n as f64)
}
fn analytical(n: u32) -> f64 {
let sum: f64 = (1..(n + 1))
.map(|i| factorial(n) / (n as f64).powi(i as i32) / factorial(n - i))
.fold(0f64, |a, v| a + v);
sum
}
fn empirical(n: u32, trials: u32, rng: &mut ThreadRng) -> f64 {
let sum: f64 = (0..trials)
.map(|_t| {
let mut item = 1u32;
let mut seen = HashSet::new();
let range = Range::new(1u32, n + 1);
for step in 0..n {
if seen.contains(&item) {
return step as f64;
}
seen.insert(item);
item = range.ind_sample(rng);
}
n as f64
})
.fold(0f64, |a, v| a + v);
sum / trials as f64
}
|
http://rosettacode.org/wiki/Averages/Simple_moving_average | Averages/Simple moving average | Computing the simple moving average of a series of numbers.
Task[edit]
Create a stateful function/class/instance that takes a period and returns a routine that takes a number as argument and returns a simple moving average of its arguments so far.
Description
A simple moving average is a method for computing an average of a stream of numbers by only averaging the last P numbers from the stream, where P is known as the period.
It can be implemented by calling an initialing routine with P as its argument, I(P), which should then return a routine that when called with individual, successive members of a stream of numbers, computes the mean of (up to), the last P of them, lets call this SMA().
The word stateful in the task description refers to the need for SMA() to remember certain information between calls to it:
The period, P
An ordered container of at least the last P numbers from each of its individual calls.
Stateful also means that successive calls to I(), the initializer, should return separate routines that do not share saved state so they could be used on two independent streams of data.
Pseudo-code for an implementation of SMA is:
function SMA(number: N):
stateful integer: P
stateful list: stream
number: average
stream.append_last(N)
if stream.length() > P:
# Only average the last P elements of the stream
stream.delete_first()
if stream.length() == 0:
average = 0
else:
average = sum( stream.values() ) / stream.length()
return average
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Smalltalk | Smalltalk | Object subclass: MovingAverage [
|valueCollection period collectedNumber sum|
MovingAverage class >> newWithPeriod: thePeriod [
|r|
r := super basicNew.
^ r initWithPeriod: thePeriod
]
initWithPeriod: thePeriod [
valueCollection := OrderedCollection new: thePeriod.
period := thePeriod.
collectedNumber := 0.
sum := 0
]
sma [ collectedNumber < period
ifTrue: [ ^ sum / collectedNumber ]
ifFalse: [ ^ sum / period ] ]
add: value [
collectedNumber < period
ifTrue: [
sum := sum + value.
valueCollection add: value.
collectedNumber := collectedNumber + 1.
]
ifFalse: [
sum := sum - (valueCollection removeFirst).
sum := sum + value.
valueCollection add: value
].
^ self sma
]
]. |
http://rosettacode.org/wiki/Attractive_numbers | Attractive numbers | A number is an attractive number if the number of its prime factors (whether distinct or not) is also prime.
Example
The number 20, whose prime decomposition is 2 × 2 × 5, is an attractive number because the number of its prime factors (3) is also prime.
Task
Show sequence items up to 120.
Reference
The OEIS entry: A063989: Numbers with a prime number of prime divisors.
| #Lua | Lua | -- Returns true if x is prime, and false otherwise
function isPrime (x)
if x < 2 then return false end
if x < 4 then return true end
if x % 2 == 0 then return false end
for d = 3, math.sqrt(x), 2 do
if x % d == 0 then return false end
end
return true
end
-- Compute the prime factors of n
function factors (n)
local facList, divisor, count = {}, 1
if n < 2 then return facList end
while not isPrime(n) do
while not isPrime(divisor) do divisor = divisor + 1 end
count = 0
while n % divisor == 0 do
n = n / divisor
table.insert(facList, divisor)
end
divisor = divisor + 1
if n == 1 then return facList end
end
table.insert(facList, n)
return facList
end
-- Main procedure
for i = 1, 120 do
if isPrime(#factors(i)) then io.write(i .. "\t") end
end |
http://rosettacode.org/wiki/Averages/Mean_time_of_day | Averages/Mean time of day | Task[edit]
A particular activity of bats occurs at these times of the day:
23:00:17, 23:40:20, 00:12:45, 00:17:19
Using the idea that there are twenty-four hours in a day,
which is analogous to there being 360 degrees in a circle,
map times of day to and from angles;
and using the ideas of Averages/Mean angle
compute and show the average time of the nocturnal activity
to an accuracy of one second of time.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #PHP | PHP |
<?php
function time2ang($tim) {
if (!is_string($tim)) return $tim;
$parts = explode(':',$tim);
if (count($parts)!=3) return $tim;
$sec = ($parts[0]*3600)+($parts[1]*60)+$parts[2];
$ang = 360.0 * ($sec/86400.0);
return $ang;
}
function ang2time($ang) {
if (!is_numeric($ang)) return $ang;
$sec = 86400.0 * $ang / 360.0;
$parts = array(floor($sec/3600),floor(($sec % 3600)/60),$sec % 60);
$tim = sprintf('%02d:%02d:%02d',$parts[0],$parts[1],$parts[2]);
return $tim;
}
function meanang($ang) {
if (!is_array($ang)) return $ang;
$sins = 0.0;
$coss = 0.0;
foreach($ang as $a) {
$sins += sin(deg2rad($a));
$coss += cos(deg2rad($a));
}
$avgsin = $sins / (0.0+count($ang));
$avgcos = $coss / (0.0+count($ang));
$avgang = rad2deg(atan2($avgsin,$avgcos));
while ($avgang < 0.0) $avgang += 360.0;
return $avgang;
}
$bats = array('23:00:17','23:40:20','00:12:45','00:17:19');
$angs = array();
foreach ($bats as $t) $angs[] = time2ang($t);
$ma = meanang($angs);
$result = ang2time($ma);
print "The mean time of day is $result (angle $ma).\n";
?>
|
http://rosettacode.org/wiki/AVL_tree | AVL tree |
This page uses content from Wikipedia. The original article was at AVL tree. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
In computer science, an AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; at no time do they differ by more than one because rebalancing is done ensure this is the case. Lookup, insertion, and deletion all take O(log n) time in both the average and worst cases, where n is the number of nodes in the tree prior to the operation. Insertions and deletions may require the tree to be rebalanced by one or more tree rotations. Note the tree of nodes comprise a set, so duplicate node keys are not allowed.
AVL trees are often compared with red-black trees because they support the same set of operations and because red-black trees also take O(log n) time for the basic operations. Because AVL trees are more rigidly balanced, they are faster than red-black trees for lookup-intensive applications. Similar to red-black trees, AVL trees are height-balanced, but in general not weight-balanced nor μ-balanced; that is, sibling nodes can have hugely differing numbers of descendants.
Task
Implement an AVL tree in the language of choice, and provide at least basic operations.
| #Scheme | Scheme | (cond-expand
(r7rs)
(chicken (import r7rs)))
(define-library (avl-trees)
;;
;; This library implements ‘persistent’ (that is, ‘immutable’) AVL
;; trees for R7RS Scheme.
;;
;; Included are generators of the key-data pairs in a tree. Because
;; the trees are persistent (‘immutable’), these generators are safe
;; from alterations of the tree.
;;
;; References:
;;
;; * Niklaus Wirth, 1976. Algorithms + Data Structures =
;; Programs. Prentice-Hall, Englewood Cliffs, New Jersey.
;;
;; * Niklaus Wirth, 2004. Algorithms and Data Structures. Updated
;; by Fyodor Tkachov, 2014.
;;
;; Note that the references do not discuss persistent
;; implementations. It seems worthwhile to compare the methods of
;; implementation.
;;
(export avl)
(export alist->avl)
(export avl->alist)
(export avl?)
(export avl-empty?)
(export avl-size)
(export avl-insert)
(export avl-delete)
(export avl-delete-values)
(export avl-has-key?)
(export avl-search)
(export avl-search-values)
(export avl-make-generator)
(export avl-pretty-print)
(export avl-check-avl-condition)
(export avl-check-usage)
(import (scheme base))
(import (scheme case-lambda))
(import (scheme process-context))
(import (scheme write))
(cond-expand
(chicken
(import (only (chicken base) define-record-printer))
(import (only (chicken format) format))) ; For debugging.
(else))
(begin
;; - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
;;
;; Tools for making generators. These use call/cc and so might be
;; inefficient in your Scheme. I am using CHICKEN, in which
;; call/cc is not so inefficient.
;;
;; Often I have made &fail a unique object rather than #f, but in
;; this case #f will suffice.
;;
(define &fail #f)
(define *suspend*
(make-parameter (lambda (x) x)))
(define (suspend v)
((*suspend*) v))
(define (fail-forever)
(let loop ()
(suspend &fail)
(loop)))
(define (make-generator-procedure thunk)
;; Make a suspendable procedure that takes no arguments. The
;; result is a simple generator of values. (This can be
;; elaborated upon for generators to take values on resumption,
;; in the manner of Icon co-expressions.)
(define (next-run return)
(define (my-suspend v)
(set! return (call/cc (lambda (resumption-point)
(set! next-run resumption-point)
(return v)))))
(parameterize ((*suspend* my-suspend))
(suspend (thunk))
(fail-forever)))
(lambda () (call/cc next-run)))
;; - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
(define-syntax avl-check-usage
(syntax-rules ()
((_ pred msg)
(or pred (usage-error msg)))))
;; - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
(define-record-type <avl>
(%avl key data bal left right)
avl?
(key %key)
(data %data)
(bal %bal)
(left %left)
(right %right))
(cond-expand
(chicken (define-record-printer (<avl> rt out)
(display "#<avl " out)
(display (%key rt) out)
(display " " out)
(display (%data rt) out)
(display " " out)
(display (%bal rt) out)
(display " " out)
(display (%left rt) out)
(display " " out)
(display (%right rt) out)
(display ">" out)))
(else))
;; - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
(define avl
(case-lambda
(() (%avl #f #f #f #f #f))
((pred<? . args) (alist->avl pred<? args))))
(define (avl-empty? tree)
(avl-check-usage
(avl? tree)
"avl-empty? expects an AVL tree as argument")
(not (%bal tree)))
(define (avl-size tree)
(define (traverse p sz)
(if (not p)
sz
(traverse (%left p) (traverse (%right p) (+ sz 1)))))
(if (avl-empty? tree)
0
(traverse tree 0)))
(define (avl-has-key? pred<? tree key)
(define (search p)
(and p
(let ((k (%key p)))
(cond ((pred<? key k) (search (%left p)))
((pred<? k key) (search (%right p)))
(else #t)))))
(avl-check-usage
(procedure? pred<?)
"avl-has-key? expects a procedure as first argument")
(and (not (avl-empty? tree))
(search tree)))
(define (avl-search pred<? tree key)
;; Return the data matching a key, or #f if the key is not
;; found. (Note that the data matching the key might be #f.)
(define (search p)
(and p
(let ((k (%key p)))
(cond ((pred<? key k) (search (%left p)))
((pred<? k key) (search (%right p)))
(else (%data p))))))
(avl-check-usage
(procedure? pred<?)
"avl-search expects a procedure as first argument")
(and (not (avl-empty? tree))
(search tree)))
(define (avl-search-values pred<? tree key)
;; Return two values: the data matching the key, or #f is the
;; key is not found; and a second value that is either #f or #t,
;; depending on whether the key is found.
(define (search p)
(if (not p)
(values #f #f)
(let ((k (%key p)))
(cond ((pred<? key k) (search (%left p)))
((pred<? k key) (search (%right p)))
(else (values (%data p) #t))))))
(avl-check-usage
(procedure? pred<?)
"avl-search-values expects a procedure as first argument")
(if (avl-empty? tree)
(values #f #f)
(search tree)))
(define (alist->avl pred<? alst)
;; Go from association list to AVL tree.
(avl-check-usage
(procedure? pred<?)
"alist->avl expects a procedure as first argument")
(let loop ((tree (avl))
(lst alst))
(if (null? lst)
tree
(let ((head (car lst)))
(loop (avl-insert pred<? tree (car head) (cdr head))
(cdr lst))))))
(define (avl->alist tree)
;; Go from AVL tree to association list. The output will be in
;; order.
(define (traverse p lst)
;; Reverse in-order traversal of the tree, to produce an
;; in-order cons-list.
(if (not p)
lst
(traverse (%left p) (cons (cons (%key p) (%data p))
(traverse (%right p) lst)))))
(if (avl-empty? tree)
'()
(traverse tree '())))
(define (avl-insert pred<? tree key data)
(define (search p fix-balance?)
(cond
((not p)
;; The key was not found. Make a new node and set
;; fix-balance?
(values (%avl key data 0 #f #f) #t))
((pred<? key (%key p))
;; Continue searching.
(let-values (((p1 fix-balance?)
(search (%left p) fix-balance?)))
(cond
((not fix-balance?)
(let ((p^ (%avl (%key p) (%data p) (%bal p)
p1 (%right p))))
(values p^ #f)))
(else
;; A new node has been inserted on the left side.
(case (%bal p)
((1)
(let ((p^ (%avl (%key p) (%data p) 0
p1 (%right p))))
(values p^ #f)))
((0)
(let ((p^ (%avl (%key p) (%data p) -1
p1 (%right p))))
(values p^ fix-balance?)))
((-1)
;; Rebalance.
(case (%bal p1)
((-1)
;; A single LL rotation.
(let* ((p^ (%avl (%key p) (%data p) 0
(%right p1) (%right p)))
(p1^ (%avl (%key p1) (%data p1) 0
(%left p1) p^)))
(values p1^ #f)))
((0 1)
;; A double LR rotation.
(let* ((p2 (%right p1))
(bal2 (%bal p2))
(p^ (%avl (%key p) (%data p)
(- (min bal2 0))
(%right p2) (%right p)))
(p1^ (%avl (%key p1) (%data p1)
(- (max bal2 0))
(%left p1) (%left p2)))
(p2^ (%avl (%key p2) (%data p2) 0
p1^ p^)))
(values p2^ #f)))
(else (internal-error))))
(else (internal-error)))))))
((pred<? (%key p) key)
;; Continue searching.
(let-values (((p1 fix-balance?)
(search (%right p) fix-balance?)))
(cond
((not fix-balance?)
(let ((p^ (%avl (%key p) (%data p) (%bal p)
(%left p) p1)))
(values p^ #f)))
(else
;; A new node has been inserted on the right side.
(case (%bal p)
((-1)
(let ((p^ (%avl (%key p) (%data p) 0
(%left p) p1)))
(values p^ #f)))
((0)
(let ((p^ (%avl (%key p) (%data p) 1
(%left p) p1)))
(values p^ fix-balance?)))
((1)
;; Rebalance.
(case (%bal p1)
((1)
;; A single RR rotation.
(let* ((p^ (%avl (%key p) (%data p) 0
(%left p) (%left p1)))
(p1^ (%avl (%key p1) (%data p1) 0
p^ (%right p1))))
(values p1^ #f)))
((-1 0)
;; A double RL rotation.
(let* ((p2 (%left p1))
(bal2 (%bal p2))
(p^ (%avl (%key p) (%data p)
(- (max bal2 0))
(%left p) (%left p2)))
(p1^ (%avl (%key p1) (%data p1)
(- (min bal2 0))
(%right p2) (%right p1)))
(p2^ (%avl (%key p2) (%data p2) 0
p^ p1^)))
(values p2^ #f)))
(else (internal-error))))
(else (internal-error)))))))
(else
;; The key was found; p is an existing node.
(values (%avl key data (%bal p) (%left p) (%right p))
#f))))
(avl-check-usage
(procedure? pred<?)
"avl-insert expects a procedure as first argument")
(if (avl-empty? tree)
(%avl key data 0 #f #f)
(let-values (((p fix-balance?) (search tree #f)))
p)))
(define (avl-delete pred<? tree key)
;; If one is not interested in whether the key was in the tree,
;; then throw away that information.
(let-values (((tree had-key?)
(avl-delete-values pred<? tree key)))
tree))
(define (balance-for-shrunken-left p)
;; Returns two values: a new p and a new fix-balance?
(case (%bal p)
((-1) (values (%avl (%key p) (%data p) 0
(%left p) (%right p))
#t))
((0) (values (%avl (%key p) (%data p) 1
(%left p) (%right p))
#f))
((1)
;; Rebalance.
(let* ((p1 (%right p))
(bal1 (%bal p1)))
(case bal1
((0)
;; A single RR rotation.
(let* ((p^ (%avl (%key p) (%data p) 1
(%left p) (%left p1)))
(p1^ (%avl (%key p1) (%data p1) -1
p^ (%right p1))))
(values p1^ #f)))
((1)
;; A single RR rotation.
(let* ((p^ (%avl (%key p) (%data p) 0
(%left p) (%left p1)))
(p1^ (%avl (%key p1) (%data p1) 0
p^ (%right p1))))
(values p1^ #t)))
((-1)
;; A double RL rotation.
(let* ((p2 (%left p1))
(bal2 (%bal p2))
(p^ (%avl (%key p) (%data p) (- (max bal2 0))
(%left p) (%left p2)))
(p1^ (%avl (%key p1) (%data p1) (- (min bal2 0))
(%right p2) (%right p1)))
(p2^ (%avl (%key p2) (%data p2) 0 p^ p1^)))
(values p2^ #t)))
(else (internal-error)))))
(else (internal-error))))
(define (balance-for-shrunken-right p)
;; Returns two values: a new p and a new fix-balance?
(case (%bal p)
((1) (values (%avl (%key p) (%data p) 0
(%left p) (%right p))
#t))
((0) (values (%avl (%key p) (%data p) -1
(%left p) (%right p))
#f))
((-1)
;; Rebalance.
(let* ((p1 (%left p))
(bal1 (%bal p1)))
(case bal1
((0)
;; A single LL rotation.
(let* ((p^ (%avl (%key p) (%data p) -1
(%right p1) (%right p)))
(p1^ (%avl (%key p1) (%data p1) 1
(%left p1) p^)))
(values p1^ #f)))
((-1)
;; A single LL rotation.
(let* ((p^ (%avl (%key p) (%data p) 0
(%right p1) (%right p)))
(p1^ (%avl (%key p1) (%data p1) 0
(%left p1) p^)))
(values p1^ #t)))
((1)
;; A double LR rotation.
(let* ((p2 (%right p1))
(bal2 (%bal p2))
(p^ (%avl (%key p) (%data p) (- (min bal2 0))
(%right p2) (%right p)))
(p1^ (%avl (%key p1) (%data p1) (- (max bal2 0))
(%left p1) (%left p2)))
(p2^ (%avl (%key p2) (%data p2) 0 p1^ p^)))
(values p2^ #t)))
(else (internal-error)))))
(else (internal-error))))
(define (avl-delete-values pred<? tree key)
(define-syntax balance-L
(syntax-rules ()
((_ p fix-balance?)
(if fix-balance?
(balance-for-shrunken-left p)
(values p #f)))))
(define-syntax balance-R
(syntax-rules ()
((_ p fix-balance?)
(if fix-balance?
(balance-for-shrunken-right p)
(values p #f)))))
(define (del r fix-balance?)
;; Returns a new r, a new fix-balance?, and key and data to be
;; ‘moved up the tree’.
(if (%right r)
(let*-values
(((q fix-balance? key^ data^)
(del (%right r) fix-balance?))
((r fix-balance?)
(balance-R (%avl (%key r) (%data r) (%bal r)
(%left r) q)
fix-balance?)))
(values r fix-balance? key^ data^))
(values (%left r) #t (%key r) (%data r))))
(define (search p fix-balance?)
;; Return three values: a new p, a new fix-balance, and
;; whether the key was found.
(cond
((not p) (values #f #f #f))
((pred<? key (%key p))
;; Recursive search down the left branch.
(let*-values
(((q fix-balance? found?)
(search (%left p) fix-balance?))
((p fix-balance?)
(balance-L (%avl (%key p) (%data p) (%bal p)
q (%right p))
fix-balance?)))
(values p fix-balance? found?)))
((pred<? (%key p) key)
;; Recursive search down the right branch.
(let*-values
(((q fix-balance? found?)
(search (%right p) fix-balance?))
((p fix-balance?)
(balance-R (%avl (%key p) (%data p) (%bal p)
(%left p) q)
fix-balance?)))
(values p fix-balance? found?)))
((not (%right p))
;; Delete p, replace it with its left branch, then
;; rebalance.
(values (%left p) #t #t))
((not (%left p))
;; Delete p, replace it with its right branch, then
;; rebalance.
(values (%right p) #t #t))
(else
;; Delete p, but it has both left and right branches,
;; and therefore may have complicated branch structure.
(let*-values
(((q fix-balance? key^ data^)
(del (%left p) fix-balance?))
((p fix-balance?)
(balance-L (%avl key^ data^ (%bal p) q (%right p))
fix-balance?)))
(values p fix-balance? #t)))))
(avl-check-usage
(procedure? pred<?)
"avl-delete-values expects a procedure as first argument")
(if (avl-empty? tree)
(values tree #f)
(let-values (((tree fix-balance? found?)
(search tree #f)))
(if found?
(values (or tree (avl)) #t)
(values tree #f)))))
(define avl-make-generator
(case-lambda
((tree) (avl-make-generator tree 1))
((tree direction)
(if (negative? direction)
(make-generator-procedure
(lambda ()
(define (traverse p)
(unless (or (not p) (avl-empty? p))
(traverse (%right p))
(suspend (cons (%key p) (%data p)))
(traverse (%left p)))
&fail)
(traverse tree)))
(make-generator-procedure
(lambda ()
(define (traverse p)
(unless (or (not p) (avl-empty? p))
(traverse (%left p))
(suspend (cons (%key p) (%data p)))
(traverse (%right p)))
&fail)
(traverse tree)))))))
(define avl-pretty-print
(case-lambda
((tree)
(avl-pretty-print tree (current-output-port)))
((tree port)
(avl-pretty-print tree port
(lambda (port key data)
(display "(" port)
(write key port)
(display ", " port)
(write data port)
(display ")" port))))
((tree port key-data-printer)
;; In-order traversal, so the printing is done in
;; order. Reflect the display diagonally to get the more
;; usual orientation of left-to-right, top-to-bottom.
(define (pad depth)
(unless (zero? depth)
(display " " port)
(pad (- depth 1))))
(define (traverse p depth)
(when p
(traverse (%left p) (+ depth 1))
(pad depth)
(key-data-printer port (%key p) (%data p))
(display "\t\tdepth = " port)
(display depth port)
(display " bal = " port)
(display (%bal p) port)
(display "\n" port)
(traverse (%right p) (+ depth 1))))
(unless (avl-empty? tree)
(traverse (%left tree) 1)
(key-data-printer port (%key tree) (%data tree))
(display "\t\tdepth = 0 bal = " port)
(display (%bal tree) port)
(display "\n" port)
(traverse (%right tree) 1)))))
(define (avl-check-avl-condition tree)
;; Check that the AVL condition is satisfied.
(define (check-heights height-L height-R)
(when (<= 2 (abs (- height-L height-R)))
(display "*** AVL condition violated ***"
(current-error-port))
(internal-error)))
(define (get-heights p)
(if (not p)
(values 0 0)
(let-values (((height-LL height-LR)
(get-heights (%left p)))
((height-RL height-RR)
(get-heights (%right p))))
(check-heights height-LL height-LR)
(check-heights height-RL height-RR)
(values (+ height-LL height-LR)
(+ height-RL height-RR)))))
(unless (avl-empty? tree)
(let-values (((height-L height-R) (get-heights tree)))
(check-heights height-L height-R))))
(define (internal-error)
(display "internal error\n" (current-error-port))
(emergency-exit 123))
(define (usage-error msg)
(display "Procedure usage error:\n" (current-error-port))
(display " " (current-error-port))
(display msg (current-error-port))
(newline (current-error-port))
(exit 1))
)) ;; end library (avl-trees)
(cond-expand
(DEMONSTRATION
(begin
(import (avl-trees))
(import (scheme base))
(import (scheme time))
(import (scheme process-context))
(import (scheme write))
(cond-expand
(chicken
(import (only (chicken format) format))) ; For debugging.
(else))
(define 2**64 (expt 2 64))
(define seed (truncate-remainder (exact (current-second)) 2**64))
(define random
;; A really slow (but presumably highly portable)
;; implementation of Donald Knuth’s linear congruential random
;; number generator, returning a rational number in [0,1). See
;; https://en.wikipedia.org/w/index.php?title=Linear_congruential_generator&oldid=1076681286
(let ((a 6364136223846793005)
(c 1442695040888963407))
(lambda ()
(let ((result (/ seed 2**64)))
(set! seed (truncate-remainder (+ (* a seed) c) 2**64))
result))))
(do ((i 0 (+ i 1)))
((= i 10))
(random))
(define (fisher-yates-shuffle keys)
(let ((n (vector-length keys)))
(do ((i 1 (+ i 1)))
((= i n))
(let* ((randnum (random))
(j (+ i (floor (* randnum (- n i)))))
(xi (vector-ref keys i))
(xj (vector-ref keys j)))
(vector-set! keys i xj)
(vector-set! keys j xi)))))
(define (display-key-data key data)
(display "(")
(write key)
(display ", ")
(write data)
(display ")"))
(define (display-tree-contents tree)
(do ((p (avl->alist tree) (cdr p)))
((null? p))
(display-key-data (caar p) (cdar p))
(newline)))
(define (error-stop)
(display "*** ERROR STOP ***\n" (current-error-port))
(emergency-exit 1))
(define n 20)
(define keys (make-vector (+ n 1)))
(do ((i 0 (+ i 1)))
((= i n))
;; To keep things more like Fortran, do not use index zero.
(vector-set! keys (+ i 1) (+ i 1)))
(fisher-yates-shuffle keys)
;; Insert key-data pairs in the shuffled order.
(define tree (avl))
(avl-check-avl-condition tree)
(do ((i 1 (+ i 1)))
((= i (+ n 1)))
(let ((ix (vector-ref keys i)))
(set! tree (avl-insert < tree ix (inexact ix)))
(avl-check-avl-condition tree)
(do ((j 1 (+ j 1)))
((= j (+ n 1)))
(let*-values (((k) (vector-ref keys j))
((has-key?) (avl-has-key? < tree k))
((data) (avl-search < tree k))
((data^ has-key?^)
(avl-search-values < tree k)))
(unless (exact? k) (error-stop))
(if (<= j i)
(unless (and has-key? data data^ has-key?^
(inexact? data) (= data k)
(inexact? data^) (= data^ k))
(error-stop))
(when (or has-key? data data^ has-key?^)
(error-stop)))))))
(display "----------------------------------------------------------------------\n")
(display "keys = ")
(write (cdr (vector->list keys)))
(newline)
(display "----------------------------------------------------------------------\n")
(avl-pretty-print tree)
(display "----------------------------------------------------------------------\n")
(display "tree size = ")
(display (avl-size tree))
(newline)
(display-tree-contents tree)
(display "----------------------------------------------------------------------\n")
;;
;; Reshuffle the keys, and change the data from inexact numbers
;; to strings.
;;
(fisher-yates-shuffle keys)
(do ((i 1 (+ i 1)))
((= i (+ n 1)))
(let ((ix (vector-ref keys i)))
(set! tree (avl-insert < tree ix (number->string ix)))
(avl-check-avl-condition tree)))
(avl-pretty-print tree)
(display "----------------------------------------------------------------------\n")
(display "tree size = ")
(display (avl-size tree))
(newline)
(display-tree-contents tree)
(display "----------------------------------------------------------------------\n")
;;
;; Reshuffle the keys, and delete the contents of the tree, but
;; also keep the original tree by saving it in a variable. Check
;; persistence of the tree.
;;
(fisher-yates-shuffle keys)
(define saved-tree tree)
(do ((i 1 (+ i 1)))
((= i (+ n 1)))
(let ((ix (vector-ref keys i)))
(set! tree (avl-delete < tree ix))
(avl-check-avl-condition tree)
(unless (= (avl-size tree) (- n i)) (error-stop))
;; Try deleting a second time.
(set! tree (avl-delete < tree ix))
(avl-check-avl-condition tree)
(unless (= (avl-size tree) (- n i)) (error-stop))
(do ((j 1 (+ j 1)))
((= j (+ n 1)))
(let ((jx (vector-ref keys j)))
(unless (eq? (avl-has-key? < tree jx) (< i j))
(error-stop))
(let ((data (avl-search < tree jx)))
(unless (eq? (not (not data)) (< i j))
(error-stop))
(unless (or (not data)
(= (string->number data) jx))
(error-stop)))
(let-values (((data found?)
(avl-search-values < tree jx)))
(unless (eq? found? (< i j)) (error-stop))
(unless (or (and (not data) (<= j i))
(and data (= (string->number data) jx)))
(error-stop)))))))
(do ((i 1 (+ i 1)))
((= i (+ n 1)))
;; Is save-tree the persistent value of the tree we just
;; deleted?
(let ((ix (vector-ref keys i)))
(unless (equal? (avl-search < saved-tree ix)
(number->string ix))
(error-stop))))
(display "forwards generator:\n")
(let ((gen (avl-make-generator saved-tree)))
(do ((pair (gen) (gen)))
((not pair))
(display-key-data (car pair) (cdr pair))
(newline)))
(display "----------------------------------------------------------------------\n")
(display "backwards generator:\n")
(let ((gen (avl-make-generator saved-tree -1)))
(do ((pair (gen) (gen)))
((not pair))
(display-key-data (car pair) (cdr pair))
(newline)))
(display "----------------------------------------------------------------------\n")
))
(else)) |
http://rosettacode.org/wiki/Averages/Mean_angle | Averages/Mean angle | When calculating the average or mean of an angle one has to take into account how angles wrap around so that any angle in degrees plus any integer multiple of 360 degrees is a measure of the same angle.
If one wanted an average direction of the wind over two readings where the first reading was of 350 degrees and the second was of 10 degrees then the average of the numbers is 180 degrees, whereas if you can note that 350 degrees is equivalent to -10 degrees and so you have two readings at 10 degrees either side of zero degrees leading to a more fitting mean angle of zero degrees.
To calculate the mean angle of several angles:
Assume all angles are on the unit circle and convert them to complex numbers expressed in real and imaginary form.
Compute the mean of the complex numbers.
Convert the complex mean to polar coordinates whereupon the phase of the complex mean is the required angular mean.
(Note that, since the mean is the sum divided by the number of numbers, and division by a positive real number does not affect the angle, you can also simply compute the sum for step 2.)
You can alternatively use this formula:
Given the angles
α
1
,
…
,
α
n
{\displaystyle \alpha _{1},\dots ,\alpha _{n}}
the mean is computed by
α
¯
=
atan2
(
1
n
⋅
∑
j
=
1
n
sin
α
j
,
1
n
⋅
∑
j
=
1
n
cos
α
j
)
{\displaystyle {\bar {\alpha }}=\operatorname {atan2} \left({\frac {1}{n}}\cdot \sum _{j=1}^{n}\sin \alpha _{j},{\frac {1}{n}}\cdot \sum _{j=1}^{n}\cos \alpha _{j}\right)}
Task[edit]
write a function/method/subroutine/... that given a list of angles in degrees returns their mean angle.
(You should use a built-in function if you have one that does this for degrees or radians).
Use the function to compute the means of these lists of angles (in degrees):
[350, 10]
[90, 180, 270, 360]
[10, 20, 30]
Show your output here.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Phix | Phix | with javascript_semantics
function MeanAngle(sequence angles)
atom x = 0, y = 0
for i=1 to length(angles) do
atom ai_rad = angles[i]*PI/180
x += cos(ai_rad)
y += sin(ai_rad)
end for
if abs(x)<1e-16 then return "not meaningful" end if
return sprintf("%g",round(atan2(y,x)*180/PI,1e10))
end function
constant AngleLists = {{350,10},{90,180,270,360},{10,20,30},{180},{0,180}}
for i=1 to length(AngleLists) do
sequence ai = AngleLists[i]
printf(1,"%16V: Mean Angle is %s\n",{ai,MeanAngle(ai)})
end for
|
http://rosettacode.org/wiki/Averages/Median | Averages/Median | Task[edit]
Write a program to find the median value of a vector of floating-point numbers.
The program need not handle the case where the vector is empty, but must handle the case where there are an even number of elements. In that case, return the average of the two middle values.
There are several approaches to this. One is to sort the elements, and then pick the element(s) in the middle.
Sorting would take at least O(n logn). Another approach would be to build a priority queue from the elements, and then extract half of the elements to get to the middle element(s). This would also take O(n logn). The best solution is to use the selection algorithm to find the median in O(n) time.
See also
Quickselect_algorithm
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #FreeBASIC | FreeBASIC | ' FB 1.05.0 Win64
Sub quicksort(a() As Double, first As Integer, last As Integer)
Dim As Integer length = last - first + 1
If length < 2 Then Return
Dim pivot As Double = a(first + length\ 2)
Dim lft As Integer = first
Dim rgt As Integer = last
While lft <= rgt
While a(lft) < pivot
lft +=1
Wend
While a(rgt) > pivot
rgt -= 1
Wend
If lft <= rgt Then
Swap a(lft), a(rgt)
lft += 1
rgt -= 1
End If
Wend
quicksort(a(), first, rgt)
quicksort(a(), lft, last)
End Sub
Function median(a() As Double) As Double
Dim lb As Integer = LBound(a)
Dim ub As Integer = UBound(a)
Dim length As Integer = ub - lb + 1
If length = 0 Then Return 0.0/0.0 '' NaN
If length = 1 Then Return a(ub)
Dim mb As Integer = (lb + ub) \2
If length Mod 2 = 1 Then Return a(mb)
Return (a(mb) + a(mb + 1))/2.0
End Function
Dim a(0 To 9) As Double = {4.4, 2.3, -1.7, 7.5, 6.6, 0.0, 1.9, 8.2, 9.3, 4.5}
quicksort(a(), 0, 9)
Print "Median for all 10 elements : "; median(a())
' now get rid of final element
Dim b(0 To 8) As Double = {4.4, 2.3, -1.7, 7.5, 6.6, 0.0, 1.9, 8.2, 9.3}
quicksort(b(), 0, 8)
Print "Median for first 9 elements : "; median(b())
Print
Print "Press any key to quit"
Sleep |
http://rosettacode.org/wiki/Averages/Pythagorean_means | Averages/Pythagorean means | Task[edit]
Compute all three of the Pythagorean means of the set of integers 1 through 10 (inclusive).
Show that
A
(
x
1
,
…
,
x
n
)
≥
G
(
x
1
,
…
,
x
n
)
≥
H
(
x
1
,
…
,
x
n
)
{\displaystyle A(x_{1},\ldots ,x_{n})\geq G(x_{1},\ldots ,x_{n})\geq H(x_{1},\ldots ,x_{n})}
for this set of positive integers.
The most common of the three means, the arithmetic mean, is the sum of the list divided by its length:
A
(
x
1
,
…
,
x
n
)
=
x
1
+
⋯
+
x
n
n
{\displaystyle A(x_{1},\ldots ,x_{n})={\frac {x_{1}+\cdots +x_{n}}{n}}}
The geometric mean is the
n
{\displaystyle n}
th root of the product of the list:
G
(
x
1
,
…
,
x
n
)
=
x
1
⋯
x
n
n
{\displaystyle G(x_{1},\ldots ,x_{n})={\sqrt[{n}]{x_{1}\cdots x_{n}}}}
The harmonic mean is
n
{\displaystyle n}
divided by the sum of the reciprocal of each item in the list:
H
(
x
1
,
…
,
x
n
)
=
n
1
x
1
+
⋯
+
1
x
n
{\displaystyle H(x_{1},\ldots ,x_{n})={\frac {n}{{\frac {1}{x_{1}}}+\cdots +{\frac {1}{x_{n}}}}}}
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Kotlin | Kotlin | import kotlin.math.round
import kotlin.math.pow
fun Collection<Double>.geometricMean() =
if (isEmpty()) Double.NaN
else (reduce { n1, n2 -> n1 * n2 }).pow(1.0 / size)
fun Collection<Double>.harmonicMean() =
if (isEmpty() || contains(0.0)) Double.NaN
else size / fold(0.0) { n1, n2 -> n1 + 1.0 / n2 }
fun Double.toFixed(len: Int = 6) =
round(this * 10.0.pow(len)) / 10.0.pow(len)
fun main() {
val list = listOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0)
val a = list.average() // arithmetic mean
val g = list.geometricMean()
val h = list.harmonicMean()
println("A = $a G = ${g.toFixed()} H = ${h.toFixed()}")
println("A >= G is ${a >= g}, G >= H is ${g >= h}")
require(g in h..a)
} |
http://rosettacode.org/wiki/Balanced_ternary | Balanced ternary | Balanced ternary is a way of representing numbers. Unlike the prevailing binary representation, a balanced ternary integer is in base 3, and each digit can have the values 1, 0, or −1.
Examples
Decimal 11 = 32 + 31 − 30, thus it can be written as "++−"
Decimal 6 = 32 − 31 + 0 × 30, thus it can be written as "+−0"
Task
Implement balanced ternary representation of integers with the following:
Support arbitrarily large integers, both positive and negative;
Provide ways to convert to and from text strings, using digits '+', '-' and '0' (unless you are already using strings to represent balanced ternary; but see requirement 5).
Provide ways to convert to and from native integer type (unless, improbably, your platform's native integer type is balanced ternary). If your native integers can't support arbitrary length, overflows during conversion must be indicated.
Provide ways to perform addition, negation and multiplication directly on balanced ternary integers; do not convert to native integers first.
Make your implementation efficient, with a reasonable definition of "efficient" (and with a reasonable definition of "reasonable").
Test case With balanced ternaries a from string "+-0++0+", b from native integer -436, c "+-++-":
write out a, b and c in decimal notation;
calculate a × (b − c), write out the result in both ternary and decimal notations.
Note: The pages generalised floating point addition and generalised floating point multiplication have code implementing arbitrary precision floating point balanced ternary.
| #REXX | REXX | /*REXX program converts decimal ◄───► balanced ternary; it also performs arithmetic. */
numeric digits 10000 /*be able to handle gihugic numbers. */
Ao = '+-0++0+' ; Abt = Ao /* [↓] 2 literals used by subroutine*/
Bo = '-436' ; Bbt = d2bt(Bo); @ = "(decimal)"
Co = '+-++-' ; Cbt = Co ; @@ = "balanced ternary ="
call btShow '[a]', Abt
call btShow '[b]', Bbt
call btShow '[c]', Cbt
say; $bt = btMul(Abt, btSub(Bbt, Cbt) )
call btShow '[a*(b-c)]', $bt
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
d2bt: procedure; parse arg x 1; x= x / 1; p= 0; $.= '-'; $.1= "+"; $.0= 0; #=
do until x==0; _= (x // (3** (p+1) ) ) % 3**p
if _== 2 then _= -1
else if _== -2 then _= 1
x= x - _ * (3**p); p= p + 1; #= $._ || #
end /*until*/; return #
/*──────────────────────────────────────────────────────────────────────────────────────*/
bt2d: procedure; parse arg x; r= reverse(x); $.= -1; $.0= 0; #= 0; _= '+'; $._= 1
do j=1 for length(x); _= substr(r, j, 1); #= # + $._ * 3 ** (j-1)
end /*j*/; return #
/*──────────────────────────────────────────────────────────────────────────────────────*/
btAdd: procedure; parse arg x,y; rx= reverse(x); ry= reverse(y); carry= 0
@.= 0; _= '-'; @._= -1; _= "+"; @._= 1; $.= '-'; $.0= 0; $.1= "+"; #=
do j=1 for max( length(x), length(y) )
x_= substr(rx, j, 1); xn= @.x_
y_= substr(ry, j, 1); yn= @.y_
s= xn + yn + carry; carry= 0
if s== 2 then do; s=-1; carry= 1; end
if s== 3 then do; s= 0; carry= 1; end
if s==-2 then do; s= 1; carry=-1; end
#= $.s || #
end /*j*/
if carry\==0 then #= $.carry || #; return btNorm(#)
/*──────────────────────────────────────────────────────────────────────────────────────*/
btMul: procedure; parse arg x 1 x1 2, y 1 y1 2; if x==0 | y==0 then return 0; S= 1; P=0
x= btNorm(x); y= btNorm(y); Lx= length(x); Ly= length(y) /*handle: 0-xxx values.*/
if x1=='-' then do; x= btNeg(x); S= -S; end /*positate the number. */
if y1=='-' then do; y= btNeg(y); S= -S; end /* " " " */
if Ly>Lx then parse value x y with y x /*optimize " " */
do until y==0 /*keep adding 'til done*/
P= btAdd(P, x ) /*multiple the hard way*/
y= btSub(y, '+') /*subtract 1 from Y.*/
end /*until*/
if S==-1 then P= btNeg(P); return P /*adjust the product's sign; return.*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
btNeg: return translate( arg(1), '-+', "+-") /*negate bal_ternary #.*/
btNorm: _= strip(arg(1), 'L', 0); if _=='' then _=0; return _ /*normalize the number.*/
btSub: return btAdd( arg(1), btNeg( arg(2) ) ) /*subtract two BT args.*/
btShow: say center( arg(1), 9) right( arg(2), 20) @@ right( bt2d(arg(2)), 9) @; return |
http://rosettacode.org/wiki/Babbage_problem | Babbage problem |
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.
For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].
Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.
| #Scala | Scala |
object BabbageProblem {
def main( args:Array[String] ): Unit = {
var x : Int = 524 // Sqrt of 269696 = 519.something
while( (x * x) % 1000000 != 269696 ){
if( x % 10 == 4 ) x = x + 2
else x = x + 8
}
println("The smallest positive integer whose square ends in 269696 = " + x )
}
}
|
http://rosettacode.org/wiki/Approximate_equality | Approximate equality | Sometimes, when testing whether the solution to a task (for example, here on Rosetta Code) is correct, the
difference in floating point calculations between different language implementations becomes significant.
For example, a difference between 32 bit and 64 bit floating point calculations may appear by
about the 8th significant digit in base 10 arithmetic.
Task
Create a function which returns true if two floating point numbers are approximately equal.
The function should allow for differences in the magnitude of numbers, so that, for example,
100000000000000.01 may be approximately equal to 100000000000000.011,
even though 100.01 is not approximately equal to 100.011.
If the language has such a feature in its standard library, this may be used instead of a custom function.
Show the function results with comparisons on the following pairs of values:
100000000000000.01, 100000000000000.011 (note: should return true)
100.01, 100.011 (note: should return false)
10000000000000.001 / 10000.0, 1000000000.0000001000
0.001, 0.0010000001
0.000000000000000000000101, 0.0
sqrt(2) * sqrt(2), 2.0
-sqrt(2) * sqrt(2), -2.0
3.14159265358979323846, 3.14159265358979324
Answers should be true for the first example and false in the second, so that just rounding the numbers to a fixed number of decimals should not be enough. Otherwise answers may vary and still be correct. See the Python code for one type of solution.
| #Raku | Raku | say 0.1 + 0.2 + 0.3 + 0.4 === 1.0000000000000000000000000000000000000000000000000000000000000000000000000; # True |
http://rosettacode.org/wiki/Approximate_equality | Approximate equality | Sometimes, when testing whether the solution to a task (for example, here on Rosetta Code) is correct, the
difference in floating point calculations between different language implementations becomes significant.
For example, a difference between 32 bit and 64 bit floating point calculations may appear by
about the 8th significant digit in base 10 arithmetic.
Task
Create a function which returns true if two floating point numbers are approximately equal.
The function should allow for differences in the magnitude of numbers, so that, for example,
100000000000000.01 may be approximately equal to 100000000000000.011,
even though 100.01 is not approximately equal to 100.011.
If the language has such a feature in its standard library, this may be used instead of a custom function.
Show the function results with comparisons on the following pairs of values:
100000000000000.01, 100000000000000.011 (note: should return true)
100.01, 100.011 (note: should return false)
10000000000000.001 / 10000.0, 1000000000.0000001000
0.001, 0.0010000001
0.000000000000000000000101, 0.0
sqrt(2) * sqrt(2), 2.0
-sqrt(2) * sqrt(2), -2.0
3.14159265358979323846, 3.14159265358979324
Answers should be true for the first example and false in the second, so that just rounding the numbers to a fixed number of decimals should not be enough. Otherwise answers may vary and still be correct. See the Python code for one type of solution.
| #ReScript | ReScript | let approx_eq = (v1, v2, epsilon) => {
abs_float (v1 -. v2) < epsilon
}
let test = (a, b) => {
let epsilon = 1e-18
Printf.printf("%g, %g => %b\n", a, b, approx_eq(a, b, epsilon))
}
{
test(100000000000000.01, 100000000000000.011)
test(100.01, 100.011)
test(10000000000000.001 /. 10000.0, 1000000000.0000001000)
test(0.001, 0.0010000001)
test(0.000000000000000000000101, 0.0)
test(sqrt(2.0) *. sqrt(2.0), 2.0)
test(-. sqrt(2.0) *. sqrt(2.0), (-2.0))
test(3.14159265358979323846, 3.14159265358979324)
}
|
http://rosettacode.org/wiki/Approximate_equality | Approximate equality | Sometimes, when testing whether the solution to a task (for example, here on Rosetta Code) is correct, the
difference in floating point calculations between different language implementations becomes significant.
For example, a difference between 32 bit and 64 bit floating point calculations may appear by
about the 8th significant digit in base 10 arithmetic.
Task
Create a function which returns true if two floating point numbers are approximately equal.
The function should allow for differences in the magnitude of numbers, so that, for example,
100000000000000.01 may be approximately equal to 100000000000000.011,
even though 100.01 is not approximately equal to 100.011.
If the language has such a feature in its standard library, this may be used instead of a custom function.
Show the function results with comparisons on the following pairs of values:
100000000000000.01, 100000000000000.011 (note: should return true)
100.01, 100.011 (note: should return false)
10000000000000.001 / 10000.0, 1000000000.0000001000
0.001, 0.0010000001
0.000000000000000000000101, 0.0
sqrt(2) * sqrt(2), 2.0
-sqrt(2) * sqrt(2), -2.0
3.14159265358979323846, 3.14159265358979324
Answers should be true for the first example and false in the second, so that just rounding the numbers to a fixed number of decimals should not be enough. Otherwise answers may vary and still be correct. See the Python code for one type of solution.
| #REXX | REXX | /*REXX program mimics an "approximately equal to" for comparing floating point numbers*/
numeric digits 15 /*what other FP hardware normally uses.*/
@.= /*assign default for the @ array. */
parse arg @.1 /*obtain optional argument from the CL.*/
if @.1='' | @.1=="," then do; @.1= 100000000000000.01 100000000000000.011
@.2= 100.01 100.011
@.3= 10000000000000.001 / 10000 1000000000.0000001000
@.4= 0.001 0.0010000001
@.5= 0.00000000000000000000101 0.0
@.6= sqrt(2) * sqrt(2) 2.0
@.7= -sqrt(2) * sqrt(2) '-2.0'
@.8= 3.14159265358979323846 3.14159265358979324
/* added ───► */ @.9= 100000000000000003.0 100000000000000004.0
end
do j=1 while @.j\=='' /*process CL argument or the array #s. */
say
say center(' processing pair ' j" ",71,'═') /*display a title for the pair of #s. */
parse value @.j with a b /*extract two values from a pair of #s.*/
say 'A=' a /*display the value of A to the term.*/
say 'B=' b /* " " " " B " " " */
say right('A approximately equal to B?', 65) word("false true", 1 + approxEQ(a,b) )
end /*j*/ /* [↑] right─justify text & true/false*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
approxEQ: procedure; parse arg x,y; return x=y /*floating point compare with 15 digits*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); numeric digits; h=d+6
numeric form; m.=9; parse value format(x,2,1,,0) 'E0' with g "E" _ .; g=g *.5'e'_ %2
do j=0 while h>9; m.j=h; h=h%2+1; end /*j*/
do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g)*.5; end /*k*/; return g/1 |
http://rosettacode.org/wiki/Balanced_brackets | Balanced brackets | Task:
Generate a string with N opening brackets [ and with N closing brackets ], in some arbitrary order.
Determine whether the generated string is balanced; that is, whether it consists entirely of pairs of opening/closing brackets (in that order), none of which mis-nest.
Examples
(empty) OK
[] OK
[][] OK
[[][]] OK
][ NOT OK
][][ NOT OK
[]][[] NOT OK
| #EchoLisp | EchoLisp |
(define (balance str)
(for/fold (closed 0) ((par str))
#:break (< closed 0 ) => closed
(+ closed
(cond
((string=? par "[") 1)
((string=? par "]") -1)
(else 0)))))
(define (task N)
(define str (list->string (append (make-list N "[") (make-list N "]"))))
(for ((i 10))
(set! str (list->string (shuffle (string->list str))))
(writeln (if (zero? (balance str)) '👍 '❌ ) str)))
(task 4)
❌ "[]]][[]["
❌ "]][][[[]"
❌ "][[[]]]["
👍 "[][[[]]]"
❌ "]][[][]["
❌ "][][[[]]"
👍 "[][][[]]"
❌ "]][[][[]"
❌ "[[]]][[]"
❌ "[[][]]]["
|
http://rosettacode.org/wiki/Append_a_record_to_the_end_of_a_text_file | Append a record to the end of a text file | Many systems offer the ability to open a file for writing, such that any data written will be appended to the end of the file. Further, the file operations will always adjust the position pointer to guarantee the end of the file, even in a multitasking environment.
This feature is most useful in the case of log files, where many jobs may be appending to the log file at the same time, or where care must be taken to avoid concurrently overwriting the same record from another job.
Task
Given a two record sample for a mythical "passwd" file:
Write these records out in the typical system format.
Ideally these records will have named fields of various types.
Close the file, then reopen the file for append.
Append a new record to the file and close the file again.
Take appropriate care to avoid concurrently overwrites from another job.
Open the file and demonstrate the new record has indeed written to the end.
Source record field types and contents.
account
password
UID
GID
fullname,office,extension,homephone,email
directory
shell
string
string
int
int
struct(string,string,string,string,string)
string
string
jsmith
x
1001
1000
Joe Smith,Room 1007,(234)555-8917,(234)555-0077,[email protected]
/home/jsmith
/bin/bash
jdoe
x
1002
1000
Jane Doe,Room 1004,(234)555-8914,(234)555-0044,[email protected]
/home/jdoe
/bin/bash
Record to be appended.
account
password
UID
GID
fullname,office,extension,homephone,email
directory
shell
string
string
int
int
struct(string,string,string,string,string)
string
string
xyz
x
1003
1000
X Yz,Room 1003,(234)555-8913,(234)555-0033,[email protected]
/home/xyz
/bin/bash
Resulting file format: should mimic Linux's /etc/passwd file format with particular attention to the "," separator used in the GECOS field. But if the specific language has a particular or unique format of storing records in text file, then this format should be named and demonstrated with an additional example.
Expected output:
Appended record: xyz:x:1003:1000:X Yz,Room 1003,(234)555-8913,(234)555-0033,[email protected]:/home/xyz:/bin/bash
Finally: Provide a summary of the language's "append record" capabilities in a table. eg.
Append Capabilities.
Data Representation
IO
Library
Append
Possible
Automatic
Append
Multi-tasking
Safe
In core
On disk
C struct
CSV text file
glibc/stdio
☑
☑
☑ (Not all, eg NFS)
Alternatively: If the language's appends can not guarantee its writes will always append, then note this restriction in the table. If possible, provide an actual code example (possibly using file/record locking) to guarantee correct concurrent appends.
| #Go | Go | package main
import (
"bytes"
"fmt"
"io"
"io/ioutil"
"os"
)
type pw struct {
account, password string
uid, gid uint
gecos
directory, shell string
}
type gecos struct {
fullname, office, extension, homephone, email string
}
func (p *pw) encode(w io.Writer) (int, error) {
return fmt.Fprintf(w, "%s:%s:%d:%d:%s,%s,%s,%s,%s:%s:%s\n",
p.account, p.password, p.uid, p.gid,
p.fullname, p.office, p.extension, p.homephone, p.email,
p.directory, p.shell)
}
// data cut and pasted from task description
var p2 = []pw{
{"jsmith", "x", 1001, 1000, gecos{"Joe Smith", "Room 1007",
"(234)555-8917", "(234)555-0077", "[email protected]"},
"/home/jsmith", "/bin/bash"},
{"jdoe", "x", 1002, 1000, gecos{"Jane Doe", "Room 1004",
"(234)555-8914", "(234)555-0044", "[email protected]"},
"/home/jsmith", "/bin/bash"},
}
var pa = pw{"xyz", "x", 1003, 1000, gecos{"X Yz", "Room 1003",
"(234)555-8913", "(234)555-0033", "[email protected]"},
"/home/xyz", "/bin/bash"}
var expected = "xyz:x:1003:1000:X Yz,Room 1003,(234)555-8913," +
"(234)555-0033,[email protected]:/home/xyz:/bin/bash"
const pfn = "mythical"
func main() {
writeTwo()
appendOneMore()
checkResult()
}
func writeTwo() {
// overwrites any existing file
f, err := os.Create(pfn)
if err != nil {
fmt.Println(err)
return
}
defer func() {
if cErr := f.Close(); cErr != nil && err == nil {
fmt.Println(cErr)
}
}()
for _, p := range p2 {
if _, err = p.encode(f); err != nil {
fmt.Println(err)
return
}
}
}
func appendOneMore() {
// file must already exist
f, err := os.OpenFile(pfn, os.O_RDWR|os.O_APPEND, 0)
if err != nil {
fmt.Println(err)
return
}
if _, err := pa.encode(f); err != nil {
fmt.Println(err)
}
if cErr := f.Close(); cErr != nil && err == nil {
fmt.Println(cErr)
}
}
func checkResult() {
// reads entire file then closes it
b, err := ioutil.ReadFile(pfn)
if err != nil {
fmt.Println(err)
return
}
if string(bytes.Split(b, []byte{'\n'})[2]) == expected {
fmt.Println("append okay")
} else {
fmt.Println("it didn't work")
}
} |
http://rosettacode.org/wiki/Associative_array/Creation | Associative array/Creation | Task
The goal is to create an associative array (also known as a dictionary, map, or hash).
Related tasks:
Associative arrays/Iteration
Hash from two arrays
See also
Array
Associative array: Creation, Iteration
Collections
Compound data type
Doubly-linked list: Definition, Element definition, Element insertion, List Traversal, Element Removal
Linked list
Queue: Definition, Usage
Set
Singly-linked list: Element definition, Element insertion, List Traversal, Element Removal
Stack
| #AutoHotkey | AutoHotkey | associative_array := {key1: "value 1", "Key with spaces and non-alphanumeric characters !*+": 23}
MsgBox % associative_array.key1
. "`n" associative_array["Key with spaces and non-alphanumeric characters !*+"] |
http://rosettacode.org/wiki/Anti-primes | Anti-primes | The anti-primes
(or highly composite numbers, sequence A002182 in the OEIS)
are the natural numbers with more factors than any smaller than itself.
Task
Generate and show here, the first twenty anti-primes.
Related tasks
Factors of an integer
Sieve of Eratosthenes
| #Common_Lisp | Common Lisp | (defun factors (n &aux (lows '()) (highs '()))
(do ((limit (1+ (isqrt n))) (factor 1 (1+ factor)))
((= factor limit)
(when (= n (* limit limit))
(push limit highs))
(remove-duplicates (nreconc lows highs)))
(multiple-value-bind (quotient remainder) (floor n factor)
(when (zerop remainder)
(push factor lows)
(push quotient highs)))))
(defun anti-prime ()
(format t "The first 20 anti-primes are :~%")
(do ((dmax 0) (c 0) (i 0 (1+ i)))
((= c 20))
(setf facts (list-length (factors i)))
(when (< dmax facts)
(format t "~d " i)
(setq dmax facts)
(incf c)))) |
http://rosettacode.org/wiki/Atomic_updates | Atomic updates |
Task
Define a data type consisting of a fixed number of 'buckets', each containing a nonnegative integer value, which supports operations to:
get the current value of any bucket
remove a specified amount from one specified bucket and add it to another, preserving the total of all bucket values, and clamping the transferred amount to ensure the values remain non-negative
In order to exercise this data type, create one set of buckets, and start three concurrent tasks:
As often as possible, pick two buckets and make their values closer to equal.
As often as possible, pick two buckets and arbitrarily redistribute their values.
At whatever rate is convenient, display (by any means) the total value and, optionally, the individual values of each bucket.
The display task need not be explicit; use of e.g. a debugger or trace tool is acceptable provided it is simple to set up to provide the display.
This task is intended as an exercise in atomic operations. The sum of the bucket values must be preserved even if the two tasks attempt to perform transfers simultaneously, and a straightforward solution is to ensure that at any time, only one transfer is actually occurring — that the transfer operation is atomic.
| #Oz | Oz | declare
%%
%% INIT
%%
NBuckets = 100
StartVal = 50
ExpectedSum = NBuckets * StartVal
%% Makes a tuple and calls Fun for every field
fun {Make Label N Fun}
R = {Tuple.make Label N}
in
for I in 1..N do R.I = {Fun} end
R
end
Buckets = {Make buckets NBuckets fun {$} {Cell.new StartVal} end}
Locks = {Make locks NBuckets Lock.new}
LockList = {Record.toList Locks}
%%
%% DISPLAY
%%
proc {Display}
Snapshot = {WithLocks LockList
fun {$}
{Record.map Buckets Cell.access}
end
}
Sum = {Record.foldL Snapshot Number.'+' 0}
in
{Print Snapshot}
{System.showInfo " sum: "#Sum}
Sum = ExpectedSum %% assert
end
%% Calls Fun with multiple locks locked and returns the result of Fun.
fun {WithLocks Ls Fun}
case Ls of L|Lr then
lock L then
{WithLocks Lr Fun}
end
[] nil then {Fun}
end
end
%%
%% MANIPULATE
%%
proc {Smooth I J}
Diff = @(Buckets.I) - @(Buckets.J) %% reading without lock: by design
Amount = Diff div 4
in
{Transfer I J Amount}
end
proc {Roughen I J}
Amount = @(Buckets.I) div 3 %% reading without lock: by design
in
{Transfer I J Amount}
end
%% Atomically transfer an amount from From to To.
%% Negative amounts are allowed;
%% will never make a bucket negative.
proc {Transfer From To Amount}
if From \= To then
%% lock in order (to avoid deadlocks)
Smaller = {Min From To}
Bigger = {Max From To}
in
lock Locks.Smaller then
lock Locks.Bigger then
FromBucket = Buckets.From
ToBucket = Buckets.To
NewFromValue = @FromBucket - Amount
NewToValue = @ToBucket + Amount
in
if NewFromValue >= 0 andthen NewToValue >= 0 then
FromBucket := NewFromValue
ToBucket := NewToValue
end
end
end
end
end
%% Returns a random bucket index.
fun {Pick}
{OS.rand} mod NBuckets + 1
end
in
%%
%% START
%%
thread for do {Smooth {Pick} {Pick}} end end
thread for do {Roughen {Pick} {Pick}} end end
for do {Display} {Time.delay 50} end |
http://rosettacode.org/wiki/Assertions | Assertions | Assertions are a way of breaking out of code when there is an error or an unexpected input.
Some languages throw exceptions and some treat it as a break point.
Task
Show an assertion in your language by asserting that an integer variable is equal to 42.
| #Liberty_BASIC | Liberty BASIC |
a=42
call assert a=42
print "passed"
a=41
call assert a=42
print "failed (we never get here)"
end
sub assert cond
if cond=0 then 'simulate error, mentioning "AssertionFailed"
AssertionFailed(-1)=0
end if
end sub
|
http://rosettacode.org/wiki/Assertions | Assertions | Assertions are a way of breaking out of code when there is an error or an unexpected input.
Some languages throw exceptions and some treat it as a break point.
Task
Show an assertion in your language by asserting that an integer variable is equal to 42.
| #Lingo | Lingo | -- in a movie script
on assert (ok, message)
if not ok then
if not voidP(message) then _player.alert(message)
abort -- exits from current call stack, i.e. also from the caller function
end if
end
-- anywhere in the code
on test
x = 42
assert(x=42, "Assertion 'x=42' failed")
put "this shows up"
x = 23
assert(x=42, "Assertion 'x=42' failed")
put "this will never show up"
end |
http://rosettacode.org/wiki/Assertions | Assertions | Assertions are a way of breaking out of code when there is an error or an unexpected input.
Some languages throw exceptions and some treat it as a break point.
Task
Show an assertion in your language by asserting that an integer variable is equal to 42.
| #Lisaac | Lisaac | ? { n = 42 }; |
http://rosettacode.org/wiki/Apply_a_callback_to_an_array | Apply a callback to an array | Task
Take a combined set of elements and apply a function to each element.
| #Clio | Clio | [1 2 3 4] * 2 + 1 -> print |
http://rosettacode.org/wiki/Apply_a_callback_to_an_array | Apply a callback to an array | Task
Take a combined set of elements and apply a function to each element.
| #Clojure | Clojure | ;; apply a named function, inc
(map inc [1 2 3 4]) |
http://rosettacode.org/wiki/Averages/Mode | Averages/Mode | Task[edit]
Write a program to find the mode value of a collection.
The case where the collection is empty may be ignored. Care must be taken to handle the case where the mode is non-unique.
If it is not appropriate or possible to support a general collection, use a vector (array), if possible. If it is not appropriate or possible to support an unspecified value type, use integers.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #ooRexx | ooRexx |
-- will work with just about any collection...
call testMode .array~of(10, 9, 8, 7, 6, 5, 4, 3, 2, 1)
call testMode .list~of(10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 0, 0, 0, .11)
call testMode .queue~of(30, 10, 20, 30, 40, 50, -100, 4.7, -11e2)
::routine testMode
use arg list
say "list =" list~makearray~toString("l", ", ")
say "mode =" mode(list)
say
::routine mode
use arg list
-- this is a good application for a bag
-- add all of the items to the bag
collector = .bag~new
collector~putAll(list)
-- now get a list of unique items
indexes = .set~new~~putall(collector)
count = 0 -- this is used to keep track of the maximums
-- now see how many of each element we ended up with
loop index over indexes
items = collector~allat(index)
newCount = items~items
if newCount > count then do
mode = items[1]
count = newCount
end
end
return mode
|
http://rosettacode.org/wiki/Associative_array/Iteration | Associative array/Iteration | Show how to iterate over the key-value pairs of an associative array, and print each pair out.
Also show how to iterate just over the keys, or the values, if there is a separate way to do that in your language.
See also
Array
Associative array: Creation, Iteration
Collections
Compound data type
Doubly-linked list: Definition, Element definition, Element insertion, List Traversal, Element Removal
Linked list
Queue: Definition, Usage
Set
Singly-linked list: Element definition, Element insertion, List Traversal, Element Removal
Stack
| #Dao | Dao |
dict = { 'def' => 1, 'abc' => 2 }
for( keyvalue in dict ) io.writeln( keyvalue );
for( key in dict.keys(); value in dict.values() ) io.writeln( key, value )
dict.iterate { [key, value]
io.writeln( key, value )
}
|
http://rosettacode.org/wiki/Associative_array/Iteration | Associative array/Iteration | Show how to iterate over the key-value pairs of an associative array, and print each pair out.
Also show how to iterate just over the keys, or the values, if there is a separate way to do that in your language.
See also
Array
Associative array: Creation, Iteration
Collections
Compound data type
Doubly-linked list: Definition, Element definition, Element insertion, List Traversal, Element Removal
Linked list
Queue: Definition, Usage
Set
Singly-linked list: Element definition, Element insertion, List Traversal, Element Removal
Stack
| #Dart | Dart |
main(){
var fruits = {
'apples': 'red',
'oranges': 'orange',
'bananas': 'yellow',
'pears': 'green',
'plums': 'purple'
};
print('Key Value pairs:');
fruits.forEach( (fruits, color) => print( '$fruits are $color' ) );
print('\nKeys only:');
fruits.keys.forEach( ( key ) => print( key ) );
print('\nValues only:');
fruits.values.forEach( ( value ) => print( value ) );
}
|
http://rosettacode.org/wiki/Apply_a_digital_filter_(direct_form_II_transposed) | Apply a digital filter (direct form II transposed) | Digital filters are used to apply a mathematical operation to a sampled signal. One of the common formulations is the "direct form II transposed" which can represent both infinite impulse response (IIR) and finite impulse response (FIR) filters, as well as being more numerically stable than other forms. [1]
Task
Filter a signal using an order 3 low-pass Butterworth filter. The coefficients for the filter are a=[1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17] and b = [0.16666667, 0.5, 0.5, 0.16666667]
The signal that needs filtering is the following vector: [-0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412, -0.662370894973, -1.00700480494, -0.404707073677 ,0.800482325044, 0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195, 0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293, 0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589]
| #Nim | Nim |
import strformat
func filter(a, b, signal: openArray[float]): seq[float] =
result.setLen(signal.len)
for i in 0..signal.high:
var tmp = 0.0
for j in 0..min(i, b.high):
tmp += b[j] * signal[i - j]
for j in 1..min(i, a.high):
tmp -= a[j] * result[i - j]
tmp /= a[0]
result[i] = tmp
#———————————————————————————————————————————————————————————————————————————————————————————————————
let a = [1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17]
let b = [0.16666667, 0.5, 0.5, 0.16666667]
let signal = [-0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412,
-0.662370894973, -1.00700480494, -0.404707073677, 0.800482325044,
0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195,
0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293,
0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589]
let result = filter(a, b, signal)
for i in 0..result.high:
stdout.write fmt"{result[i]: .8f}"
stdout.write if (i + 1) mod 5 != 0: ", " else: "\n" |
http://rosettacode.org/wiki/Apply_a_digital_filter_(direct_form_II_transposed) | Apply a digital filter (direct form II transposed) | Digital filters are used to apply a mathematical operation to a sampled signal. One of the common formulations is the "direct form II transposed" which can represent both infinite impulse response (IIR) and finite impulse response (FIR) filters, as well as being more numerically stable than other forms. [1]
Task
Filter a signal using an order 3 low-pass Butterworth filter. The coefficients for the filter are a=[1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17] and b = [0.16666667, 0.5, 0.5, 0.16666667]
The signal that needs filtering is the following vector: [-0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412, -0.662370894973, -1.00700480494, -0.404707073677 ,0.800482325044, 0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195, 0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293, 0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589]
| #Objeck | Objeck | class DigitalFilter {
function : Main(args : String[]) ~ Nil {
a := [1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17];
b := [0.16666667, 0.5, 0.5, 0.16666667];
signal := [-0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412,
-0.662370894973, -1.00700480494, -0.404707073677, 0.800482325044,
0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195,
0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293,
0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589];
result := Filter(a, b, signal);
each(i : result) {
System.IO.Console->Print(result[i])->Print(((i + 1) % 5 <> 0) ? ",\t" : "\n");
};
}
function : Filter(a : Float[], b : Float[], signal : Float[]) ~ Float[] {
result := Float->New[signal->Size()];
each(i : signal) {
tmp := 0.0;
each(j : b) {
if(i-j >= 0) {
tmp += b[j] * signal[i - j];
};
};
each(j : a) {
if(i-j >= 0) {
tmp -= a[j] * result[i - j];
};
};
tmp /= a[0];
result[i] := tmp;
};
return result;
}
} |
http://rosettacode.org/wiki/Averages/Arithmetic_mean | Averages/Arithmetic mean | Task[edit]
Write a program to find the mean (arithmetic average) of a numeric vector.
In case of a zero-length input, since the mean of an empty set of numbers is ill-defined, the program may choose to behave in any way it deems appropriate, though if the programming language has an established convention for conveying math errors or undefined values, it's preferable to follow it.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #EasyLang | EasyLang | func mean . f[] r .
for i range len f[]
s += f[i]
.
r = s / len f[]
.
f[] = [ 1 2 3 4 5 6 7 8 ]
call mean f[] r
print r |
http://rosettacode.org/wiki/Averages/Arithmetic_mean | Averages/Arithmetic mean | Task[edit]
Write a program to find the mean (arithmetic average) of a numeric vector.
In case of a zero-length input, since the mean of an empty set of numbers is ill-defined, the program may choose to behave in any way it deems appropriate, though if the programming language has an established convention for conveying math errors or undefined values, it's preferable to follow it.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #EchoLisp | EchoLisp |
(lib 'math)
(mean '(1 2 3 4)) ;; mean of a list
→ 2.5
(mean #(1 2 3 4)) ;; mean of a vector
→ 2.5
(lib 'sequences)
(mean [1 3 .. 10]) ;; mean of a sequence
→ 5
;; error handling
(mean 'elvis)
⛔ error: mean : expected sequence : elvis
(mean ())
💣 error: mean : null is not an object
(mean #())
😐 warning: mean : zero-divide : empty-vector
→ 0
(mean [2 2 .. 2])
😁 warning: mean : zero-divide : empty-sequence
→ 0
|
http://rosettacode.org/wiki/Associative_array/Merging | Associative array/Merging | Task
Define two associative arrays, where one represents the following "base" data:
Key
Value
"name"
"Rocket Skates"
"price"
12.75
"color"
"yellow"
And the other represents "update" data:
Key
Value
"price"
15.25
"color"
"red"
"year"
1974
Merge these into a new associative array that contains every key found in either of the source ones. Each key should map to the value in the second (update) table if that exists, or else to the value in the first (base) table. If possible, do this in a way that does not mutate the original two associative arrays. Obviously this should be done in a way that would work for any data, not just the specific data given here, but in this example the result should be:
Key
Value
"name"
"Rocket Skates"
"price"
15.25
"color"
"red"
"year"
1974
| #Wren | Wren | var mergeMaps = Fn.new { |m1, m2|
var m3 = {}
for (key in m1.keys) m3[key] = m1[key]
for (key in m2.keys) m3[key] = m2[key]
return m3
}
var base = { "name": "Rocket Skates" , "price": 12.75, "color": "yellow" }
var update = { "price": 15.25, "color": "red", "year": 1974 }
var merged = mergeMaps.call(base, update)
System.print(merged) |
http://rosettacode.org/wiki/Associative_array/Merging | Associative array/Merging | Task
Define two associative arrays, where one represents the following "base" data:
Key
Value
"name"
"Rocket Skates"
"price"
12.75
"color"
"yellow"
And the other represents "update" data:
Key
Value
"price"
15.25
"color"
"red"
"year"
1974
Merge these into a new associative array that contains every key found in either of the source ones. Each key should map to the value in the second (update) table if that exists, or else to the value in the first (base) table. If possible, do this in a way that does not mutate the original two associative arrays. Obviously this should be done in a way that would work for any data, not just the specific data given here, but in this example the result should be:
Key
Value
"name"
"Rocket Skates"
"price"
15.25
"color"
"red"
"year"
1974
| #Vlang | Vlang | type Generic = int|string|f64
type Assoc = map[string]Generic
fn merge(base Assoc, update Assoc) Assoc {
mut result := Assoc(map[string]Generic{})
for k, v in base {
result[k] = v
}
for k, v in update {
result[k] = v
}
return result
}
fn main() {
base := Assoc({"name": Generic("Rocket Skates"), "price": 12.75, "color": "yellow"})
update := Assoc({"price": Generic(15.25), "color": "red", "year": 1974})
result := merge(base, update)
for k,v in result {
println('$k: $v')
}
} |
http://rosettacode.org/wiki/Associative_array/Merging | Associative array/Merging | Task
Define two associative arrays, where one represents the following "base" data:
Key
Value
"name"
"Rocket Skates"
"price"
12.75
"color"
"yellow"
And the other represents "update" data:
Key
Value
"price"
15.25
"color"
"red"
"year"
1974
Merge these into a new associative array that contains every key found in either of the source ones. Each key should map to the value in the second (update) table if that exists, or else to the value in the first (base) table. If possible, do this in a way that does not mutate the original two associative arrays. Obviously this should be done in a way that would work for any data, not just the specific data given here, but in this example the result should be:
Key
Value
"name"
"Rocket Skates"
"price"
15.25
"color"
"red"
"year"
1974
| #Wren_2 | Wren | var mergeMaps = Fn.new { |m1, m2|
var m3 = {}
for (key in m1.keys) m3[key] = m1[key]
for (key in m2.keys) m3[key] = m2[key]
return m3
}
var base = { "name": "Rocket Skates" , "price": 12.75, "color": "yellow" }
var update = { "price": 15.25, "color": "red", "year": 1974 }
var merged = mergeMaps.call(base, update)
System.print(merged) |
http://rosettacode.org/wiki/Average_loop_length | Average loop length | Let f be a uniformly-randomly chosen mapping from the numbers 1..N to the numbers 1..N (note: not necessarily a permutation of 1..N; the mapping could produce a number in more than one way or not at all). At some point, the sequence 1, f(1), f(f(1))... will contain a repetition, a number that occurring for the second time in the sequence.
Task
Write a program or a script that estimates, for each N, the average length until the first such repetition.
Also calculate this expected length using an analytical formula, and optionally compare the simulated result with the theoretical one.
This problem comes from the end of Donald Knuth's Christmas tree lecture 2011.
Example of expected output:
N average analytical (error)
=== ========= ============ =========
1 1.0000 1.0000 ( 0.00%)
2 1.4992 1.5000 ( 0.05%)
3 1.8784 1.8889 ( 0.56%)
4 2.2316 2.2188 ( 0.58%)
5 2.4982 2.5104 ( 0.49%)
6 2.7897 2.7747 ( 0.54%)
7 3.0153 3.0181 ( 0.09%)
8 3.2429 3.2450 ( 0.07%)
9 3.4536 3.4583 ( 0.14%)
10 3.6649 3.6602 ( 0.13%)
11 3.8091 3.8524 ( 1.12%)
12 3.9986 4.0361 ( 0.93%)
13 4.2074 4.2123 ( 0.12%)
14 4.3711 4.3820 ( 0.25%)
15 4.5275 4.5458 ( 0.40%)
16 4.6755 4.7043 ( 0.61%)
17 4.8877 4.8579 ( 0.61%)
18 4.9951 5.0071 ( 0.24%)
19 5.1312 5.1522 ( 0.41%)
20 5.2699 5.2936 ( 0.45%)
| #Scala | Scala |
import scala.util.Random
object AverageLoopLength extends App {
val factorial: LazyList[Double] = 1 #:: factorial.zip(LazyList.from(1)).map(n => n._2 * factorial(n._2 - 1))
val results = for (n <- 1 to 20;
avg = tested(n, 1000000);
theory = expected(n)
) yield (n, avg, theory, (avg / theory - 1) * 100)
def expected(n: Int): Double = (for (i <- 1 to n) yield factorial(n) / Math.pow(n, i) / factorial(n - i)).sum
def tested(n: Int, times: Int): Double = (for (i <- 1 to times) yield trial(n)).sum / times
def trial(n: Int): Double = {
var count = 0
var x = 1
var bits = 0
while ((bits & x) == 0) {
count = count + 1
bits = bits | x
x = 1 << Random.nextInt(n)
}
count
}
println("n avg exp diff")
println("------------------------------------")
results foreach { n => {
println(f"${n._1}%2d ${n._2}%2.6f ${n._3}%2.6f ${n._4}%2.3f%%")
}
}
}
|
http://rosettacode.org/wiki/Averages/Simple_moving_average | Averages/Simple moving average | Computing the simple moving average of a series of numbers.
Task[edit]
Create a stateful function/class/instance that takes a period and returns a routine that takes a number as argument and returns a simple moving average of its arguments so far.
Description
A simple moving average is a method for computing an average of a stream of numbers by only averaging the last P numbers from the stream, where P is known as the period.
It can be implemented by calling an initialing routine with P as its argument, I(P), which should then return a routine that when called with individual, successive members of a stream of numbers, computes the mean of (up to), the last P of them, lets call this SMA().
The word stateful in the task description refers to the need for SMA() to remember certain information between calls to it:
The period, P
An ordered container of at least the last P numbers from each of its individual calls.
Stateful also means that successive calls to I(), the initializer, should return separate routines that do not share saved state so they could be used on two independent streams of data.
Pseudo-code for an implementation of SMA is:
function SMA(number: N):
stateful integer: P
stateful list: stream
number: average
stream.append_last(N)
if stream.length() > P:
# Only average the last P elements of the stream
stream.delete_first()
if stream.length() == 0:
average = 0
else:
average = sum( stream.values() ) / stream.length()
return average
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Swift | Swift | struct SimpleMovingAverage {
var period: Int
var numbers = [Double]()
mutating func addNumber(_ n: Double) -> Double {
numbers.append(n)
if numbers.count > period {
numbers.removeFirst()
}
guard !numbers.isEmpty else {
return 0
}
return numbers.reduce(0, +) / Double(numbers.count)
}
}
for period in [3, 5] {
print("Moving average with period \(period)")
var averager = SimpleMovingAverage(period: period)
for n in [1.0, 2, 3, 4, 5, 5, 4, 3, 2, 1] {
print("n: \(n); average \(averager.addNumber(n))")
}
} |
http://rosettacode.org/wiki/Attractive_numbers | Attractive numbers | A number is an attractive number if the number of its prime factors (whether distinct or not) is also prime.
Example
The number 20, whose prime decomposition is 2 × 2 × 5, is an attractive number because the number of its prime factors (3) is also prime.
Task
Show sequence items up to 120.
Reference
The OEIS entry: A063989: Numbers with a prime number of prime divisors.
| #Maple | Maple | attractivenumbers := proc(n::posint)
local an, i;
an :=[]:
for i from 1 to n do
if isprime(NumberTheory:-NumberOfPrimeFactors(i)) then
an := [op(an), i]:
end if:
end do:
end proc:
attractivenumbers(120); |
http://rosettacode.org/wiki/Attractive_numbers | Attractive numbers | A number is an attractive number if the number of its prime factors (whether distinct or not) is also prime.
Example
The number 20, whose prime decomposition is 2 × 2 × 5, is an attractive number because the number of its prime factors (3) is also prime.
Task
Show sequence items up to 120.
Reference
The OEIS entry: A063989: Numbers with a prime number of prime divisors.
| #Mathematica_.2F_Wolfram_Language | Mathematica / Wolfram Language | ClearAll[AttractiveNumberQ]
AttractiveNumberQ[n_Integer] := FactorInteger[n][[All, 2]] // Total // PrimeQ
Reap[Do[If[AttractiveNumberQ[i], Sow[i]], {i, 120}]][[2, 1]] |
http://rosettacode.org/wiki/Averages/Mean_time_of_day | Averages/Mean time of day | Task[edit]
A particular activity of bats occurs at these times of the day:
23:00:17, 23:40:20, 00:12:45, 00:17:19
Using the idea that there are twenty-four hours in a day,
which is analogous to there being 360 degrees in a circle,
map times of day to and from angles;
and using the ideas of Averages/Mean angle
compute and show the average time of the nocturnal activity
to an accuracy of one second of time.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #PicoLisp | PicoLisp | (load "@lib/math.l")
(de meanTime (Lst)
(let Tim
(*/
(atan2
(sum '((S) (sin (*/ ($tim S) pi 43200))) Lst)
(sum '((S) (cos (*/ ($tim S) pi 43200))) Lst) )
43200 pi )
(tim$ (% (+ Tim 86400) 86400) T) ) ) |
http://rosettacode.org/wiki/Averages/Mean_time_of_day | Averages/Mean time of day | Task[edit]
A particular activity of bats occurs at these times of the day:
23:00:17, 23:40:20, 00:12:45, 00:17:19
Using the idea that there are twenty-four hours in a day,
which is analogous to there being 360 degrees in a circle,
map times of day to and from angles;
and using the ideas of Averages/Mean angle
compute and show the average time of the nocturnal activity
to an accuracy of one second of time.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #PL.2FI | PL/I | *process source attributes xref;
avt: Proc options(main);
/*--------------------------------------------------------------------
* 25.06.2014 Walter Pachl taken from REXX
*-------------------------------------------------------------------*/
Dcl (addr,hbound,sin,cos,atan) Builtin;
Dcl sysprint Print;
Dcl times(4) Char(8) Init('23:00:17','23:40:20','00:12:45','00:17:19');
Dcl time Char(8);
Dcl (alpha,x,y,ss,ww) Dec Float(18) Init(0);
Dcl day Bin Fixed(31) Init(86400);
Dcl pi Dec Float(18) Init(3.14159265358979323846);
Dcl (i,h,m,s) bin Fixed(31) Init(0);
Do i=1 To hbound(times); /* loop over times */
time=times(i); /* pick a time */
alpha=t2a(time); /* convert to angle (radians) */
x=x+sin(alpha); /* accumulate sines */
y=y+cos(alpha); /* accumulate cosines */
End;
ww=atan(x/y); /* compute average angle */
ss=ww*day/(2*pi); /* convert to seconds */
If ss<0 Then ss=ss+day; /* avoid negative value */
m=ss/60; /* split into hh mm ss */
s=ss-m*60;
h=m/60;
m=m-h*60;
Put Edit(h,':',m,':',s)(Skip,3(p'99',a));
t2a: Procedure(t) Returns(Bin Float(18)); /* convert time to angle */
Dcl t Char(8);
Dcl 1 tt Based(addr(t)),
2 hh Pic'99',
2 * Char(1),
2 mm Pic'99',
2 * Char(1),
2 ss Pic'99';
Dcl sec Bin Fixed(31);
Dcl a Bin Float(18);
sec=(hh*60+mm)*60+ss;
If sec>(day/2) Then
sec=sec-day;
a=2*pi*sec/day;
Return (a);
End;
End; |
http://rosettacode.org/wiki/AVL_tree | AVL tree |
This page uses content from Wikipedia. The original article was at AVL tree. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
In computer science, an AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; at no time do they differ by more than one because rebalancing is done ensure this is the case. Lookup, insertion, and deletion all take O(log n) time in both the average and worst cases, where n is the number of nodes in the tree prior to the operation. Insertions and deletions may require the tree to be rebalanced by one or more tree rotations. Note the tree of nodes comprise a set, so duplicate node keys are not allowed.
AVL trees are often compared with red-black trees because they support the same set of operations and because red-black trees also take O(log n) time for the basic operations. Because AVL trees are more rigidly balanced, they are faster than red-black trees for lookup-intensive applications. Similar to red-black trees, AVL trees are height-balanced, but in general not weight-balanced nor μ-balanced; that is, sibling nodes can have hugely differing numbers of descendants.
Task
Implement an AVL tree in the language of choice, and provide at least basic operations.
| #Sidef | Sidef | class AVLtree {
has root = nil
struct Node {
Number key,
Number balance = 0,
Node left = nil,
Node right = nil,
Node parent = nil,
}
method insert(key) {
if (root == nil) {
root = Node(key)
return true
}
var n = root
var parent = nil
loop {
if (n.key == key) {
return false
}
parent = n
var goLeft = (n.key > key)
n = (goLeft ? n.left : n.right)
if (n == nil) {
var tn = Node(key, parent: parent)
if (goLeft) {
parent.left = tn
}
else {
parent.right = tn
}
self.rebalance(parent)
break
}
}
return true
}
method delete_key(delKey) {
if (root == nil) { return nil }
var n = root
var parent = root
var delNode = nil
var child = root
while (child != nil) {
parent = n
n = child
child = (delKey >= n.key ? n.right : n.left)
if (delKey == n.key) {
delNode = n
}
}
if (delNode != nil) {
delNode.key = n.key
child = (n.left != nil ? n.left : n.right)
if (root.key == delKey) {
root = child
}
else {
if (parent.left == n) {
parent.left = child
}
else {
parent.right = child
}
self.rebalance(parent)
}
}
}
method rebalance(n) {
if (n == nil) { return nil }
self.setBalance(n)
given (n.balance) {
when (-2) {
if (self.height(n.left.left) >= self.height(n.left.right)) {
n = self.rotate(n, :right)
}
else {
n = self.rotate_twice(n, :left, :right)
}
}
when (2) {
if (self.height(n.right.right) >= self.height(n.right.left)) {
n = self.rotate(n, :left)
}
else {
n = self.rotate_twice(n, :right, :left)
}
}
}
if (n.parent != nil) {
self.rebalance(n.parent)
}
else {
root = n
}
}
method rotate(a, dir) {
var b = (dir == :left ? a.right : a.left)
b.parent = a.parent
(dir == :left) ? (a.right = b.left)
: (a.left = b.right)
if (a.right != nil) {
a.right.parent = a
}
b.$dir = a
a.parent = b
if (b.parent != nil) {
if (b.parent.right == a) {
b.parent.right = b
}
else {
b.parent.left = b
}
}
self.setBalance(a, b)
return b
}
method rotate_twice(n, dir1, dir2) {
n.left = self.rotate(n.left, dir1)
self.rotate(n, dir2)
}
method height(n) {
if (n == nil) { return -1 }
1 + Math.max(self.height(n.left), self.height(n.right))
}
method setBalance(*nodes) {
nodes.each { |n|
n.balance = (self.height(n.right) - self.height(n.left))
}
}
method printBalance {
self.printBalance(root)
}
method printBalance(n) {
if (n != nil) {
self.printBalance(n.left)
print(n.balance, ' ')
self.printBalance(n.right)
}
}
}
var tree = AVLtree()
say "Inserting values 1 to 10"
{|i| tree.insert(i) } << 1..10
print "Printing balance: "
tree.printBalance |
http://rosettacode.org/wiki/Averages/Mean_angle | Averages/Mean angle | When calculating the average or mean of an angle one has to take into account how angles wrap around so that any angle in degrees plus any integer multiple of 360 degrees is a measure of the same angle.
If one wanted an average direction of the wind over two readings where the first reading was of 350 degrees and the second was of 10 degrees then the average of the numbers is 180 degrees, whereas if you can note that 350 degrees is equivalent to -10 degrees and so you have two readings at 10 degrees either side of zero degrees leading to a more fitting mean angle of zero degrees.
To calculate the mean angle of several angles:
Assume all angles are on the unit circle and convert them to complex numbers expressed in real and imaginary form.
Compute the mean of the complex numbers.
Convert the complex mean to polar coordinates whereupon the phase of the complex mean is the required angular mean.
(Note that, since the mean is the sum divided by the number of numbers, and division by a positive real number does not affect the angle, you can also simply compute the sum for step 2.)
You can alternatively use this formula:
Given the angles
α
1
,
…
,
α
n
{\displaystyle \alpha _{1},\dots ,\alpha _{n}}
the mean is computed by
α
¯
=
atan2
(
1
n
⋅
∑
j
=
1
n
sin
α
j
,
1
n
⋅
∑
j
=
1
n
cos
α
j
)
{\displaystyle {\bar {\alpha }}=\operatorname {atan2} \left({\frac {1}{n}}\cdot \sum _{j=1}^{n}\sin \alpha _{j},{\frac {1}{n}}\cdot \sum _{j=1}^{n}\cos \alpha _{j}\right)}
Task[edit]
write a function/method/subroutine/... that given a list of angles in degrees returns their mean angle.
(You should use a built-in function if you have one that does this for degrees or radians).
Use the function to compute the means of these lists of angles (in degrees):
[350, 10]
[90, 180, 270, 360]
[10, 20, 30]
Show your output here.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #PHP | PHP | <?php
$samples = array(
'1st' => array(350, 10),
'2nd' => array(90, 180, 270, 360),
'3rd' => array(10, 20, 30)
);
foreach($samples as $key => $sample){
echo 'Mean angle for ' . $key . ' sample: ' . meanAngle($sample) . ' degrees.' . PHP_EOL;
}
function meanAngle ($angles){
$y_part = $x_part = 0;
$size = count($angles);
for ($i = 0; $i < $size; $i++){
$x_part += cos(deg2rad($angles[$i]));
$y_part += sin(deg2rad($angles[$i]));
}
$x_part /= $size;
$y_part /= $size;
return rad2deg(atan2($y_part, $x_part));
}
?> |
http://rosettacode.org/wiki/Averages/Median | Averages/Median | Task[edit]
Write a program to find the median value of a vector of floating-point numbers.
The program need not handle the case where the vector is empty, but must handle the case where there are an even number of elements. In that case, return the average of the two middle values.
There are several approaches to this. One is to sort the elements, and then pick the element(s) in the middle.
Sorting would take at least O(n logn). Another approach would be to build a priority queue from the elements, and then extract half of the elements to get to the middle element(s). This would also take O(n logn). The best solution is to use the selection algorithm to find the median in O(n) time.
See also
Quickselect_algorithm
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #GAP | GAP | Median := function(v)
local n, w;
w := SortedList(v);
n := Length(v);
return (w[QuoInt(n + 1, 2)] + w[QuoInt(n, 2) + 1]) / 2;
end;
a := [41, 56, 72, 17, 93, 44, 32];
b := [41, 72, 17, 93, 44, 32];
Median(a);
# 44
Median(b);
# 85/2 |
http://rosettacode.org/wiki/Averages/Median | Averages/Median | Task[edit]
Write a program to find the median value of a vector of floating-point numbers.
The program need not handle the case where the vector is empty, but must handle the case where there are an even number of elements. In that case, return the average of the two middle values.
There are several approaches to this. One is to sort the elements, and then pick the element(s) in the middle.
Sorting would take at least O(n logn). Another approach would be to build a priority queue from the elements, and then extract half of the elements to get to the middle element(s). This would also take O(n logn). The best solution is to use the selection algorithm to find the median in O(n) time.
See also
Quickselect_algorithm
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Go | Go | package main
import (
"fmt"
"sort"
)
func main() {
fmt.Println(median([]float64{3, 1, 4, 1})) // prints 2
fmt.Println(median([]float64{3, 1, 4, 1, 5})) // prints 3
}
func median(a []float64) float64 {
sort.Float64s(a)
half := len(a) / 2
m := a[half]
if len(a)%2 == 0 {
m = (m + a[half-1]) / 2
}
return m
} |
http://rosettacode.org/wiki/Averages/Pythagorean_means | Averages/Pythagorean means | Task[edit]
Compute all three of the Pythagorean means of the set of integers 1 through 10 (inclusive).
Show that
A
(
x
1
,
…
,
x
n
)
≥
G
(
x
1
,
…
,
x
n
)
≥
H
(
x
1
,
…
,
x
n
)
{\displaystyle A(x_{1},\ldots ,x_{n})\geq G(x_{1},\ldots ,x_{n})\geq H(x_{1},\ldots ,x_{n})}
for this set of positive integers.
The most common of the three means, the arithmetic mean, is the sum of the list divided by its length:
A
(
x
1
,
…
,
x
n
)
=
x
1
+
⋯
+
x
n
n
{\displaystyle A(x_{1},\ldots ,x_{n})={\frac {x_{1}+\cdots +x_{n}}{n}}}
The geometric mean is the
n
{\displaystyle n}
th root of the product of the list:
G
(
x
1
,
…
,
x
n
)
=
x
1
⋯
x
n
n
{\displaystyle G(x_{1},\ldots ,x_{n})={\sqrt[{n}]{x_{1}\cdots x_{n}}}}
The harmonic mean is
n
{\displaystyle n}
divided by the sum of the reciprocal of each item in the list:
H
(
x
1
,
…
,
x
n
)
=
n
1
x
1
+
⋯
+
1
x
n
{\displaystyle H(x_{1},\ldots ,x_{n})={\frac {n}{{\frac {1}{x_{1}}}+\cdots +{\frac {1}{x_{n}}}}}}
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Lasso | Lasso | define arithmetic_mean(a::staticarray)::decimal => {
//sum of the list divided by its length
return (with e in #a sum #e) / decimal(#a->size)
}
define geometric_mean(a::staticarray)::decimal => {
// The geometric mean is the nth root of the product of the list
local(prod = 1)
with e in #a do => { #prod *= #e }
return math_pow(#prod,1/decimal(#a->size))
}
define harmonic_mean(a::staticarray)::decimal => {
// The harmonic mean is n divided by the sum of the reciprocal of each item in the list
return decimal(#a->size)/(with e in #a sum 1/decimal(#e))
}
arithmetic_mean(generateSeries(1,10)->asStaticArray)
geometric_mean(generateSeries(1,10)->asStaticArray)
harmonic_mean(generateSeries(1,10)->asStaticArray) |
http://rosettacode.org/wiki/Balanced_ternary | Balanced ternary | Balanced ternary is a way of representing numbers. Unlike the prevailing binary representation, a balanced ternary integer is in base 3, and each digit can have the values 1, 0, or −1.
Examples
Decimal 11 = 32 + 31 − 30, thus it can be written as "++−"
Decimal 6 = 32 − 31 + 0 × 30, thus it can be written as "+−0"
Task
Implement balanced ternary representation of integers with the following:
Support arbitrarily large integers, both positive and negative;
Provide ways to convert to and from text strings, using digits '+', '-' and '0' (unless you are already using strings to represent balanced ternary; but see requirement 5).
Provide ways to convert to and from native integer type (unless, improbably, your platform's native integer type is balanced ternary). If your native integers can't support arbitrary length, overflows during conversion must be indicated.
Provide ways to perform addition, negation and multiplication directly on balanced ternary integers; do not convert to native integers first.
Make your implementation efficient, with a reasonable definition of "efficient" (and with a reasonable definition of "reasonable").
Test case With balanced ternaries a from string "+-0++0+", b from native integer -436, c "+-++-":
write out a, b and c in decimal notation;
calculate a × (b − c), write out the result in both ternary and decimal notations.
Note: The pages generalised floating point addition and generalised floating point multiplication have code implementing arbitrary precision floating point balanced ternary.
| #Ruby | Ruby | class BalancedTernary
include Comparable
def initialize(str = "")
if str =~ /[^-+0]+/
raise ArgumentError, "invalid BalancedTernary number: #{str}"
end
@digits = trim0(str)
end
I2BT = {0 => ["0",0], 1 => ["+",0], 2 => ["-",1]}
def self.from_int(value)
n = value.to_i
digits = ""
while n != 0
quo, rem = n.divmod(3)
bt, carry = I2BT[rem]
digits = bt + digits
n = quo + carry
end
new(digits)
end
BT2I = {"-" => -1, "0" => 0, "+" => 1}
def to_int
@digits.chars.inject(0) do |sum, char|
sum = 3 * sum + BT2I[char]
end
end
alias :to_i :to_int
def to_s
@digits.dup # String is mutable
end
alias :inspect :to_s
def <=>(other)
to_i <=> other.to_i
end
ADDITION_TABLE = {
"---" => ["-","0"], "--0" => ["-","+"], "--+" => ["0","-"],
"-0-" => ["-","+"], "-00" => ["0","-"], "-0+" => ["0","0"],
"-+-" => ["0","-"], "-+0" => ["0","0"], "-++" => ["0","+"],
"0--" => ["-","+"], "0-0" => ["0","-"], "0-+" => ["0","0"],
"00-" => ["0","-"], "000" => ["0","0"], "00+" => ["0","+"],
"0+-" => ["0","0"], "0+0" => ["0","+"], "0++" => ["+","-"],
"+--" => ["0","-"], "+-0" => ["0","0"], "+-+" => ["0","+"],
"+0-" => ["0","0"], "+00" => ["0","+"], "+0+" => ["+","-"],
"++-" => ["0","+"], "++0" => ["+","-"], "+++" => ["+","0"],
}
def +(other)
maxl = [to_s.length, other.to_s.length].max
a = pad0_reverse(to_s, maxl)
b = pad0_reverse(other.to_s, maxl)
carry = "0"
sum = a.zip( b ).inject("") do |sum, (c1, c2)|
carry, digit = ADDITION_TABLE[carry + c1 + c2]
sum = digit + sum
end
self.class.new(carry + sum)
end
MULTIPLICATION_TABLE = {
"-" => "+0-",
"0" => "000",
"+" => "-0+",
}
def *(other)
product = self.class.new
other.to_s.each_char do |bdigit|
row = to_s.tr("-0+", MULTIPLICATION_TABLE[bdigit])
product += self.class.new(row)
product << 1
end
product >> 1
end
# negation
def -@()
self.class.new(@digits.tr('-+','+-'))
end
# subtraction
def -(other)
self + (-other)
end
# shift left
def <<(count)
@digits = trim0(@digits + "0"*count)
self
end
# shift right
def >>(count)
@digits[-count..-1] = "" if count > 0
@digits = trim0(@digits)
self
end
private
def trim0(str)
str = str.sub(/^0+/, "")
str = "0" if str.empty?
str
end
def pad0_reverse(str, len)
str.rjust(len, "0").reverse.chars
end
end
a = BalancedTernary.new("+-0++0+")
b = BalancedTernary.from_int(-436)
c = BalancedTernary.new("+-++-")
%w[a b c a*(b-c)].each do |exp|
val = eval(exp)
puts "%8s :%13s,%8d" % [exp, val, val.to_i]
end |
http://rosettacode.org/wiki/Babbage_problem | Babbage problem |
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.
For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].
Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.
| #Scheme | Scheme |
(define (digits n)
(string->list (number->string n)))
(define (ends-with list tail)
;; does list end with tail?
(starts-with (reverse list)
(reverse tail)))
(define (starts-with list head)
(cond ((null? head)
#t)
((null? list)
#f)
((equal? (car list) (car head))
(starts-with (cdr list) (cdr head)))
(else
#f)))
(let loop ((i 1))
(if (ends-with (digits (* i i)) (digits 269696))
i
(loop (+ i 1))))
;; 25264
|
http://rosettacode.org/wiki/Approximate_equality | Approximate equality | Sometimes, when testing whether the solution to a task (for example, here on Rosetta Code) is correct, the
difference in floating point calculations between different language implementations becomes significant.
For example, a difference between 32 bit and 64 bit floating point calculations may appear by
about the 8th significant digit in base 10 arithmetic.
Task
Create a function which returns true if two floating point numbers are approximately equal.
The function should allow for differences in the magnitude of numbers, so that, for example,
100000000000000.01 may be approximately equal to 100000000000000.011,
even though 100.01 is not approximately equal to 100.011.
If the language has such a feature in its standard library, this may be used instead of a custom function.
Show the function results with comparisons on the following pairs of values:
100000000000000.01, 100000000000000.011 (note: should return true)
100.01, 100.011 (note: should return false)
10000000000000.001 / 10000.0, 1000000000.0000001000
0.001, 0.0010000001
0.000000000000000000000101, 0.0
sqrt(2) * sqrt(2), 2.0
-sqrt(2) * sqrt(2), -2.0
3.14159265358979323846, 3.14159265358979324
Answers should be true for the first example and false in the second, so that just rounding the numbers to a fixed number of decimals should not be enough. Otherwise answers may vary and still be correct. See the Python code for one type of solution.
| #Ruby | Ruby | require "bigdecimal"
testvalues = [[100000000000000.01, 100000000000000.011],
[100.01, 100.011],
[10000000000000.001 / 10000.0, 1000000000.0000001000],
[0.001, 0.0010000001],
[0.000000000000000000000101, 0.0],
[(2**0.5) * (2**0.5), 2.0],
[-(2**0.5) * (2**0.5), -2.0],
[BigDecimal("3.14159265358979323846"), 3.14159265358979324],
[Float::NAN, Float::NAN,],
[Float::INFINITY, Float::INFINITY],
]
class Numeric
def close_to?(num, tol = Float::EPSILON)
return true if self == num
return false if (self.to_f.nan? or num.to_f.nan?) # NaN is not even close to itself
return false if [self, num].count( Float::INFINITY) == 1 # Infinity is only close to itself
return false if [self, num].count(-Float::INFINITY) == 1
(self-num).abs <= tol * ([self.abs, num.abs].max)
end
end
testvalues.each do |a,b|
puts "#{a} #{a.close_to?(b) ? '≈' : '≉'} #{b}"
end
|
http://rosettacode.org/wiki/Approximate_equality | Approximate equality | Sometimes, when testing whether the solution to a task (for example, here on Rosetta Code) is correct, the
difference in floating point calculations between different language implementations becomes significant.
For example, a difference between 32 bit and 64 bit floating point calculations may appear by
about the 8th significant digit in base 10 arithmetic.
Task
Create a function which returns true if two floating point numbers are approximately equal.
The function should allow for differences in the magnitude of numbers, so that, for example,
100000000000000.01 may be approximately equal to 100000000000000.011,
even though 100.01 is not approximately equal to 100.011.
If the language has such a feature in its standard library, this may be used instead of a custom function.
Show the function results with comparisons on the following pairs of values:
100000000000000.01, 100000000000000.011 (note: should return true)
100.01, 100.011 (note: should return false)
10000000000000.001 / 10000.0, 1000000000.0000001000
0.001, 0.0010000001
0.000000000000000000000101, 0.0
sqrt(2) * sqrt(2), 2.0
-sqrt(2) * sqrt(2), -2.0
3.14159265358979323846, 3.14159265358979324
Answers should be true for the first example and false in the second, so that just rounding the numbers to a fixed number of decimals should not be enough. Otherwise answers may vary and still be correct. See the Python code for one type of solution.
| #Rust | Rust | /// Return whether the two numbers `a` and `b` are close.
/// Closeness is determined by the `epsilon` parameter -
/// the numbers are considered close if the difference between them
/// is no more than epsilon * max(abs(a), abs(b)).
fn isclose(a: f64, b: f64, epsilon: f64) -> bool {
(a - b).abs() <= a.abs().max(b.abs()) * epsilon
}
fn main() {
fn sqrt(x: f64) -> f64 { x.sqrt() }
macro_rules! test {
($a: expr, $b: expr) => {
let operator = if isclose($a, $b, 1.0e-9) { '≈' } else { '≉' };
println!("{:>28} {} {}", stringify!($a), operator, stringify!($b))
}
}
test!(100000000000000.01, 100000000000000.011);
test!(100.01, 100.011);
test!(10000000000000.001/10000.0, 1000000000.0000001000);
test!(0.001, 0.0010000001);
test!(0.000000000000000000000101, 0.0);
test!( sqrt(2.0) * sqrt(2.0), 2.0);
test!(-sqrt(2.0) * sqrt(2.0), -2.0);
test!(3.14159265358979323846, 3.14159265358979324);
} |
http://rosettacode.org/wiki/Balanced_brackets | Balanced brackets | Task:
Generate a string with N opening brackets [ and with N closing brackets ], in some arbitrary order.
Determine whether the generated string is balanced; that is, whether it consists entirely of pairs of opening/closing brackets (in that order), none of which mis-nest.
Examples
(empty) OK
[] OK
[][] OK
[[][]] OK
][ NOT OK
][][ NOT OK
[]][[] NOT OK
| #Elena | Elena | import system'routines;
import extensions;
import extensions'text;
randomBrackets(len)
{
if (0 == len)
{
^emptyString
}
else
{
var brackets :=
Array.allocate(len).populate:(i => $91)
+
Array.allocate(len).populate:(i => $93);
brackets := brackets.randomize(len * 2);
^ brackets.summarize(new StringWriter()).toString()
}
}
extension op
{
get isBalanced()
{
var counter := new Integer(0);
self.seekEach:(ch => counter.append((ch==$91).iif(1,-1)) < 0);
^ (0 == counter)
}
}
public program()
{
for(int len := 0, len < 9, len += 1)
{
var str := randomBrackets(len);
console.printLine("""",str,"""",str.isBalanced ? " is balanced" : " is not balanced")
};
console.readChar()
} |
http://rosettacode.org/wiki/Append_a_record_to_the_end_of_a_text_file | Append a record to the end of a text file | Many systems offer the ability to open a file for writing, such that any data written will be appended to the end of the file. Further, the file operations will always adjust the position pointer to guarantee the end of the file, even in a multitasking environment.
This feature is most useful in the case of log files, where many jobs may be appending to the log file at the same time, or where care must be taken to avoid concurrently overwriting the same record from another job.
Task
Given a two record sample for a mythical "passwd" file:
Write these records out in the typical system format.
Ideally these records will have named fields of various types.
Close the file, then reopen the file for append.
Append a new record to the file and close the file again.
Take appropriate care to avoid concurrently overwrites from another job.
Open the file and demonstrate the new record has indeed written to the end.
Source record field types and contents.
account
password
UID
GID
fullname,office,extension,homephone,email
directory
shell
string
string
int
int
struct(string,string,string,string,string)
string
string
jsmith
x
1001
1000
Joe Smith,Room 1007,(234)555-8917,(234)555-0077,[email protected]
/home/jsmith
/bin/bash
jdoe
x
1002
1000
Jane Doe,Room 1004,(234)555-8914,(234)555-0044,[email protected]
/home/jdoe
/bin/bash
Record to be appended.
account
password
UID
GID
fullname,office,extension,homephone,email
directory
shell
string
string
int
int
struct(string,string,string,string,string)
string
string
xyz
x
1003
1000
X Yz,Room 1003,(234)555-8913,(234)555-0033,[email protected]
/home/xyz
/bin/bash
Resulting file format: should mimic Linux's /etc/passwd file format with particular attention to the "," separator used in the GECOS field. But if the specific language has a particular or unique format of storing records in text file, then this format should be named and demonstrated with an additional example.
Expected output:
Appended record: xyz:x:1003:1000:X Yz,Room 1003,(234)555-8913,(234)555-0033,[email protected]:/home/xyz:/bin/bash
Finally: Provide a summary of the language's "append record" capabilities in a table. eg.
Append Capabilities.
Data Representation
IO
Library
Append
Possible
Automatic
Append
Multi-tasking
Safe
In core
On disk
C struct
CSV text file
glibc/stdio
☑
☑
☑ (Not all, eg NFS)
Alternatively: If the language's appends can not guarantee its writes will always append, then note this restriction in the table. If possible, provide an actual code example (possibly using file/record locking) to guarantee correct concurrent appends.
| #Groovy | Groovy | class PasswdRecord {
String account, password, directory, shell
int uid, gid
SourceRecord source
private static final fs = ':'
private static final fieldNames = ['account', 'password', 'uid', 'gid', 'source', 'directory', 'shell']
private static final stringFields = ['account', 'password', 'directory', 'shell']
private static final intFields = ['uid', 'gid']
PasswdRecord(String line = null) {
if (!line) return
def fields = line.split(fs)
if (fields.size() != fieldNames.size()) {
throw new IllegalArgumentException(
"Passwd record must have exactly ${fieldNames.size()} '${fs}'-delimited fields")
}
(0..<fields.size()).each { i ->
switch (fieldNames[i]) {
case stringFields: this[fieldNames[i]] = fields[i]; break
case intFields: this[fieldNames[i]] = fields[i] as Integer; break
default /* source */: this.source = new SourceRecord(fields[i]); break
}
}
}
@Override String toString() { fieldNames.collect { "${this[it]}${fs}" }.sum()[0..-2] }
}
class SourceRecord {
String fullname, office, extension, homephone, email
private static final fs = ','
private static final fieldNames =
['fullname', 'office', 'extension', 'homephone', 'email']
SourceRecord(String line = null) {
if (!line) return
def fields = line.split(fs)
if (fields.size() != fieldNames.size()) {
throw new IllegalArgumentException(
"Source record must have exactly ${fieldNames.size()} '${fs}'-delimited fields")
}
(0..<fields.size()).each { i ->
this[fieldNames[i]] = fields[i]
}
}
@Override String toString() { fieldNames.collect { "${this[it]}${fs}" }.sum()[0..-2] }
}
def appendNewPasswdRecord = {
PasswdRecord pwr = new PasswdRecord().with { p ->
(account, password, uid, gid) = ['xyz', 'x', 1003, 1000]
source = new SourceRecord().with { s ->
(fullname, office, extension, homephone, email) =
['X Yz', 'Room 1003', '(234)555-8913', '(234)555-0033', '[email protected]']
s
}
(directory, shell) = ['/home/xyz', '/bin/bash']
p
};
new File('passwd.txt').withWriterAppend { w ->
w.append(pwr as String)
w.append('\r\n')
}
} |
http://rosettacode.org/wiki/Associative_array/Creation | Associative array/Creation | Task
The goal is to create an associative array (also known as a dictionary, map, or hash).
Related tasks:
Associative arrays/Iteration
Hash from two arrays
See also
Array
Associative array: Creation, Iteration
Collections
Compound data type
Doubly-linked list: Definition, Element definition, Element insertion, List Traversal, Element Removal
Linked list
Queue: Definition, Usage
Set
Singly-linked list: Element definition, Element insertion, List Traversal, Element Removal
Stack
| #AutoIt | AutoIt | ; Associative arrays in AutoIt.
; All the required functions are below the examples.
; Initialize an error handler to deal with any COM errors..
global $oMyError = ObjEvent("AutoIt.Error", "AAError")
; first example, simple.
global $simple
; Initialize your array ...
AAInit($simple)
AAAdd($simple, "Appple", "fruit")
AAAdd($simple, "Dog", "animal")
AAAdd($simple, "Silicon", "tetravalent metalloid semiconductor")
ConsoleWrite("It is well-known that Silicon is a " & AAGetItem($simple, "Silicon") & "." & @CRLF)
ConsoleWrite(@CRLF)
; A more interesting example..
$ini_path = "AA_Test.ini"
; Put this prefs section in your ini file..
; [test]
; foo=foo value
; foo2=foo2 value
; bar=bar value
; bar2=bar2 value
global $associative_array
AAInit($associative_array)
; We are going to convert this 2D array into a cute associative array where we
; can access the values by simply using their respective key names..
$test_array = IniReadSection($ini_path, "test")
for $z = 1 to 2 ; do it twice, to show that the items are *really* there!
for $i = 1 to $test_array[0][0]
$key_name = $test_array[$i][0]
ConsoleWrite("Adding '" & $key_name & "'.." & @CRLF)
; key already exists in "$associative_array", use the pre-determined value..
if AAExists($associative_array, $key_name) then
$this_value = AAGetItem($associative_array, $key_name)
ConsoleWrite("key_name ALREADY EXISTS! : =>" & $key_name & "<=" & @CRLF)
else
$this_value = $test_array[$i][1]
; store left=right value pair in AA
if $this_value then
AAAdd($associative_array, $key_name, $this_value)
endif
endif
next
next
ConsoleWrite(@CRLF & "Array Count: =>" & AACount($associative_array) & "<=" & @CRLF)
AAList($associative_array)
ConsoleWrite(@CRLF & "Removing 'foo'..")
AARemove($associative_array, "foo")
ConsoleWrite(@CRLF & "Array Count: =>" & AACount($associative_array) & "<=" & @CRLF)
AAList($associative_array)
AAWipe($associative_array)
; end
func AAInit(ByRef $dict_obj)
$dict_obj = ObjCreate("Scripting.Dictionary")
endfunc
; Adds a key and item pair to a Dictionary object..
func AAAdd(ByRef $dict_obj, $key, $val)
$dict_obj.Add($key, $val)
If @error Then return SetError(1, 1, -1)
endfunc
; Removes a key and item pair from a Dictionary object..
func AARemove(ByRef $dict_obj, $key)
$dict_obj.Remove($key)
If @error Then return SetError(1, 1, -1)
endfunc
; Returns true if a specified key exists in the associative array, false if not..
func AAExists(ByRef $dict_obj, $key)
return $dict_obj.Exists($key)
endfunc
; Returns a value for a specified key name in the associative array..
func AAGetItem(ByRef $dict_obj, $key)
return $dict_obj.Item($key)
endfunc
; Returns the total number of keys in the array..
func AACount(ByRef $dict_obj)
return $dict_obj.Count
endfunc
; List all the "Key" > "Item" pairs in the array..
func AAList(ByRef $dict_obj)
ConsoleWrite("AAList: =>" & @CRLF)
local $k = $dict_obj.Keys ; Get the keys
; local $a = $dict_obj.Items ; Get the items (for reference)
for $i = 0 to AACount($dict_obj) -1 ; Iterate the array
ConsoleWrite($k[$i] & " ==> " & AAGetItem($dict_obj, $k[$i]) & @CRLF)
next
endfunc
; Wipe the array, obviously.
func AAWipe(ByRef $dict_obj)
$dict_obj.RemoveAll()
endfunc
; Oh oh!
func AAError()
Local $err = $oMyError.number
If $err = 0 Then $err = -1
SetError($err) ; to check for after this function returns
endfunc
;; End AA Functions.
|
http://rosettacode.org/wiki/Anti-primes | Anti-primes | The anti-primes
(or highly composite numbers, sequence A002182 in the OEIS)
are the natural numbers with more factors than any smaller than itself.
Task
Generate and show here, the first twenty anti-primes.
Related tasks
Factors of an integer
Sieve of Eratosthenes
| #Cowgol | Cowgol | include "cowgol.coh";
const AMOUNT := 20;
sub countFactors(n: uint16): (count: uint16) is
var i: uint16 := 1;
count := 1;
while i <= n/2 loop
if n%i == 0 then
count := count + 1;
end if;
i := i + 1;
end loop;
end sub;
var max: uint16 := 0;
var seen: uint8 := 0;
var n: uint16 := 1;
var f: uint16 := 0;
while seen < AMOUNT loop;
f := countFactors(n);
if f > max then
print_i16(n);
print_char(' ');
max := f;
seen := seen + 1;
end if;
n := n + 1;
end loop;
print_nl(); |
http://rosettacode.org/wiki/Anti-primes | Anti-primes | The anti-primes
(or highly composite numbers, sequence A002182 in the OEIS)
are the natural numbers with more factors than any smaller than itself.
Task
Generate and show here, the first twenty anti-primes.
Related tasks
Factors of an integer
Sieve of Eratosthenes
| #Crystal | Crystal | def count_divisors(n : Int64) : Int64
return 1_i64 if n < 2
count = 2_i64
i = 2
while i <= n // 2
count += 1 if n % i == 0
i += 1
end
count
end
max_div = 0_i64
count = 0_i64
print "The first 20 anti-primes are: "
n = 1_i64
while count < 20
d = count_divisors n
if d > max_div
print "#{n} "
max_div = d
count += 1
end
n += 1
end
puts ""
|
http://rosettacode.org/wiki/Atomic_updates | Atomic updates |
Task
Define a data type consisting of a fixed number of 'buckets', each containing a nonnegative integer value, which supports operations to:
get the current value of any bucket
remove a specified amount from one specified bucket and add it to another, preserving the total of all bucket values, and clamping the transferred amount to ensure the values remain non-negative
In order to exercise this data type, create one set of buckets, and start three concurrent tasks:
As often as possible, pick two buckets and make their values closer to equal.
As often as possible, pick two buckets and arbitrarily redistribute their values.
At whatever rate is convenient, display (by any means) the total value and, optionally, the individual values of each bucket.
The display task need not be explicit; use of e.g. a debugger or trace tool is acceptable provided it is simple to set up to provide the display.
This task is intended as an exercise in atomic operations. The sum of the bucket values must be preserved even if the two tasks attempt to perform transfers simultaneously, and a straightforward solution is to ensure that at any time, only one transfer is actually occurring — that the transfer operation is atomic.
| #PARI.2FGP | PARI/GP | use strict;
use 5.10.0;
use threads 'yield';
use threads::shared;
my @a :shared = (100) x 10;
my $stop :shared = 0;
sub pick2 {
my $i = int(rand(10));
my $j;
$j = int(rand(10)) until $j != $i;
($i, $j)
}
sub even {
lock @a;
my ($i, $j) = pick2;
my $sum = $a[$i] + $a[$j];
$a[$i] = int($sum / 2);
$a[$j] = $sum - $a[$i];
}
sub rand_move {
lock @a;
my ($i, $j) = pick2;
my $x = int(rand $a[$i]);
$a[$i] -= $x;
$a[$j] += $x;
}
sub show {
lock @a;
my $sum = 0;
$sum += $_ for (@a);
printf "%4d", $_ for @a;
print " total $sum\n";
}
my $t1 = async { even until $stop }
my $t2 = async { rand_move until $stop }
my $t3 = async {
for (1 .. 10) {
show;
sleep(1);
}
$stop = 1;
};
$t1->join; $t2->join; $t3->join; |
http://rosettacode.org/wiki/Assertions | Assertions | Assertions are a way of breaking out of code when there is an error or an unexpected input.
Some languages throw exceptions and some treat it as a break point.
Task
Show an assertion in your language by asserting that an integer variable is equal to 42.
| #Lua | Lua | a = 5
assert (a == 42)
assert (a == 42,'\''..a..'\' is not the answer to life, the universe, and everything') |
http://rosettacode.org/wiki/Assertions | Assertions | Assertions are a way of breaking out of code when there is an error or an unexpected input.
Some languages throw exceptions and some treat it as a break point.
Task
Show an assertion in your language by asserting that an integer variable is equal to 42.
| #M2000_Interpreter | M2000 Interpreter |
Module Assert {
\\ This is a global object named Rec
Global Group Rec {
Private:
document doc$="Error List at "+date$(today)+" "+time$(now)+{
}
Public:
lastfilename$="noname.err"
Module Error(a$) {
if a$="" then exit
.doc$<=" "+a$+{
}
flush error
}
Module Reset {
Clear .doc$
}
Module Display {
Report .doc$
}
Module SaveIt {
.lastfilename$<=replace$("/", "-","Err"+date$(today)+time$(now)+".err")
Save.Doc .doc$,.lastfilename$
}
}
Module Checkit {
Function Error1 (x) {
if x<10 then Print "Normal" : exit
=130 ' error code
}
Call Error1(5)
Try ok {
Call Error1(100)
}
If not Ok then Rec.Error Error$ : Flush Error
Test "breakpoint A" ' open Control form, show code as executed, press next or close it
Try {
Report "Run this"
Error "Hello"
Report "Not run this"
}
Rec.Error Error$
Module Error1 (x) {
if x<10 then Print "Normal" : exit
Error "Big Error"
}
Try ok {
Error1 100
}
If Error then Rec.Error Error$
}
Checkit
Rec.Display
Rec.SaveIt
win "notepad.exe", dir$+Rec.lastfilename$
}
Assert
|
http://rosettacode.org/wiki/Assertions | Assertions | Assertions are a way of breaking out of code when there is an error or an unexpected input.
Some languages throw exceptions and some treat it as a break point.
Task
Show an assertion in your language by asserting that an integer variable is equal to 42.
| #Maple | Maple | a := 5:
ASSERT( a = 42 );
ASSERT( a = 42, "a is not the answer to life, the universe, and everything" ); |
http://rosettacode.org/wiki/Apply_a_callback_to_an_array | Apply a callback to an array | Task
Take a combined set of elements and apply a function to each element.
| #CLU | CLU | % This procedure will call a given procedure with each element
% of the given array. Thanks to CLU's type parameterization,
% it will work for any type of element.
apply_to_all = proc [T: type] (a: array[T], f: proctype(int,T))
for i: int in array[T]$indexes(a) do
f(i, a[i])
end
end apply_to_all
% Callbacks for both string and int
show_int = proc (i, val: int)
po: stream := stream$primary_output()
stream$putl(po, "array[" || int$unparse(i) || "] = " || int$unparse(val));
end show_int
show_string = proc (i: int, val: string)
po: stream := stream$primary_output()
stream$putl(po, "array[" || int$unparse(i) || "] = " || val);
end show_string
% Here's how to use them
start_up = proc ()
po: stream := stream$primary_output()
ints: array[int] := array[int]$[2, 3, 5, 7, 11]
strings: array[string] := array[string]$
["enemy", "lasagna", "robust", "below", "wax"]
stream$putl(po, "Ints: ")
apply_to_all[int](ints, show_int)
stream$putl(po, "\nStrings: ")
apply_to_all[string](strings, show_string)
end start_up |
http://rosettacode.org/wiki/Apply_a_callback_to_an_array | Apply a callback to an array | Task
Take a combined set of elements and apply a function to each element.
| #COBOL | COBOL | IDENTIFICATION DIVISION.
PROGRAM-ID. Map.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 Table-Size CONSTANT 30.
LOCAL-STORAGE SECTION.
01 I USAGE UNSIGNED-INT.
LINKAGE SECTION.
01 Table-Param.
03 Table-Values USAGE COMP-2 OCCURS Table-Size TIMES.
01 Func-Id PIC X(30).
PROCEDURE DIVISION USING Table-Param Func-Id.
PERFORM VARYING I FROM 1 BY 1 UNTIL Table-Size < I
CALL Func-Id USING BY REFERENCE Table-Values (I)
END-PERFORM
GOBACK
. |
http://rosettacode.org/wiki/Averages/Mode | Averages/Mode | Task[edit]
Write a program to find the mode value of a collection.
The case where the collection is empty may be ignored. Care must be taken to handle the case where the mode is non-unique.
If it is not appropriate or possible to support a general collection, use a vector (array), if possible. If it is not appropriate or possible to support an unspecified value type, use integers.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Oz | Oz | declare
fun {Mode Xs}
Freq = {Dictionary.new}
for X in Xs do
Freq.X := {CondSelect Freq X 0} + 1
end
MaxCount = {FoldL {Dictionary.items Freq} Max 0}
in
for Value#Count in {Dictionary.entries Freq} collect:C do
if Count == MaxCount then
{C Value}
end
end
end
in
{Show {Mode [1 2 3 3 2 1 1]}}
{Show {Mode [1 2 3 3 2 1]}} |
http://rosettacode.org/wiki/Associative_array/Iteration | Associative array/Iteration | Show how to iterate over the key-value pairs of an associative array, and print each pair out.
Also show how to iterate just over the keys, or the values, if there is a separate way to do that in your language.
See also
Array
Associative array: Creation, Iteration
Collections
Compound data type
Doubly-linked list: Definition, Element definition, Element insertion, List Traversal, Element Removal
Linked list
Queue: Definition, Usage
Set
Singly-linked list: Element definition, Element insertion, List Traversal, Element Removal
Stack
| #Delphi | Delphi | program AssociativeArrayIteration;
{$APPTYPE CONSOLE}
uses SysUtils, Generics.Collections;
var
i: Integer;
s: string;
lDictionary: TDictionary<string, Integer>;
lPair: TPair<string, Integer>;
begin
lDictionary := TDictionary<string, Integer>.Create;
try
lDictionary.Add('foo', 5);
lDictionary.Add('bar', 10);
lDictionary.Add('baz', 15);
lDictionary.AddOrSetValue('foo', 6);
for lPair in lDictionary do
Writeln(Format('Pair: %s = %d', [lPair.Key, lPair.Value]));
for s in lDictionary.Keys do
Writeln('Key: ' + s);
for i in lDictionary.Values do
Writeln('Value: ', i);
finally
lDictionary.Free;
end;
end. |
http://rosettacode.org/wiki/Apply_a_digital_filter_(direct_form_II_transposed) | Apply a digital filter (direct form II transposed) | Digital filters are used to apply a mathematical operation to a sampled signal. One of the common formulations is the "direct form II transposed" which can represent both infinite impulse response (IIR) and finite impulse response (FIR) filters, as well as being more numerically stable than other forms. [1]
Task
Filter a signal using an order 3 low-pass Butterworth filter. The coefficients for the filter are a=[1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17] and b = [0.16666667, 0.5, 0.5, 0.16666667]
The signal that needs filtering is the following vector: [-0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412, -0.662370894973, -1.00700480494, -0.404707073677 ,0.800482325044, 0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195, 0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293, 0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589]
| #ooRexx | ooRexx | /* REXX */
a=.array~of(1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17)
b=.array~of(0.16666667, 0.5, 0.5, 0.16666667)
s=.array~of(-0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412,,
-0.662370894973, -1.00700480494, -0.404707073677 ,0.800482325044,,
0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195,,
0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293,,
0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589)
ret=.array~new(s~items)~~fill(0) /* create array and fill with zeroes */
Call filter a,b,s,ret
Do i=1 To ret~items
Say format(i,2) format(ret[i],2,12)
End
Exit
::Routine filter
Use Arg a,b,s,ret
Do i=1 To s~items
temp=0
Do j=1 To b~items
if i-j>=0 Then
temp=temp+b[j]*s[i-j+1]
End
Do j=1 To a~items
if i-j>=0 Then Do
u=i-j+1
temp=temp-a[j]*ret[u]
End
End
ret[i]=temp/a[1]
End
Return
::OPTIONS digits 24 /* Numeric Digits 24, everywhere */
|
http://rosettacode.org/wiki/Apply_a_digital_filter_(direct_form_II_transposed) | Apply a digital filter (direct form II transposed) | Digital filters are used to apply a mathematical operation to a sampled signal. One of the common formulations is the "direct form II transposed" which can represent both infinite impulse response (IIR) and finite impulse response (FIR) filters, as well as being more numerically stable than other forms. [1]
Task
Filter a signal using an order 3 low-pass Butterworth filter. The coefficients for the filter are a=[1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17] and b = [0.16666667, 0.5, 0.5, 0.16666667]
The signal that needs filtering is the following vector: [-0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412, -0.662370894973, -1.00700480494, -0.404707073677 ,0.800482325044, 0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195, 0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293, 0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589]
| #Perl | Perl | use strict;
use List::AllUtils 'natatime';
sub TDF_II_filter {
our(@signal,@a,@b);
local(*signal,*a,*b) = (shift, shift, shift);
my @out = (0) x $#signal;
for my $i (0..@signal-1) {
my $this;
map { $this += $b[$_] * $signal[$i-$_] if $i-$_ >= 0 } 0..@b;
map { $this -= $a[$_] * $out[$i-$_] if $i-$_ >= 0 } 0..@a;
$out[$i] = $this / $a[0];
}
@out
}
my @signal = (
-0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412,
-0.662370894973, -1.00700480494, -0.404707073677, 0.800482325044,
0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195,
0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293,
0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589
);
my @a = ( 1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17 );
my @b = ( 0.16666667, 0.5, 0.5, 0.16666667 );
my @filtered = TDF_II_filter(\@signal, \@a, \@b);
my $iter = natatime 5, @filtered;
while( my @values = $iter->() ) {
printf(' %10.6f' x 5 . "\n", @values);
}
|
http://rosettacode.org/wiki/Averages/Arithmetic_mean | Averages/Arithmetic mean | Task[edit]
Write a program to find the mean (arithmetic average) of a numeric vector.
In case of a zero-length input, since the mean of an empty set of numbers is ill-defined, the program may choose to behave in any way it deems appropriate, though if the programming language has an established convention for conveying math errors or undefined values, it's preferable to follow it.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #ECL | ECL |
AveVal(SET OF INTEGER s) := AVE(s);
//example usage
SetVals := [14,9,16,20,91];
AveVal(SetVals) //returns 30.0 ;
|
http://rosettacode.org/wiki/Averages/Arithmetic_mean | Averages/Arithmetic mean | Task[edit]
Write a program to find the mean (arithmetic average) of a numeric vector.
In case of a zero-length input, since the mean of an empty set of numbers is ill-defined, the program may choose to behave in any way it deems appropriate, though if the programming language has an established convention for conveying math errors or undefined values, it's preferable to follow it.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Elena | Elena | import extensions;
extension op
{
average()
{
real sum := 0;
int count := 0;
var enumerator := self.enumerator();
while (enumerator.next())
{
sum += enumerator.get();
count += 1;
};
^ sum / count
}
}
public program()
{
var array := new int[]{1, 2, 3, 4, 5, 6, 7, 8};
console.printLine(
"Arithmetic mean of {",array.asEnumerable(),"} is ",
array.average()).readChar()
} |
http://rosettacode.org/wiki/Associative_array/Merging | Associative array/Merging | Task
Define two associative arrays, where one represents the following "base" data:
Key
Value
"name"
"Rocket Skates"
"price"
12.75
"color"
"yellow"
And the other represents "update" data:
Key
Value
"price"
15.25
"color"
"red"
"year"
1974
Merge these into a new associative array that contains every key found in either of the source ones. Each key should map to the value in the second (update) table if that exists, or else to the value in the first (base) table. If possible, do this in a way that does not mutate the original two associative arrays. Obviously this should be done in a way that would work for any data, not just the specific data given here, but in this example the result should be:
Key
Value
"name"
"Rocket Skates"
"price"
15.25
"color"
"red"
"year"
1974
| #zkl | zkl | base:=Dictionary(
"name", "Rocket Skates",
"price", 12.75,
"color", "yellow",);
update:=Dictionary(
"price", 15.25,
"color", "red",
"year", 1974,);
update.pump( new:=base.copy() );
new.pump(Void,fcn([(k,v)]){ println("%s\t%s".fmt(k,v)) }); |
http://rosettacode.org/wiki/Average_loop_length | Average loop length | Let f be a uniformly-randomly chosen mapping from the numbers 1..N to the numbers 1..N (note: not necessarily a permutation of 1..N; the mapping could produce a number in more than one way or not at all). At some point, the sequence 1, f(1), f(f(1))... will contain a repetition, a number that occurring for the second time in the sequence.
Task
Write a program or a script that estimates, for each N, the average length until the first such repetition.
Also calculate this expected length using an analytical formula, and optionally compare the simulated result with the theoretical one.
This problem comes from the end of Donald Knuth's Christmas tree lecture 2011.
Example of expected output:
N average analytical (error)
=== ========= ============ =========
1 1.0000 1.0000 ( 0.00%)
2 1.4992 1.5000 ( 0.05%)
3 1.8784 1.8889 ( 0.56%)
4 2.2316 2.2188 ( 0.58%)
5 2.4982 2.5104 ( 0.49%)
6 2.7897 2.7747 ( 0.54%)
7 3.0153 3.0181 ( 0.09%)
8 3.2429 3.2450 ( 0.07%)
9 3.4536 3.4583 ( 0.14%)
10 3.6649 3.6602 ( 0.13%)
11 3.8091 3.8524 ( 1.12%)
12 3.9986 4.0361 ( 0.93%)
13 4.2074 4.2123 ( 0.12%)
14 4.3711 4.3820 ( 0.25%)
15 4.5275 4.5458 ( 0.40%)
16 4.6755 4.7043 ( 0.61%)
17 4.8877 4.8579 ( 0.61%)
18 4.9951 5.0071 ( 0.24%)
19 5.1312 5.1522 ( 0.41%)
20 5.2699 5.2936 ( 0.45%)
| #Scheme | Scheme |
(import (scheme base)
(scheme write)
(srfi 1 lists)
(only (srfi 13 strings) string-pad-right)
(srfi 27 random-bits))
(define (analytical-function n)
(define (factorial n)
(fold * 1 (iota n 1)))
;
(fold (lambda (i sum)
(+ sum
(/ (factorial n) (expt n i) (factorial (- n i)))))
0
(iota n 1)))
(define (simulation n runs)
(define (single-simulation)
(random-source-randomize! default-random-source)
(let ((vec (make-vector n #f)))
(let loop ((count 0)
(num (random-integer n)))
(if (vector-ref vec num)
count
(begin (vector-set! vec num #t)
(loop (+ 1 count)
(random-integer n)))))))
;;
(let loop ((total 0)
(run runs))
(if (zero? run)
(/ total runs)
(loop (+ total (single-simulation))
(- run 1)))))
(display " N average formula (error) \n")
(display "=== ========= ========= =========\n")
(for-each
(lambda (n)
(let ((simulation (inexact (simulation n 10000)))
(formula (inexact (analytical-function n))))
(display
(string-append
" "
(string-pad-right (number->string n) 3)
" "
(string-pad-right (number->string simulation) 6)
" "
(string-pad-right (number->string formula) 6)
" ("
(string-pad-right
(number->string (* 100 (/ (- simulation formula) formula)))
5)
"%)"))
(newline)))
(iota 20 1))
|
http://rosettacode.org/wiki/Averages/Simple_moving_average | Averages/Simple moving average | Computing the simple moving average of a series of numbers.
Task[edit]
Create a stateful function/class/instance that takes a period and returns a routine that takes a number as argument and returns a simple moving average of its arguments so far.
Description
A simple moving average is a method for computing an average of a stream of numbers by only averaging the last P numbers from the stream, where P is known as the period.
It can be implemented by calling an initialing routine with P as its argument, I(P), which should then return a routine that when called with individual, successive members of a stream of numbers, computes the mean of (up to), the last P of them, lets call this SMA().
The word stateful in the task description refers to the need for SMA() to remember certain information between calls to it:
The period, P
An ordered container of at least the last P numbers from each of its individual calls.
Stateful also means that successive calls to I(), the initializer, should return separate routines that do not share saved state so they could be used on two independent streams of data.
Pseudo-code for an implementation of SMA is:
function SMA(number: N):
stateful integer: P
stateful list: stream
number: average
stream.append_last(N)
if stream.length() > P:
# Only average the last P elements of the stream
stream.delete_first()
if stream.length() == 0:
average = 0
else:
average = sum( stream.values() ) / stream.length()
return average
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Tcl | Tcl | oo::class create SimpleMovingAverage {
variable vals idx
constructor {{period 3}} {
set idx end-[expr {$period-1}]
set vals {}
}
method val x {
set vals [lrange [list {*}$vals $x] $idx end]
expr {[tcl::mathop::+ {*}$vals]/double([llength $vals])}
}
} |
http://rosettacode.org/wiki/Attractive_numbers | Attractive numbers | A number is an attractive number if the number of its prime factors (whether distinct or not) is also prime.
Example
The number 20, whose prime decomposition is 2 × 2 × 5, is an attractive number because the number of its prime factors (3) is also prime.
Task
Show sequence items up to 120.
Reference
The OEIS entry: A063989: Numbers with a prime number of prime divisors.
| #Modula-2 | Modula-2 | MODULE AttractiveNumbers;
FROM InOut IMPORT WriteCard, WriteLn;
CONST
Max = 120;
VAR
n, col: CARDINAL;
Prime: ARRAY [1..Max] OF BOOLEAN;
PROCEDURE Sieve;
VAR i, j: CARDINAL;
BEGIN
Prime[1] := FALSE;
FOR i := 2 TO Max DO
Prime[i] := TRUE;
END;
FOR i := 2 TO Max DIV 2 DO
IF Prime[i] THEN
j := i*2;
WHILE j <= Max DO
Prime[j] := FALSE;
j := j + i;
END;
END;
END;
END Sieve;
PROCEDURE Factors(n: CARDINAL): CARDINAL;
VAR i, factors: CARDINAL;
BEGIN
factors := 0;
FOR i := 2 TO Max DO
IF i > n THEN
RETURN factors;
END;
IF Prime[i] THEN
WHILE n MOD i = 0 DO
n := n DIV i;
factors := factors + 1;
END;
END;
END;
RETURN factors;
END Factors;
BEGIN
Sieve();
col := 0;
FOR n := 2 TO Max DO
IF Prime[Factors(n)] THEN
WriteCard(n, 4);
col := col + 1;
IF col MOD 15 = 0 THEN
WriteLn();
END;
END;
END;
WriteLn();
END AttractiveNumbers. |
http://rosettacode.org/wiki/Averages/Mean_time_of_day | Averages/Mean time of day | Task[edit]
A particular activity of bats occurs at these times of the day:
23:00:17, 23:40:20, 00:12:45, 00:17:19
Using the idea that there are twenty-four hours in a day,
which is analogous to there being 360 degrees in a circle,
map times of day to and from angles;
and using the ideas of Averages/Mean angle
compute and show the average time of the nocturnal activity
to an accuracy of one second of time.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #PowerShell | PowerShell |
function Get-MeanTimeOfDay
{
[CmdletBinding()]
[OutputType([timespan])]
Param
(
[Parameter(Mandatory=$true,
ValueFromPipeline=$true,
ValueFromPipelineByPropertyName=$true)]
[ValidatePattern("(?:2[0-3]|[01]?[0-9])[:.][0-5]?[0-9][:.][0-5]?[0-9]")]
[string[]]
$Time
)
Begin
{
[double[]]$angles = @()
function ConvertFrom-Time ([timespan]$Time)
{
[double]((360 * $Time.Hours / 24) + (360 * $Time.Minutes / (24 * 60)) + (360 * $Time.Seconds / (24 * 3600)))
}
function ConvertTo-Time ([double]$Angle)
{
$t = New-TimeSpan -Hours ([int](24 * 60 * 60 * $Angle / 360) / 3600) `
-Minutes (([int](24 * 60 * 60 * $Angle / 360) % 3600 - [int](24 * 60 * 60 * $Angle / 360) % 60) / 60) `
-Seconds ([int]((24 * 60 * 60 * $Angle / 360) % 60))
if ($t.Days -gt 0)
{
return ($t - (New-TimeSpan -Hours 1))
}
$t
}
function Get-MeanAngle ([double[]]$Angles)
{
[double]$x,$y = 0
for ($i = 0; $i -lt $Angles.Count; $i++)
{
$x += [Math]::Cos($Angles[$i] * [Math]::PI / 180)
$y += [Math]::Sin($Angles[$i] * [Math]::PI / 180)
}
$result = [Math]::Atan2(($y / $Angles.Count), ($x / $Angles.Count)) * 180 / [Math]::PI
if ($result -lt 0)
{
return ($result + 360)
}
$result
}
}
Process
{
$angles += ConvertFrom-Time $_
}
End
{
ConvertTo-Time (Get-MeanAngle $angles)
}
}
|
http://rosettacode.org/wiki/AVL_tree | AVL tree |
This page uses content from Wikipedia. The original article was at AVL tree. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
In computer science, an AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; at no time do they differ by more than one because rebalancing is done ensure this is the case. Lookup, insertion, and deletion all take O(log n) time in both the average and worst cases, where n is the number of nodes in the tree prior to the operation. Insertions and deletions may require the tree to be rebalanced by one or more tree rotations. Note the tree of nodes comprise a set, so duplicate node keys are not allowed.
AVL trees are often compared with red-black trees because they support the same set of operations and because red-black trees also take O(log n) time for the basic operations. Because AVL trees are more rigidly balanced, they are faster than red-black trees for lookup-intensive applications. Similar to red-black trees, AVL trees are height-balanced, but in general not weight-balanced nor μ-balanced; that is, sibling nodes can have hugely differing numbers of descendants.
Task
Implement an AVL tree in the language of choice, and provide at least basic operations.
| #Simula | Simula | CLASS AVL;
BEGIN
! AVL TREE ADAPTED FROM JULIENNE WALKER'S PRESENTATION AT ;
! HTTP://ETERNALLYCONFUZZLED.COM/TUTS/DATASTRUCTURES/JSW_TUT_AVL.ASPX. ;
! THIS PORT USES SIMILAR INDENTIFIER NAMES. ;
! THE KEY INTERFACE MUST BE SUPPORTED BY DATA STORED IN THE AVL TREE. ;
CLASS KEY;
VIRTUAL:
PROCEDURE LESS IS BOOLEAN PROCEDURE LESS (K); REF(KEY) K;;
PROCEDURE EQUAL IS BOOLEAN PROCEDURE EQUAL(K); REF(KEY) K;;
BEGIN
END KEY;
! NODE IS A NODE IN AN AVL TREE. ;
CLASS NODE(DATA); REF(KEY) DATA; ! ANYTHING COMPARABLE WITH LESS AND EQUAL. ;
BEGIN
INTEGER BALANCE; ! BALANCE FACTOR ;
REF(NODE) ARRAY LINK(0:1); ! CHILDREN, INDEXED BY "DIRECTION", 0 OR 1. ;
END NODE;
! A LITTLE READABILITY FUNCTION FOR RETURNING THE OPPOSITE OF A DIRECTION, ;
! WHERE A DIRECTION IS 0 OR 1. ;
! WHERE JW WRITES !DIR, THIS CODE HAS OPP(DIR). ;
INTEGER PROCEDURE OPP(DIR); INTEGER DIR;
BEGIN
OPP := 1 - DIR;
END OPP;
! SINGLE ROTATION ;
REF(NODE) PROCEDURE SINGLE(ROOT, DIR); REF(NODE) ROOT; INTEGER DIR;
BEGIN
REF(NODE) SAVE;
SAVE :- ROOT.LINK(OPP(DIR));
ROOT.LINK(OPP(DIR)) :- SAVE.LINK(DIR);
SAVE.LINK(DIR) :- ROOT;
SINGLE :- SAVE;
END SINGLE;
! DOUBLE ROTATION ;
REF(NODE) PROCEDURE DOUBLE(ROOT, DIR); REF(NODE) ROOT; INTEGER DIR;
BEGIN
REF(NODE) SAVE;
SAVE :- ROOT.LINK(OPP(DIR)).LINK(DIR);
ROOT.LINK(OPP(DIR)).LINK(DIR) :- SAVE.LINK(OPP(DIR));
SAVE.LINK(OPP(DIR)) :- ROOT.LINK(OPP(DIR));
ROOT.LINK(OPP(DIR)) :- SAVE;
SAVE :- ROOT.LINK(OPP(DIR));
ROOT.LINK(OPP(DIR)) :- SAVE.LINK(DIR);
SAVE.LINK(DIR) :- ROOT;
DOUBLE :- SAVE;
END DOUBLE;
! ADJUST BALANCE FACTORS AFTER DOUBLE ROTATION ;
PROCEDURE ADJUSTBALANCE(ROOT, DIR, BAL); REF(NODE) ROOT; INTEGER DIR, BAL;
BEGIN
REF(NODE) N, NN;
N :- ROOT.LINK(DIR);
NN :- N.LINK(OPP(DIR));
IF NN.BALANCE = 0 THEN BEGIN ROOT.BALANCE := 0; N.BALANCE := 0; END ELSE
IF NN.BALANCE = BAL THEN BEGIN ROOT.BALANCE := -BAL; N.BALANCE := 0; END
ELSE BEGIN ROOT.BALANCE := 0; N.BALANCE := BAL; END;
NN.BALANCE := 0;
END ADJUSTBALANCE;
REF(NODE) PROCEDURE INSERTBALANCE(ROOT, DIR); REF(NODE) ROOT; INTEGER DIR;
BEGIN REF(NODE) N; INTEGER BAL;
N :- ROOT.LINK(DIR);
BAL := 2*DIR - 1;
IF N.BALANCE = BAL THEN
BEGIN
ROOT.BALANCE := 0;
N.BALANCE := 0;
INSERTBALANCE :- SINGLE(ROOT, OPP(DIR));
END ELSE
BEGIN
ADJUSTBALANCE(ROOT, DIR, BAL);
INSERTBALANCE :- DOUBLE(ROOT, OPP(DIR));
END;
END INSERTBALANCE;
CLASS TUPLE(N,B); REF(NODE) N; BOOLEAN B;;
REF(TUPLE) PROCEDURE INSERTR(ROOT, DATA); REF(NODE) ROOT; REF(KEY) DATA;
BEGIN
IF ROOT == NONE THEN
INSERTR :- NEW TUPLE(NEW NODE(DATA), FALSE)
ELSE
BEGIN
REF(TUPLE) T; BOOLEAN DONE; INTEGER DIR;
DIR := 0;
IF ROOT.DATA.LESS(DATA) THEN
DIR := 1;
T :- INSERTR(ROOT.LINK(DIR), DATA);
ROOT.LINK(DIR) :- T.N;
DONE := T.B;
IF DONE THEN INSERTR :- NEW TUPLE(ROOT, TRUE) ELSE
BEGIN
ROOT.BALANCE := ROOT.BALANCE + 2*DIR - 1;
IF ROOT.BALANCE = 0 THEN
INSERTR :- NEW TUPLE(ROOT, TRUE) ELSE
IF ROOT.BALANCE = 1 OR ROOT.BALANCE = -1 THEN
INSERTR :- NEW TUPLE(ROOT, FALSE)
ELSE
INSERTR :- NEW TUPLE(INSERTBALANCE(ROOT, DIR), TRUE);
END;
END;
END INSERTR;
! INSERT A NODE INTO THE AVL TREE. ;
! DATA IS INSERTED EVEN IF OTHER DATA WITH THE SAME KEY ALREADY EXISTS. ;
PROCEDURE INSERT(TREE, DATA); NAME TREE; REF(NODE) TREE; REF(KEY) DATA;
BEGIN
REF(TUPLE) T;
T :- INSERTR(TREE, DATA);
TREE :- T.N;
END INSERT;
REF(TUPLE) PROCEDURE REMOVEBALANCE(ROOT, DIR); REF(NODE) ROOT; INTEGER DIR;
BEGIN REF(NODE) N; INTEGER BAL;
N :- ROOT.LINK(OPP(DIR));
BAL := 2*DIR - 1;
IF N.BALANCE = -BAL THEN
BEGIN ROOT.BALANCE := 0; N.BALANCE := 0;
REMOVEBALANCE :- NEW TUPLE(SINGLE(ROOT, DIR), FALSE);
END ELSE
IF N.BALANCE = BAL THEN
BEGIN ADJUSTBALANCE(ROOT, OPP(DIR), -BAL);
REMOVEBALANCE :- NEW TUPLE(DOUBLE(ROOT, DIR), FALSE);
END ELSE
BEGIN ROOT.BALANCE := -BAL; N.BALANCE := BAL;
REMOVEBALANCE :- NEW TUPLE(SINGLE(ROOT, DIR), TRUE);
END
END REMOVEBALANCE;
REF(TUPLE) PROCEDURE REMOVER(ROOT, DATA); REF(NODE) ROOT; REF(KEY) DATA;
BEGIN INTEGER DIR; BOOLEAN DONE; REF(TUPLE) T;
IF ROOT == NONE THEN
REMOVER :- NEW TUPLE(NONE, FALSE)
ELSE
IF ROOT.DATA.EQUAL(DATA) THEN
BEGIN
IF ROOT.LINK(0) == NONE THEN
BEGIN
REMOVER :- NEW TUPLE(ROOT.LINK(1), FALSE);
GOTO L;
END
ELSE IF ROOT.LINK(1) == NONE THEN
BEGIN
REMOVER :- NEW TUPLE(ROOT.LINK(0), FALSE);
GOTO L;
END
ELSE
BEGIN REF(NODE) HEIR;
HEIR :- ROOT.LINK(0);
WHILE HEIR.LINK(1) =/= NONE DO
HEIR :- HEIR.LINK(1);
ROOT.DATA :- HEIR.DATA;
DATA :- HEIR.DATA;
END;
END;
DIR := 0;
IF ROOT.DATA.LESS(DATA) THEN
DIR := 1;
T :- REMOVER(ROOT.LINK(DIR), DATA); ROOT.LINK(DIR) :- T.N; DONE := T.B;
IF DONE THEN
BEGIN
REMOVER :- NEW TUPLE(ROOT, TRUE);
GOTO L;
END;
ROOT.BALANCE := ROOT.BALANCE + 1 - 2*DIR;
IF ROOT.BALANCE = 1 OR ROOT.BALANCE = -1 THEN
REMOVER :- NEW TUPLE(ROOT, TRUE)
ELSE IF ROOT.BALANCE = 0 THEN
REMOVER :- NEW TUPLE(ROOT, FALSE)
ELSE
REMOVER :- REMOVEBALANCE(ROOT, DIR);
L:
END REMOVER;
! REMOVE A SINGLE ITEM FROM AN AVL TREE. ;
! IF KEY DOES NOT EXIST, FUNCTION HAS NO EFFECT. ;
PROCEDURE REMOVE(TREE, DATA); NAME TREE; REF(NODE) TREE; REF(KEY) DATA;
BEGIN REF(TUPLE) T;
T :- REMOVER(TREE, DATA);
TREE :- T.N;
END REMOVEM;
END. |
http://rosettacode.org/wiki/Averages/Mean_angle | Averages/Mean angle | When calculating the average or mean of an angle one has to take into account how angles wrap around so that any angle in degrees plus any integer multiple of 360 degrees is a measure of the same angle.
If one wanted an average direction of the wind over two readings where the first reading was of 350 degrees and the second was of 10 degrees then the average of the numbers is 180 degrees, whereas if you can note that 350 degrees is equivalent to -10 degrees and so you have two readings at 10 degrees either side of zero degrees leading to a more fitting mean angle of zero degrees.
To calculate the mean angle of several angles:
Assume all angles are on the unit circle and convert them to complex numbers expressed in real and imaginary form.
Compute the mean of the complex numbers.
Convert the complex mean to polar coordinates whereupon the phase of the complex mean is the required angular mean.
(Note that, since the mean is the sum divided by the number of numbers, and division by a positive real number does not affect the angle, you can also simply compute the sum for step 2.)
You can alternatively use this formula:
Given the angles
α
1
,
…
,
α
n
{\displaystyle \alpha _{1},\dots ,\alpha _{n}}
the mean is computed by
α
¯
=
atan2
(
1
n
⋅
∑
j
=
1
n
sin
α
j
,
1
n
⋅
∑
j
=
1
n
cos
α
j
)
{\displaystyle {\bar {\alpha }}=\operatorname {atan2} \left({\frac {1}{n}}\cdot \sum _{j=1}^{n}\sin \alpha _{j},{\frac {1}{n}}\cdot \sum _{j=1}^{n}\cos \alpha _{j}\right)}
Task[edit]
write a function/method/subroutine/... that given a list of angles in degrees returns their mean angle.
(You should use a built-in function if you have one that does this for degrees or radians).
Use the function to compute the means of these lists of angles (in degrees):
[350, 10]
[90, 180, 270, 360]
[10, 20, 30]
Show your output here.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #PicoLisp | PicoLisp | (load "@lib/math.l")
(de meanAngle (Lst)
(*/
(atan2
(sum '((A) (sin (*/ A pi 180.0))) Lst)
(sum '((A) (cos (*/ A pi 180.0))) Lst) )
180.0 pi ) )
(for L '((350.0 10.0) (90.0 180.0 270.0 360.0) (10.0 20.0 30.0))
(prinl
"The mean angle of ["
(glue ", " (mapcar round L '(0 .)))
"] is: " (round (meanAngle L))) ) |
http://rosettacode.org/wiki/Averages/Mean_angle | Averages/Mean angle | When calculating the average or mean of an angle one has to take into account how angles wrap around so that any angle in degrees plus any integer multiple of 360 degrees is a measure of the same angle.
If one wanted an average direction of the wind over two readings where the first reading was of 350 degrees and the second was of 10 degrees then the average of the numbers is 180 degrees, whereas if you can note that 350 degrees is equivalent to -10 degrees and so you have two readings at 10 degrees either side of zero degrees leading to a more fitting mean angle of zero degrees.
To calculate the mean angle of several angles:
Assume all angles are on the unit circle and convert them to complex numbers expressed in real and imaginary form.
Compute the mean of the complex numbers.
Convert the complex mean to polar coordinates whereupon the phase of the complex mean is the required angular mean.
(Note that, since the mean is the sum divided by the number of numbers, and division by a positive real number does not affect the angle, you can also simply compute the sum for step 2.)
You can alternatively use this formula:
Given the angles
α
1
,
…
,
α
n
{\displaystyle \alpha _{1},\dots ,\alpha _{n}}
the mean is computed by
α
¯
=
atan2
(
1
n
⋅
∑
j
=
1
n
sin
α
j
,
1
n
⋅
∑
j
=
1
n
cos
α
j
)
{\displaystyle {\bar {\alpha }}=\operatorname {atan2} \left({\frac {1}{n}}\cdot \sum _{j=1}^{n}\sin \alpha _{j},{\frac {1}{n}}\cdot \sum _{j=1}^{n}\cos \alpha _{j}\right)}
Task[edit]
write a function/method/subroutine/... that given a list of angles in degrees returns their mean angle.
(You should use a built-in function if you have one that does this for degrees or radians).
Use the function to compute the means of these lists of angles (in degrees):
[350, 10]
[90, 180, 270, 360]
[10, 20, 30]
Show your output here.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #PL.2FI | PL/I | averages: procedure options (main); /* 31 August 2012 */
declare b1(2) fixed initial (350, 10);
declare b2(4) fixed initial (90, 180, 270, 360);
declare b3(3) fixed initial (10, 20, 30);
put edit ( b1) (f(7));
put edit ( ' mean=', mean(b1) ) (a, f(7) );
put skip edit ( b3) (f(7));
put edit ( ' mean=', mean(b3) ) (a, f(7) );
put skip edit ( b2) (f(7));
put edit ( ' mean=', mean(b2) ) (a, f(7) );
mean: procedure (a) returns (fixed);
declare a(*) float (18);
return ( atand(sum(sind(a))/hbound(a), sum(cosd(a))/hbound(a) ) );
end mean;
end averages; |
http://rosettacode.org/wiki/Averages/Mean_angle | Averages/Mean angle | When calculating the average or mean of an angle one has to take into account how angles wrap around so that any angle in degrees plus any integer multiple of 360 degrees is a measure of the same angle.
If one wanted an average direction of the wind over two readings where the first reading was of 350 degrees and the second was of 10 degrees then the average of the numbers is 180 degrees, whereas if you can note that 350 degrees is equivalent to -10 degrees and so you have two readings at 10 degrees either side of zero degrees leading to a more fitting mean angle of zero degrees.
To calculate the mean angle of several angles:
Assume all angles are on the unit circle and convert them to complex numbers expressed in real and imaginary form.
Compute the mean of the complex numbers.
Convert the complex mean to polar coordinates whereupon the phase of the complex mean is the required angular mean.
(Note that, since the mean is the sum divided by the number of numbers, and division by a positive real number does not affect the angle, you can also simply compute the sum for step 2.)
You can alternatively use this formula:
Given the angles
α
1
,
…
,
α
n
{\displaystyle \alpha _{1},\dots ,\alpha _{n}}
the mean is computed by
α
¯
=
atan2
(
1
n
⋅
∑
j
=
1
n
sin
α
j
,
1
n
⋅
∑
j
=
1
n
cos
α
j
)
{\displaystyle {\bar {\alpha }}=\operatorname {atan2} \left({\frac {1}{n}}\cdot \sum _{j=1}^{n}\sin \alpha _{j},{\frac {1}{n}}\cdot \sum _{j=1}^{n}\cos \alpha _{j}\right)}
Task[edit]
write a function/method/subroutine/... that given a list of angles in degrees returns their mean angle.
(You should use a built-in function if you have one that does this for degrees or radians).
Use the function to compute the means of these lists of angles (in degrees):
[350, 10]
[90, 180, 270, 360]
[10, 20, 30]
Show your output here.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #PowerShell | PowerShell |
function Get-MeanAngle ([double[]]$Angles)
{
$x = ($Angles | ForEach-Object {[Math]::Cos($_ * [Math]::PI / 180)} | Measure-Object -Average).Average
$y = ($Angles | ForEach-Object {[Math]::Sin($_ * [Math]::PI / 180)} | Measure-Object -Average).Average
[Math]::Atan2($y, $x) * 180 / [Math]::PI
}
|
http://rosettacode.org/wiki/Averages/Median | Averages/Median | Task[edit]
Write a program to find the median value of a vector of floating-point numbers.
The program need not handle the case where the vector is empty, but must handle the case where there are an even number of elements. In that case, return the average of the two middle values.
There are several approaches to this. One is to sort the elements, and then pick the element(s) in the middle.
Sorting would take at least O(n logn). Another approach would be to build a priority queue from the elements, and then extract half of the elements to get to the middle element(s). This would also take O(n logn). The best solution is to use the selection algorithm to find the median in O(n) time.
See also
Quickselect_algorithm
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Groovy | Groovy | def median(Iterable col) {
def s = col as SortedSet
if (s == null) return null
if (s.empty) return 0
def n = s.size()
def m = n.intdiv(2)
def l = s.collect { it }
n%2 == 1 ? l[m] : (l[m] + l[m-1])/2
} |
http://rosettacode.org/wiki/Averages/Pythagorean_means | Averages/Pythagorean means | Task[edit]
Compute all three of the Pythagorean means of the set of integers 1 through 10 (inclusive).
Show that
A
(
x
1
,
…
,
x
n
)
≥
G
(
x
1
,
…
,
x
n
)
≥
H
(
x
1
,
…
,
x
n
)
{\displaystyle A(x_{1},\ldots ,x_{n})\geq G(x_{1},\ldots ,x_{n})\geq H(x_{1},\ldots ,x_{n})}
for this set of positive integers.
The most common of the three means, the arithmetic mean, is the sum of the list divided by its length:
A
(
x
1
,
…
,
x
n
)
=
x
1
+
⋯
+
x
n
n
{\displaystyle A(x_{1},\ldots ,x_{n})={\frac {x_{1}+\cdots +x_{n}}{n}}}
The geometric mean is the
n
{\displaystyle n}
th root of the product of the list:
G
(
x
1
,
…
,
x
n
)
=
x
1
⋯
x
n
n
{\displaystyle G(x_{1},\ldots ,x_{n})={\sqrt[{n}]{x_{1}\cdots x_{n}}}}
The harmonic mean is
n
{\displaystyle n}
divided by the sum of the reciprocal of each item in the list:
H
(
x
1
,
…
,
x
n
)
=
n
1
x
1
+
⋯
+
1
x
n
{\displaystyle H(x_{1},\ldots ,x_{n})={\frac {n}{{\frac {1}{x_{1}}}+\cdots +{\frac {1}{x_{n}}}}}}
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Liberty_BASIC | Liberty BASIC | for i = 1 to 10
a = a + i
next
ArithmeticMean = a/10
b = 1
for i = 1 to 10
b = b * i
next
GeometricMean = b ^ (1/10)
for i = 1 to 10
c = c + (1/i)
next
HarmonicMean = 10/c
print "ArithmeticMean: ";ArithmeticMean
print "Geometric Mean: ";GeometricMean
print "Harmonic Mean: ";HarmonicMean
if (ArithmeticMean>=GeometricMean) and (GeometricMean>=HarmonicMean) then
print "True"
else
print "False"
end if
|
http://rosettacode.org/wiki/Balanced_ternary | Balanced ternary | Balanced ternary is a way of representing numbers. Unlike the prevailing binary representation, a balanced ternary integer is in base 3, and each digit can have the values 1, 0, or −1.
Examples
Decimal 11 = 32 + 31 − 30, thus it can be written as "++−"
Decimal 6 = 32 − 31 + 0 × 30, thus it can be written as "+−0"
Task
Implement balanced ternary representation of integers with the following:
Support arbitrarily large integers, both positive and negative;
Provide ways to convert to and from text strings, using digits '+', '-' and '0' (unless you are already using strings to represent balanced ternary; but see requirement 5).
Provide ways to convert to and from native integer type (unless, improbably, your platform's native integer type is balanced ternary). If your native integers can't support arbitrary length, overflows during conversion must be indicated.
Provide ways to perform addition, negation and multiplication directly on balanced ternary integers; do not convert to native integers first.
Make your implementation efficient, with a reasonable definition of "efficient" (and with a reasonable definition of "reasonable").
Test case With balanced ternaries a from string "+-0++0+", b from native integer -436, c "+-++-":
write out a, b and c in decimal notation;
calculate a × (b − c), write out the result in both ternary and decimal notations.
Note: The pages generalised floating point addition and generalised floating point multiplication have code implementing arbitrary precision floating point balanced ternary.
| #Rust | Rust | use std::{
cmp::min,
convert::{TryFrom, TryInto},
fmt,
ops::{Add, Mul, Neg},
str::FromStr,
};
fn main() -> Result<(), &'static str> {
let a = BalancedTernary::from_str("+-0++0+")?;
let b = BalancedTernary::from(-436);
let c = BalancedTernary::from_str("+-++-")?;
println!("a = {} = {}", a, i128::try_from(a.clone())?);
println!("b = {} = {}", b, i128::try_from(b.clone())?);
println!("c = {} = {}", c, i128::try_from(c.clone())?);
let d = a * (b + -c);
println!("a * (b - c) = {} = {}", d, i128::try_from(d.clone())?);
let e = BalancedTernary::from_str(
"+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++",
)?;
assert_eq!(i128::try_from(e).is_err(), true);
Ok(())
}
#[derive(Clone, Copy, PartialEq)]
enum Trit {
Zero,
Pos,
Neg,
}
impl TryFrom<char> for Trit {
type Error = &'static str;
fn try_from(value: char) -> Result<Self, Self::Error> {
match value {
'0' => Ok(Self::Zero),
'+' => Ok(Self::Pos),
'-' => Ok(Self::Neg),
_ => Err("Invalid character for balanced ternary"),
}
}
}
impl From<Trit> for char {
fn from(x: Trit) -> Self {
match x {
Trit::Zero => '0',
Trit::Pos => '+',
Trit::Neg => '-',
}
}
}
impl Add for Trit {
// (Carry, Current)
type Output = (Self, Self);
fn add(self, rhs: Self) -> Self::Output {
use Trit::{Neg, Pos, Zero};
match (self, rhs) {
(Zero, x) | (x, Zero) => (Zero, x),
(Pos, Neg) | (Neg, Pos) => (Zero, Zero),
(Pos, Pos) => (Pos, Neg),
(Neg, Neg) => (Neg, Pos),
}
}
}
impl Mul for Trit {
type Output = Self;
fn mul(self, rhs: Self) -> Self::Output {
use Trit::{Neg, Pos, Zero};
match (self, rhs) {
(Zero, _) | (_, Zero) => Zero,
(Pos, Pos) | (Neg, Neg) => Pos,
(Pos, Neg) | (Neg, Pos) => Neg,
}
}
}
impl Neg for Trit {
type Output = Self;
fn neg(self) -> Self::Output {
match self {
Trit::Zero => Trit::Zero,
Trit::Pos => Trit::Neg,
Trit::Neg => Trit::Pos,
}
}
}
// The vector is stored in reverse from how it would be viewed, as
// operations tend to work backwards
#[derive(Clone)]
struct BalancedTernary(Vec<Trit>);
impl fmt::Display for BalancedTernary {
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
write!(
f,
"{}",
self.0
.iter()
.rev()
.map(|&d| char::from(d))
.collect::<String>()
)
}
}
impl Add for BalancedTernary {
type Output = Self;
fn add(self, rhs: Self) -> Self::Output {
use Trit::Zero;
// Trim leading zeroes
fn trim(v: &mut Vec<Trit>) {
while let Some(last_elem) = v.pop() {
if last_elem != Zero {
v.push(last_elem);
break;
}
}
}
if rhs.0.is_empty() {
// A balanced ternary shouldn't be empty
if self.0.is_empty() {
return BalancedTernary(vec![Zero]);
}
return self;
}
let length = min(self.0.len(), rhs.0.len());
let mut sum = Vec::new();
let mut carry = vec![Zero];
for i in 0..length {
let (carry_dig, digit) = self.0[i] + rhs.0[i];
sum.push(digit);
carry.push(carry_dig);
}
// At least one of these two loops will be ignored
for i in length..self.0.len() {
sum.push(self.0[i]);
}
for i in length..rhs.0.len() {
sum.push(rhs.0[i]);
}
trim(&mut sum);
trim(&mut carry);
BalancedTernary(sum) + BalancedTernary(carry)
}
}
// This version of `Mul` requires an implementation of the `Add` trait
impl Mul for BalancedTernary {
type Output = Self;
fn mul(self, rhs: Self) -> Self::Output {
let mut results = Vec::with_capacity(rhs.0.len());
for i in 0..rhs.0.len() {
let mut digits = vec![Trit::Zero; i];
for j in 0..self.0.len() {
digits.push(self.0[j] * rhs.0[i]);
}
results.push(BalancedTernary(digits));
}
#[allow(clippy::suspicious_arithmetic_impl)]
results
.into_iter()
.fold(BalancedTernary(vec![Trit::Zero]), |acc, x| acc + x)
}
}
impl Neg for BalancedTernary {
type Output = Self;
fn neg(self) -> Self::Output {
BalancedTernary(self.0.iter().map(|&x| -x).collect())
}
}
impl FromStr for BalancedTernary {
type Err = &'static str;
fn from_str(s: &str) -> Result<Self, Self::Err> {
s.chars()
.rev()
.map(|c| c.try_into())
.collect::<Result<_, _>>()
.map(BalancedTernary)
}
}
impl From<i128> for BalancedTernary {
fn from(x: i128) -> Self {
let mut v = Vec::new();
let mut curr = x;
loop {
let rem = curr % 3;
match rem {
0 => v.push(Trit::Zero),
1 | -2 => v.push(Trit::Pos),
2 | -1 => v.push(Trit::Neg),
_ => unreachable!(),
}
let offset = (rem as f64 / 3.0).round() as i128;
curr = curr / 3 + offset;
if curr == 0 {
break;
}
}
BalancedTernary(v)
}
}
impl TryFrom<BalancedTernary> for i128 {
type Error = &'static str;
fn try_from(value: BalancedTernary) -> Result<Self, Self::Error> {
value
.0
.iter()
.enumerate()
.try_fold(0_i128, |acc, (i, character)| {
let size_err = "Balanced ternary string is too large to fit into 16 bytes";
let index: u32 = i.try_into().map_err(|_| size_err)?;
match character {
Trit::Zero => Ok(acc),
Trit::Pos => 3_i128
.checked_pow(index)
.and_then(|x| acc.checked_add(x))
.ok_or(size_err),
Trit::Neg => 3_i128
.checked_pow(index)
.and_then(|x| acc.checked_sub(x))
.ok_or(size_err),
}
})
}
}
|
http://rosettacode.org/wiki/Babbage_problem | Babbage problem |
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.
For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].
Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.
| #Scilab | Scilab | n=2;
flag=%F
while ~flag
n = n+2;
if pmodulo(n*n,1000000)==269696 then
flag=%T;
end
end
disp(n); |
http://rosettacode.org/wiki/Babbage_problem | Babbage problem |
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.
For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].
Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.
| #Seed7 | Seed7 | $ include "seed7_05.s7i";
const proc: main is func
local
var integer: current is 0;
begin
while current ** 2 rem 1000000 <> 269696 do
incr(current);
end while;
writeln("The square of " <& current <& " is " <& current ** 2);
end func; |
http://rosettacode.org/wiki/Approximate_equality | Approximate equality | Sometimes, when testing whether the solution to a task (for example, here on Rosetta Code) is correct, the
difference in floating point calculations between different language implementations becomes significant.
For example, a difference between 32 bit and 64 bit floating point calculations may appear by
about the 8th significant digit in base 10 arithmetic.
Task
Create a function which returns true if two floating point numbers are approximately equal.
The function should allow for differences in the magnitude of numbers, so that, for example,
100000000000000.01 may be approximately equal to 100000000000000.011,
even though 100.01 is not approximately equal to 100.011.
If the language has such a feature in its standard library, this may be used instead of a custom function.
Show the function results with comparisons on the following pairs of values:
100000000000000.01, 100000000000000.011 (note: should return true)
100.01, 100.011 (note: should return false)
10000000000000.001 / 10000.0, 1000000000.0000001000
0.001, 0.0010000001
0.000000000000000000000101, 0.0
sqrt(2) * sqrt(2), 2.0
-sqrt(2) * sqrt(2), -2.0
3.14159265358979323846, 3.14159265358979324
Answers should be true for the first example and false in the second, so that just rounding the numbers to a fixed number of decimals should not be enough. Otherwise answers may vary and still be correct. See the Python code for one type of solution.
| #Scala | Scala | object Approximate extends App {
val (ok, notOk, ε) = ("👌", "❌", 1e-18d)
private def approxEquals(value: Double, other: Double, epsilon: Double) =
scala.math.abs(value - other) < epsilon
private def test(a: BigDecimal, b: BigDecimal, expected: Boolean): Unit = {
val result = approxEquals(a.toDouble, b.toDouble, ε)
println(f"$a%40.24f ≅ $b%40.24f => $result%5s ${if (expected == result) ok else notOk}")
}
test(BigDecimal("100000000000000.010"), BigDecimal("100000000000000.011"), true)
test(BigDecimal("100.01"), BigDecimal("100.011"), false)
test(BigDecimal(10000000000000.001 / 10000.0), BigDecimal("1000000000.0000001000"), false)
test(BigDecimal("0.001"), BigDecimal("0.0010000001"), false)
test(BigDecimal("0.000000000000000000000101"), BigDecimal(0), true)
test(BigDecimal(math.sqrt(2) * math.sqrt(2d)), BigDecimal(2.0), false)
test(BigDecimal(-Math.sqrt(2) * Math.sqrt(2)), BigDecimal(-2.0), false)
test(BigDecimal("3.14159265358979323846"), BigDecimal("3.14159265358979324"), true)
} |
http://rosettacode.org/wiki/Approximate_equality | Approximate equality | Sometimes, when testing whether the solution to a task (for example, here on Rosetta Code) is correct, the
difference in floating point calculations between different language implementations becomes significant.
For example, a difference between 32 bit and 64 bit floating point calculations may appear by
about the 8th significant digit in base 10 arithmetic.
Task
Create a function which returns true if two floating point numbers are approximately equal.
The function should allow for differences in the magnitude of numbers, so that, for example,
100000000000000.01 may be approximately equal to 100000000000000.011,
even though 100.01 is not approximately equal to 100.011.
If the language has such a feature in its standard library, this may be used instead of a custom function.
Show the function results with comparisons on the following pairs of values:
100000000000000.01, 100000000000000.011 (note: should return true)
100.01, 100.011 (note: should return false)
10000000000000.001 / 10000.0, 1000000000.0000001000
0.001, 0.0010000001
0.000000000000000000000101, 0.0
sqrt(2) * sqrt(2), 2.0
-sqrt(2) * sqrt(2), -2.0
3.14159265358979323846, 3.14159265358979324
Answers should be true for the first example and false in the second, so that just rounding the numbers to a fixed number of decimals should not be enough. Otherwise answers may vary and still be correct. See the Python code for one type of solution.
| #Sidef | Sidef | [
100000000000000.01, 100000000000000.011,
100.01, 100.011,
10000000000000.001 / 10000.0, 1000000000.0000001000,
0.001, 0.0010000001,
0.000000000000000000000101, 0.0,
sqrt(2) * sqrt(2), 2.0,
-sqrt(2) * sqrt(2), -2.0,
sqrt(-2) * sqrt(-2), -2.0,
cbrt(3)**3, 3,
cbrt(-3)**3, -3,
100000000000000003.0, 100000000000000004.0,
3.14159265358979323846, 3.14159265358979324
].each_slice(2, {|a,b|
say ("#{a} ≅ #{b}: ", a ≅ b)
}) |
http://rosettacode.org/wiki/Balanced_brackets | Balanced brackets | Task:
Generate a string with N opening brackets [ and with N closing brackets ], in some arbitrary order.
Determine whether the generated string is balanced; that is, whether it consists entirely of pairs of opening/closing brackets (in that order), none of which mis-nest.
Examples
(empty) OK
[] OK
[][] OK
[[][]] OK
][ NOT OK
][][ NOT OK
[]][[] NOT OK
| #Elixir | Elixir | defmodule Balanced_brackets do
def task do
Enum.each(0..5, fn n ->
brackets = generate(n)
result = is_balanced(brackets) |> task_balanced
IO.puts "#{brackets} is #{result}"
end)
end
defp generate( 0 ), do: []
defp generate( n ) do
for _ <- 1..2*n, do: Enum.random ["[", "]"]
end
def is_balanced( brackets ), do: is_balanced_loop( brackets, 0 )
defp is_balanced_loop( _, n ) when n < 0, do: false
defp is_balanced_loop( [], 0 ), do: true
defp is_balanced_loop( [], _n ), do: false
defp is_balanced_loop( ["[" | t], n ), do: is_balanced_loop( t, n + 1 )
defp is_balanced_loop( ["]" | t], n ), do: is_balanced_loop( t, n - 1 )
defp task_balanced( true ), do: "OK"
defp task_balanced( false ), do: "NOT OK"
end
Balanced_brackets.task |
http://rosettacode.org/wiki/Append_a_record_to_the_end_of_a_text_file | Append a record to the end of a text file | Many systems offer the ability to open a file for writing, such that any data written will be appended to the end of the file. Further, the file operations will always adjust the position pointer to guarantee the end of the file, even in a multitasking environment.
This feature is most useful in the case of log files, where many jobs may be appending to the log file at the same time, or where care must be taken to avoid concurrently overwriting the same record from another job.
Task
Given a two record sample for a mythical "passwd" file:
Write these records out in the typical system format.
Ideally these records will have named fields of various types.
Close the file, then reopen the file for append.
Append a new record to the file and close the file again.
Take appropriate care to avoid concurrently overwrites from another job.
Open the file and demonstrate the new record has indeed written to the end.
Source record field types and contents.
account
password
UID
GID
fullname,office,extension,homephone,email
directory
shell
string
string
int
int
struct(string,string,string,string,string)
string
string
jsmith
x
1001
1000
Joe Smith,Room 1007,(234)555-8917,(234)555-0077,[email protected]
/home/jsmith
/bin/bash
jdoe
x
1002
1000
Jane Doe,Room 1004,(234)555-8914,(234)555-0044,[email protected]
/home/jdoe
/bin/bash
Record to be appended.
account
password
UID
GID
fullname,office,extension,homephone,email
directory
shell
string
string
int
int
struct(string,string,string,string,string)
string
string
xyz
x
1003
1000
X Yz,Room 1003,(234)555-8913,(234)555-0033,[email protected]
/home/xyz
/bin/bash
Resulting file format: should mimic Linux's /etc/passwd file format with particular attention to the "," separator used in the GECOS field. But if the specific language has a particular or unique format of storing records in text file, then this format should be named and demonstrated with an additional example.
Expected output:
Appended record: xyz:x:1003:1000:X Yz,Room 1003,(234)555-8913,(234)555-0033,[email protected]:/home/xyz:/bin/bash
Finally: Provide a summary of the language's "append record" capabilities in a table. eg.
Append Capabilities.
Data Representation
IO
Library
Append
Possible
Automatic
Append
Multi-tasking
Safe
In core
On disk
C struct
CSV text file
glibc/stdio
☑
☑
☑ (Not all, eg NFS)
Alternatively: If the language's appends can not guarantee its writes will always append, then note this restriction in the table. If possible, provide an actual code example (possibly using file/record locking) to guarantee correct concurrent appends.
| #Haskell | Haskell |
{-# LANGUAGE RecordWildCards #-}
import System.IO
import Data.List (intercalate)
data Gecos = Gecos { fullname :: String
, office :: String
, extension :: String
, homephone :: String
, email :: String
}
data Record = Record { account :: String
, password :: String
, uid :: Int
, gid :: Int
, directory :: String
, shell :: String
, gecos :: Gecos
}
instance Show Gecos where
show (Gecos {..}) = intercalate "," [fullname, office, extension, homephone, email]
instance Show Record where
show (Record {..}) = intercalate ":" [account, password, show uid, show gid, show gecos, directory, shell]
addRecord :: String -> Record -> IO ()
addRecord path r = appendFile path (show r)
|
http://rosettacode.org/wiki/Associative_array/Creation | Associative array/Creation | Task
The goal is to create an associative array (also known as a dictionary, map, or hash).
Related tasks:
Associative arrays/Iteration
Hash from two arrays
See also
Array
Associative array: Creation, Iteration
Collections
Compound data type
Doubly-linked list: Definition, Element definition, Element insertion, List Traversal, Element Removal
Linked list
Queue: Definition, Usage
Set
Singly-linked list: Element definition, Element insertion, List Traversal, Element Removal
Stack
| #AWK | AWK | BEGIN {
a["red"] = 0xff0000
a["green"] = 0x00ff00
a["blue"] = 0x0000ff
for (i in a) {
printf "%8s %06x\n", i, a[i]
}
# deleting a key/value
delete a["red"]
for (i in a) {
print i
}
# check if a key exists
print ( "red" in a ) # print 0
print ( "blue" in a ) # print 1
} |
http://rosettacode.org/wiki/Anti-primes | Anti-primes | The anti-primes
(or highly composite numbers, sequence A002182 in the OEIS)
are the natural numbers with more factors than any smaller than itself.
Task
Generate and show here, the first twenty anti-primes.
Related tasks
Factors of an integer
Sieve of Eratosthenes
| #D | D | import std.stdio;
int countDivisors(int n) {
if (n < 2) {
return 1;
}
int count = 2; // 1 and n
for (int i = 2; i <= n/2; ++i) {
if (n % i == 0) {
++count;
}
}
return count;
}
void main() {
int maxDiv, count;
writeln("The first 20 anti-primes are:");
for (int n = 1; count < 20; ++n) {
int d = countDivisors(n);
if (d > maxDiv) {
write(n, ' ');
maxDiv = d;
count++;
}
}
writeln;
} |
http://rosettacode.org/wiki/Anti-primes | Anti-primes | The anti-primes
(or highly composite numbers, sequence A002182 in the OEIS)
are the natural numbers with more factors than any smaller than itself.
Task
Generate and show here, the first twenty anti-primes.
Related tasks
Factors of an integer
Sieve of Eratosthenes
| #Delphi | Delphi | defmodule AntiPrimes do
def divcount(n) when is_integer(n), do: divcount(n, 1, 0)
def divcount(n, d, count) when d * d > n, do: count
def divcount(n, d, count) do
divs = case rem(n, d) do
0 ->
case n - d * d do
0 -> 1
_ -> 2
end
_ -> 0
end
divcount(n, d + 1, count + divs)
end
def antiprimes(n), do: antiprimes(n, 1, 0, [])
def antiprimes(0, _, _, l), do: Enum.reverse(l)
def antiprimes(n, m, max, l) do
count = divcount(m)
case count > max do
true -> antiprimes(n-1, m+1, count, [m|l])
false -> antiprimes(n, m+1, max, l)
end
end
def main() do
:io.format("The first 20 anti-primes are ~w~n", [antiprimes(20)])
end
end |
http://rosettacode.org/wiki/Atomic_updates | Atomic updates |
Task
Define a data type consisting of a fixed number of 'buckets', each containing a nonnegative integer value, which supports operations to:
get the current value of any bucket
remove a specified amount from one specified bucket and add it to another, preserving the total of all bucket values, and clamping the transferred amount to ensure the values remain non-negative
In order to exercise this data type, create one set of buckets, and start three concurrent tasks:
As often as possible, pick two buckets and make their values closer to equal.
As often as possible, pick two buckets and arbitrarily redistribute their values.
At whatever rate is convenient, display (by any means) the total value and, optionally, the individual values of each bucket.
The display task need not be explicit; use of e.g. a debugger or trace tool is acceptable provided it is simple to set up to provide the display.
This task is intended as an exercise in atomic operations. The sum of the bucket values must be preserved even if the two tasks attempt to perform transfers simultaneously, and a straightforward solution is to ensure that at any time, only one transfer is actually occurring — that the transfer operation is atomic.
| #Perl | Perl | use strict;
use 5.10.0;
use threads 'yield';
use threads::shared;
my @a :shared = (100) x 10;
my $stop :shared = 0;
sub pick2 {
my $i = int(rand(10));
my $j;
$j = int(rand(10)) until $j != $i;
($i, $j)
}
sub even {
lock @a;
my ($i, $j) = pick2;
my $sum = $a[$i] + $a[$j];
$a[$i] = int($sum / 2);
$a[$j] = $sum - $a[$i];
}
sub rand_move {
lock @a;
my ($i, $j) = pick2;
my $x = int(rand $a[$i]);
$a[$i] -= $x;
$a[$j] += $x;
}
sub show {
lock @a;
my $sum = 0;
$sum += $_ for (@a);
printf "%4d", $_ for @a;
print " total $sum\n";
}
my $t1 = async { even until $stop }
my $t2 = async { rand_move until $stop }
my $t3 = async {
for (1 .. 10) {
show;
sleep(1);
}
$stop = 1;
};
$t1->join; $t2->join; $t3->join; |
http://rosettacode.org/wiki/Assertions | Assertions | Assertions are a way of breaking out of code when there is an error or an unexpected input.
Some languages throw exceptions and some treat it as a break point.
Task
Show an assertion in your language by asserting that an integer variable is equal to 42.
| #Mathematica_.2F_Wolfram_Language | Mathematica / Wolfram Language | Assert[var===42] |
http://rosettacode.org/wiki/Assertions | Assertions | Assertions are a way of breaking out of code when there is an error or an unexpected input.
Some languages throw exceptions and some treat it as a break point.
Task
Show an assertion in your language by asserting that an integer variable is equal to 42.
| #MATLAB_.2F_Octave | MATLAB / Octave | assert(x == 42,'x = %d, not 42.',x); |
http://rosettacode.org/wiki/Assertions | Assertions | Assertions are a way of breaking out of code when there is an error or an unexpected input.
Some languages throw exceptions and some treat it as a break point.
Task
Show an assertion in your language by asserting that an integer variable is equal to 42.
| #Metafont | Metafont | def assert(expr t) = if not (t): errmessage("assertion failed") fi enddef; |
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