Rosetta Code

Knuth's algorithm S: Difference between revisions

Page Discussion

Knuth's algorithm S (view source)

Revision as of 19:49, 16 March 2024

59,274 bytes added ,  2 months ago
added RPL
(added RPL)
 
(119 intermediate revisions by 44 users not shown)
Line 2:
This is a method of randomly sampling n items from a set of M items, with equal probability; where M >= n and M, the number of items is unknown until the end.
This means that the equal probability sampling should be maintained for all successive items > n as they become available (although the content of successive samples can change).
 
 
;The algorithm:
#:* Select the first n items as the sample as they become available;
#:* For the i-th item where i > n, have a random chance of n/i of keeping it. If failing this chance, the sample remains the same. If not, have it randomly (1/n) replace one of the previously selected n items of the sample.
#:* Repeat #&nbsp; 2<sup>nd</sup> step &nbsp; for any subsequent items.
 
 
;The Task:
#:* Create a function <code>s_of_n_creator</code> that given <math>n</math> the maximum sample size, returns a function <code>s_of_n</code> that takes one parameter, <code>item</code>.
#:* Function <code>s_of_n</code> when called with successive items returns an equi-weighted random sample of up to n of its items so far, each time it is called, calculated using Knuths Algorithm S.
#:* Test your functions by printing and showing the frequency of occurrences of the selected digits from 100,000 repetitions of:
:::# Use the s_of_n_creator with n == 3 to generate an s_of_n.
:::# call s_of_n with each of the digits 0 to 9 in order, keeping the returned three digits of its random sampling from its last call with argument item=9.
 
 
Note: A class taking n and generating a callable instance/function might also be used.
 
 
;Reference:
* The Art of Computer Programming, Vol 2, 3.4.2 p.142
 
 
;Cf.
;Related tasks:
* [[One of n lines in a file]]
* [[Accumulator factory]]
<br><br>
 
=={{header|11l}}==
{{trans|Python}}
 
<syntaxhighlight lang="11l">T S_of_n_creator
Int n
i = 0
[Int] sample
 
F (n)
.n = n
 
F ()(item)
.i++
I .i <= .n
.sample.append(item)
E I random:(.i) < .n
.sample[random:(.n)] = item
 
V binarr = [0] * 10
V items = Array(0..9)
print(‘Single run samples for n = 3:’)
V s_of_n = S_of_n_creator(3)
L(item) items
s_of_n(item)
print(‘ Item: #. -> sample: #.’.format(item, s_of_n.sample))
 
L 100000
s_of_n = S_of_n_creator(3)
L(item) items
s_of_n(item)
L(s) s_of_n.sample
binarr[s]++
print("\nTest item frequencies for 100000 runs:\n "(enumerate(binarr).map((i, x) -> ‘#.:#.’.format(i, x)).join("\n ")))</syntaxhighlight>
 
{{out}}
<pre>
Single run samples for n = 3:
Item: 0 -> sample: [0]
Item: 1 -> sample: [0, 1]
Item: 2 -> sample: [0, 1, 2]
Item: 3 -> sample: [3, 1, 2]
Item: 4 -> sample: [3, 1, 2]
Item: 5 -> sample: [3, 1, 2]
Item: 6 -> sample: [3, 6, 2]
Item: 7 -> sample: [3, 7, 2]
Item: 8 -> sample: [3, 7, 2]
Item: 9 -> sample: [3, 7, 2]
 
Test item frequencies for 100000 runs:
0:30229
1:30182
2:29981
3:30058
4:29749
5:29952
6:30102
7:29955
8:29917
9:29875
</pre>
 
=={{header|Ada}}==
 
Instead of defining a function S_of_N_Creator, we define a generic packgage with that name. The generic parameters are N (=Sample_Size) and the type of the items to be sampled:
 
<syntaxhighlight lang="ada">generic
Sample_Size: Positive;
type Item_Type is private;
package S_Of_N_Creator is
 
subtype Index_Type is Positive range 1 .. Sample_Size;
type Item_Array is array (Index_Type) of Item_Type;
 
procedure Update(New_Item: Item_Type);
function Result return Item_Array;
 
end S_Of_N_Creator;</syntaxhighlight>
 
Here is the implementation of that package:
 
<syntaxhighlight lang="ada">with Ada.Numerics.Float_Random, Ada.Numerics.Discrete_Random;
 
package body S_Of_N_Creator is
 
package F_Rnd renames Ada.Numerics.Float_Random;
F_Gen: F_Rnd.Generator;
 
package D_Rnd is new Ada.Numerics.Discrete_Random(Index_Type);
D_Gen: D_Rnd.Generator;
 
Item_Count: Natural := 0; -- this is a global counter
Sample: Item_Array; -- also used globally
 
procedure Update(New_Item: Item_Type) is
begin
Item_Count := Item_Count + 1;
if Item_Count <= Sample_Size then
-- select the first Sample_Size items as the sample
Sample(Item_Count) := New_Item;
else
-- for I-th item, I > Sample_Size: Sample_Size/I chance of keeping it
if (Float(Sample_Size)/Float(Item_Count)) > F_Rnd.Random(F_Gen) then
-- randomly (1/Sample_Size) replace one of the items of the sample
Sample(D_Rnd.Random(D_Gen)) := New_Item;
end if;
end if;
end Update;
 
function Result return Item_Array is
begin
Item_Count := 0; -- ready to start another run
return Sample;
end Result;
 
begin
D_Rnd.Reset(D_Gen); -- at package instantiation, initialize rnd-generators
F_Rnd.Reset(F_Gen);
end S_Of_N_Creator;</syntaxhighlight>
 
The main program:
 
<syntaxhighlight lang="ada">with S_Of_N_Creator, Ada.Text_IO;
 
procedure Test_S_Of_N is
 
Repetitions: constant Positive := 100_000;
type D_10 is range 0 .. 9;
 
-- the instantiation of the generic package S_Of_N_Creator generates
-- a package with the desired functionality
package S_Of_3 is new S_Of_N_Creator(Sample_Size => 3, Item_Type => D_10);
 
Sample: S_Of_3.Item_Array;
Result: array(D_10) of Natural := (others => 0);
 
begin
for J in 1 .. Repetitions loop
-- get Sample
for Dig in D_10 loop
S_Of_3.Update(Dig);
end loop;
Sample := S_Of_3.Result;
 
-- update current Result
for Item in Sample'Range loop
Result(Sample(Item)) := Result(Sample(Item)) + 1;
end loop;
end loop;
 
-- finally: output Result
for Dig in Result'Range loop
Ada.Text_IO.Put(D_10'Image(Dig) & ":"
& Natural'Image(Result(Dig)) & "; ");
end loop;
end Test_S_Of_N;</syntaxhighlight>
 
A sample output:
 
<pre> 0: 30008; 1: 30056; 2: 30080; 3: 29633; 4: 29910; 5: 30293; 6: 30105; 7: 29924; 8: 29871; 9: 30120; </pre>
 
=={{header|BBC BASIC}}==
{{works with|BBC BASIC for Windows}}
At each of the 100000 repetitions not only is a new function created but also new copies of its PRIVATE variables '''index%''' and '''samples%()'''. Creating such a large number of variables at run-time impacts adversely on execution speed and isn't to be recommended, other than to meet the artificial requirements of the task.
<syntaxhighlight lang="bbcbasic"> HIMEM = PAGE + 20000000
PRINT "Single run samples for n = 3:"
SofN% = FNs_of_n_creator(3)
FOR I% = 0 TO 9
!^a%() = FN(SofN%)(I%)
PRINT " For item " ; I% " sample(s) = " FNshowarray(a%(), I%+1)
NEXT
DIM cnt%(9)
PRINT '"Digit counts after 100000 runs:"
FOR rep% = 1 TO 100000
IF (rep% MOD 1000) = 0 PRINT ; rep% ; CHR$(13) ;
F% = FNs_of_n_creator(3)
FOR I% = 0 TO 9
!^a%() = FN(F%)(I%)
NEXT
cnt%(a%(1)) += 1 : cnt%(a%(2)) += 1 : cnt%(a%(3)) += 1
NEXT
FOR digit% = 0 TO 9
PRINT " " ; digit% " : " ; cnt%(digit%)
NEXT
END
REM Dynamically creates this function:
REM DEF FNfunction(item%) : PRIVATE samples%(), index%
REM DIM samples%(n%) : = FNs_of_n(item%, samples%(), index%)
DEF FNs_of_n_creator(n%)
LOCAL p%, f$
f$ = "(item%) : " + CHR$&0E + " samples%(), index% : " + \
\ CHR$&DE + " samples%(" + STR$(n%) + ") : = " + \
\ CHR$&A4 + "s_of_n(item%, samples%(), index%)"
DIM p% LEN(f$) + 4 : $(p%+4) = f$ : !p% = p%+4
= p%
DEF FNs_of_n(D%, s%(), RETURN I%)
LOCAL N%
N% = DIM(s%(),1)
I% += 1
IF I% <= N% THEN
s%(I%) = D%
ELSE
IF RND(I%) <= N% s%(RND(N%)) = D%
ENDIF
= !^s%()
DEF FNshowarray(a%(), n%)
LOCAL i%, a$
a$ = "["
IF n% > DIM(a%(),1) n% = DIM(a%(),1)
FOR i% = 1 TO n%
a$ += STR$(a%(i%)) + ", "
NEXT
= LEFT$(LEFT$(a$)) + "]"</syntaxhighlight>
'''Output:'''
<pre>
Single run samples for n = 3:
For item 0 sample(s) = [0]
For item 1 sample(s) = [0, 1]
For item 2 sample(s) = [0, 1, 2]
For item 3 sample(s) = [0, 1, 2]
For item 4 sample(s) = [0, 1, 4]
For item 5 sample(s) = [0, 1, 4]
For item 6 sample(s) = [0, 1, 6]
For item 7 sample(s) = [0, 1, 6]
For item 8 sample(s) = [8, 1, 6]
For item 9 sample(s) = [8, 1, 9]
 
Digit counts after 100000 runs:
0 : 30068
1 : 30017
2 : 30378
3 : 29640
4 : 30153
5 : 29994
6 : 29941
7 : 29781
8 : 29918
9 : 30110
</pre>
 
=={{header|C}}==
Instead of returning a closure we set the environment in a structure:
<syntaxhighlight lang="c">#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <time.h>
 
struct s_env {
unsigned int n, i;
size_t size;
void *sample;
};
 
void s_of_n_init(struct s_env *s_env, size_t size, unsigned int n)
{
s_env->i = 0;
s_env->n = n;
s_env->size = size;
s_env->sample = malloc(n * size);
}
 
void sample_set_i(struct s_env *s_env, unsigned int i, void *item)
{
memcpy(s_env->sample + i * s_env->size, item, s_env->size);
}
 
void *s_of_n(struct s_env *s_env, void *item)
{
s_env->i++;
if (s_env->i <= s_env->n)
sample_set_i(s_env, s_env->i - 1, item);
else if ((rand() % s_env->i) < s_env->n)
sample_set_i(s_env, rand() % s_env->n, item);
return s_env->sample;
}
 
int *test(unsigned int n, int *items_set, unsigned int num_items)
{
int i;
struct s_env s_env;
s_of_n_init(&s_env, sizeof(items_set[0]), n);
for (i = 0; i < num_items; i++) {
s_of_n(&s_env, (void *) &items_set[i]);
}
return (int *)s_env.sample;
}
 
int main()
{
unsigned int i, j;
unsigned int n = 3;
unsigned int num_items = 10;
unsigned int *frequencies;
int *items_set;
srand(time(NULL));
items_set = malloc(num_items * sizeof(int));
frequencies = malloc(num_items * sizeof(int));
for (i = 0; i < num_items; i++) {
items_set[i] = i;
frequencies[i] = 0;
}
for (i = 0; i < 100000; i++) {
int *res = test(n, items_set, num_items);
for (j = 0; j < n; j++) {
frequencies[res[j]]++;
}
free(res);
}
for (i = 0; i < num_items; i++) {
printf(" %d", frequencies[i]);
}
puts("");
return 0;
}</syntaxhighlight>
 
Sample output:
<pre> 29980 29746 30111 30034 29922 29720 30222 30183 29995 30087</pre>
 
=={{header|C++}}==
{{works with|C++11}}
<syntaxhighlight lang="cpp">#include <iostream>
#include <functional>
#include <vector>
#include <cstdlib>
#include <ctime>
 
template <typename T>
std::function<std::vector<T>(T)> s_of_n_creator(int n) {
std::vector<T> sample;
int i = 0;
return [=](T item) mutable {
i++;
if (i <= n) {
sample.push_back(item);
} else if (std::rand() % i < n) {
sample[std::rand() % n] = item;
}
return sample;
};
}
 
int main() {
std::srand(std::time(NULL));
int bin[10] = {0};
for (int trial = 0; trial < 100000; trial++) {
auto s_of_n = s_of_n_creator<int>(3);
std::vector<int> sample;
for (int i = 0; i < 10; i++)
sample = s_of_n(i);
for (int s : sample)
bin[s]++;
}
for (int x : bin)
std::cout << x << std::endl;
return 0;
}</syntaxhighlight>
{{out}}
<pre>
30052
29740
30197
30223
29857
29688
30095
29803
30098
30247
</pre>
 
Class-based version:
<syntaxhighlight lang="cpp">#include <iostream>
#include <vector>
#include <cstdlib>
#include <ctime>
 
template <typename T>
class SOfN {
std::vector<T> sample;
int i;
const int n;
public:
SOfN(int _n) : i(0), n(_n) { }
std::vector<T> operator()(T item) {
i++;
if (i <= n) {
sample.push_back(item);
} else if (std::rand() % i < n) {
sample[std::rand() % n] = item;
}
return sample;
}
};
 
int main() {
std::srand(std::time(NULL));
int bin[10] = {0};
for (int trial = 0; trial < 100000; trial++) {
SOfN<int> s_of_n(3);
std::vector<int> sample;
for (int i = 0; i < 10; i++)
sample = s_of_n(i);
for (std::vector<int>::const_iterator i = sample.begin(); i != sample.end(); i++)
bin[*i]++;
}
for (int i = 0; i < 10; i++)
std::cout << bin[i] << std::endl;
return 0;
}</syntaxhighlight>
 
=={{header|Clojure}}==
The Clojure approach to problems like this is to define a function which takes an accumulator state and an input item and produces the updated state.
Here the accumulator state is the current sample and the number of items processed.
This function is then used in a ''reduce'' call with an initial state and a list of items.
<syntaxhighlight lang="clojure">(defn s-of-n-fn-creator [n]
(fn [[sample iprev] item]
(let [i (inc iprev)]
(if (<= i n)
[(conj sample item) i]
(let [r (rand-int i)]
(if (< r n)
[(assoc sample r item) i]
[sample i]))))))
(def s-of-3-fn (s-of-n-fn-creator 3))
 
(->> #(reduce s-of-3-fn [[] 0] (range 10))
(repeatedly 100000)
(map first)
flatten
frequencies
sort
println)
</syntaxhighlight>
Sample output:
<syntaxhighlight lang="text">([0 29924] [1 30053] [2 30018] [3 29765] [4 29974] [5 30225] [6 30082] [7 29996] [8 30128] [9 29835])</syntaxhighlight>
 
If we really need a stateful (thread safe!) function for some reason, we can get it like this:
<syntaxhighlight lang="clojure">(defn s-of-n-creator [n]
(let [state (atom [[] 0])
s-of-n-fn (s-of-n-fn-creator n)]
(fn [item]
(first (swap! state s-of-n-fn item)))))</syntaxhighlight>
 
=={{header|CoffeeScript}}==
<syntaxhighlight lang="coffeescript">
s_of_n_creator = (n) ->
arr = []
cnt = 0
(elem) ->
cnt += 1
if cnt <= n
arr.push elem
else
pos = Math.floor(Math.random() * cnt)
if pos < n
arr[pos] = elem
arr.sort()
 
sample_size = 3
range = [0..9]
num_trials = 100000
 
counts = {}
 
for digit in range
counts[digit] = 0
for i in [1..num_trials]
s_of_n = s_of_n_creator(sample_size)
for digit in range
sample = s_of_n(digit)
for digit in sample
counts[digit] += 1
 
for digit in range
console.log digit, counts[digit]
</syntaxhighlight>
output
<syntaxhighlight lang="text">
> coffee knuth_sample.coffee
0 29899
1 29841
2 29930
3 30058
4 29932
5 29948
6 30047
7 30114
8 29976
9 30255
</syntaxhighlight>
 
=={{header|Common Lisp}}==
<syntaxhighlight lang ="lisp">(setfdefun *randoms-state*n-creator (make-random-state t)n)
(let ((sample (make-array n :initial-element nil))
(i 0))
(lambda (item)
(if (<= (incf i) n)
(setf (aref sample (1- i)) item)
(when (< (random i) n)
(setf (aref sample (random n)) item)))
sample)))
 
(defun makealgorithm-selectors (n)
(let ((i*random-state* 0)(make-random-state rest))
(lambdafrequency (&optionalmake-array '(x10) nil x:initial-pelement 0)))
(loop repeat 100000
(if (and x-p (< (random (incf i)) n))
for s-of-n = (s-n-creator 3)
(if (< (length res) n)
do (flet ((s-of-n (item)
(push x res)
(setf (elt res (randomfuncall s-of-n)) xitem)))
res))) (map nil
(lambda (i)
(incf (aref frequency i)))
(loop for i from 0 below 9
do (s-of-n i)
finally (return (s-of-n 9))))))
frequency))
 
(princ (algorithm-s))
;;; test
</syntaxhighlight>output<syntaxhighlight lang="text">#(30026 30023 29754 30017 30267 29997 29932 29990 29965 30029)</syntaxhighlight>
(loop repeat 100000
with freq = (make-array 10 :initial-element 0)
do (let ((f (make-selector 3)))
(mapc f '(0 1 2 3 4 5 6 7 8 9))
(mapc (lambda (i) (incf (aref freq i)))
(funcall f)))
finally (prin1 freq))</lang>output<lang>#(30026 30023 29754 30017 30267 29997 29932 29990 29965 30029)</lang>
 
=={{header|D}}==
<syntaxhighlight lang="d">import std.stdio, std.random;
{{trans|Python}}
<lang d>import std.stdio, std.random, std.range, std.algorithm;
 
auto s_of_n_creatorsofN_creator(in int n) {
size_t i;
int[] sample;
 
int i;
typeof(sample)return s_of_n(in int item) {
i++;
if (i <= n) {
// Keep first n items
sample ~= item;
} else if (uniform(0.0, 1.0)uniform01 < (castdouble(doublen)n / i)) {
//sample[uniform(0, Keepn)] = item;
sample = remove(sample, uniform(0, n));
sample ~= item;
}
return sample;
};
return &s_of_n;
}
 
void main() {
int[10]enum binnRuns = 100_000;
autosize_t[10] items = iota(bin.length);
writeln("Single run samples for n = 3:");
auto s_of_n1 = s_of_n_creator(3);
foreach (item; items) {
auto sample = s_of_n1(item);
writefln(" Item: %d -> sample: %s", item, sample);
}
 
foreach (immutable trial; 0 .. nRuns) {
enum nruns = 1_000_000;
immutable sofn = sofN_creator(3);
foreach (trial; 0 .. nruns) {
auto s_of_n2 = s_of_n_creator(3);
int[] sample;
foreach (immutable item; items0 .. bin.length)
sample = s_of_n2sofn(item);
foreach (immutable s; sample)
bin[s]++;
}
writefln("\nTestItem item frequenciescounts for %d runs:\n%s", nrunsnRuns, bin);
}</syntaxhighlight>
foreach (i, d; bin)
{{out}}
writefln(" %d: %d", i, d);
<pre>Item counts for 100000 runs:
}</lang>
[30191, 29886, 29988, 30149, 30251, 29997, 29748, 29909, 30041, 29840]</pre>
Example output:
<pre>Single run samples for n = 3:
Item: 0 -> sample: [0]
Item: 1 -> sample: [0, 1]
Item: 2 -> sample: [0, 1, 2]
Item: 3 -> sample: [0, 1, 2]
Item: 4 -> sample: [0, 1, 4]
Item: 5 -> sample: [0, 1, 4]
Item: 6 -> sample: [1, 4, 6]
Item: 7 -> sample: [1, 6, 7]
Item: 8 -> sample: [6, 7, 8]
Item: 9 -> sample: [7, 8, 9]
 
===Faster Version===
Test item frequencies for 1000000 runs:
<syntaxhighlight lang="d">import std.stdio, std.random, std.algorithm;
0: 300033
 
1: 299914
struct SOfN(size_t n) {
2: 299505
size_t i;
3: 300033
int[n] sample = void;
4: 299704
 
5: 299893
int[] next(in size_t item, ref Xorshift rng) {
6: 299871
7: 300297 i++;
if (i <= n)
8: 300292
sample[i - 1] = item;
9: 300458</pre>
else if (rng.uniform01 < (double(n) / i))
sample[uniform(0, n, rng)] = item;
return sample[0 .. min(i, $)];
}
}
 
void main() {
enum nRuns = 100_000;
size_t[10] bin;
auto rng = Xorshift(0);
 
foreach (immutable trial; 0 .. nRuns) {
SOfN!3 sofn;
foreach (immutable item; 0 .. bin.length - 1)
sofn.next(item, rng);
foreach (immutable s; sofn.next(bin.length - 1, rng))
bin[s]++;
}
writefln("Item counts for %d runs:\n%s", nRuns, bin);
}</syntaxhighlight>
 
=={{header|Elena}}==
ELENA 6.x :
<syntaxhighlight lang="elena">import system'dynamic;
import extensions;
import system'routines;
import system'collections;
extension algorithmOp
{
s_of_n()
{
var counter := new Integer();
var n := self;
^ new ArrayList().mixInto(new
{
eval(i)
{
counter.append(1);
 
if (weak self.Length < n)
{
weak self.append(i)
}
else
{
if(randomGenerator.nextInt(counter) < n)
{ weak self[randomGenerator.nextInt(n)] := i }
};
 
^ weak self.Value
}
})
}
}
public program()
{
var bin := Array.allocate(10).populate::(n => new Integer());
for(int trial := 0; trial < 10000; trial += 1)
{
var s_of_n := 3.s_of_n();
for(int n := 0; n < 10; n += 1)
{
var sample := s_of_n.eval(n);
if (n == 9)
{ sample.forEach::(i){ bin[i].append(1) } }
}
};
console.printLine(bin).readChar()
}</syntaxhighlight>
{{out}}
<pre>
3001,3052,3033,2973,2981,3060,3003,2975,2959,2963
</pre>
 
=={{header|Elixir}}==
<syntaxhighlight lang="elixir">
defmodule Knuth do
def s_of_n_creator(n), do: {n, 1, []}
 
def s_of_n({n, i, ys}, x) do
cond do
i <= n -> {n, i+1, [x|ys]}
 
:rand.uniform(i) <= n ->
{n, i+1, List.replace_at(ys, :rand.uniform(n)-1, x)}
 
true -> {n, i+1, ys}
end
end
end
 
results = Enum.reduce(1..100000, %{}, fn _, freq ->
{_, _, xs} = Enum.reduce(1..10, Knuth.s_of_n_creator(3), fn x, s ->
Knuth.s_of_n(s, x)
end)
Enum.reduce(xs, freq, fn x, freq ->
Map.put(freq, x, (freq[x] || 0) + 1)
end)
end)
 
IO.inspect results
</syntaxhighlight>
Output:
<pre>%{1 => 30138, 2 => 29980, 3 => 29992, 4 => 29975, 5 => 30110, 6 => 29825,
7 => 29896, 8 => 30188, 9 => 29898, 10 => 29998}</pre>
 
=={{header|F_Sharp|F#}}==
<syntaxhighlight lang="fsharp">
let N=System.Random 23 //Nigel Galloway: August 7th., 2018
let s_of_n_creator i = fun g->Seq.fold(fun (n:_[]) g->if N.Next()%(g+1)>i-1 then n else n.[N.Next()%i]<-g;n) (Array.ofSeq (Seq.take i g)) (Seq.skip i g)
let s_of_n<'n> = s_of_n_creator 3
printfn "using an input array -> %A" (List.init 100000 (fun _->s_of_n [|0..9|]) |> Array.concat |> Array.countBy id |> Array.sort)
printfn "using an input list -> %A" (List.init 100000 (fun _->s_of_n [0..9]) |> Array.concat |> Array.countBy id |> Array.sort)
</syntaxhighlight>
{{out}}
<pre>
using an input array -> [|(0, 30162); (1, 30151); (2, 29894); (3, 29766); (4, 30117); (5, 29976); (6, 29916); (7, 29994); (8, 29890); (9, 30134)|]
using an input list -> [|(0, 29936); (1, 29973); (2, 29880); (3, 30160); (4, 30126); (5, 30123); (6, 30062); (7, 30053); (8, 29892); (9, 29795)|]
</pre>
 
=={{header|Go}}==
<langsyntaxhighlight lang="go">package main
 
import (
"fmt"
"math/rand"
"time"
)
 
func sOfNCreator(n int) func(byte) []byte {
s := make([]byte, 0, 3n)
m := n
return func(item byte) []byte {
if len(s) < 3n {
s = append(s, item)
} else {
Line 141 ⟶ 754:
 
func main() {
rand.Seed(time.NanosecondsNow().UnixNano())
var freq [10]int
for r := 0; r < 1e5; r++ {
Line 153 ⟶ 766:
}
fmt.Println(freq)
}</langsyntaxhighlight>
Output:
<pre>
[30075 29955 30024 30095 30031 30018 29973 29642 30156 30031]
</pre>
 
=={{header|Haskell}}==
 
{{libheader|containers}}
{{libheader|MonadRandom}}
{{libheader|random}}
{{libheader|mtl}}
 
<syntaxhighlight lang="haskell">
import Control.Monad.Random
import Control.Monad.State
import qualified Data.Map as M
import System.Random
 
-- s_of_n_creator :: Int -> a -> RandT StdGen (State (Int, [a])) [a]
s_of_n_creator :: Int -> a -> StateT (Int, [a]) (Rand StdGen) [a]
s_of_n_creator n v = do
(i, vs) <- get
let i' = i + 1
if i' <= n
then do
let vs' = v : vs
put (i', vs')
pure vs'
else do
j <- getRandomR (1, i')
if j > n
then do
put (i', vs)
pure vs
else do
k <- getRandomR (0, n - 1)
let (f, (_ : b)) = splitAt k vs
vs' = v : f ++ b
put (i', vs')
pure vs'
 
sample :: Int -> Rand StdGen [Int]
sample n =
let s_of_n = s_of_n_creator n
in snd <$> execStateT (traverse s_of_n [0 .. 9 :: Int]) (0, [])
 
incEach :: (Ord a, Num b) => M.Map a b -> [a] -> M.Map a b
incEach m ks = foldl (\m' k -> M.insertWith (+) k 1 m') m ks
 
sampleInc :: Int -> M.Map Int Double -> Rand StdGen (M.Map Int Double)
sampleInc n m = do
s <- sample n
pure $ incEach m s
 
main :: IO ()
main = do
let counts = M.empty :: M.Map Int Double
n = 100000
gen <- getStdGen
counts <- evalRandIO $ foldM (\c _ -> sampleInc 3 c) M.empty [1 .. n]
print (fmap (/ n) counts)
</syntaxhighlight>
 
=={{header|Icon}} and {{header|Unicon}}==
 
The following solution makes use of the <tt>makeProc</tt> procedure
defined in the <tt>UniLib</tt> library and so is Unicon specific. However,
the solution can be modified to work in Icon as well.
 
Technically, <tt>s_of_n_creator</tt> returns a <i>co-expression</i>,
not a function. In Unicon, the calling syntax for this
co-expression is indistinguishable from that of a function.
<syntaxhighlight lang="unicon">import Utils
 
procedure main(A)
freq := table(0)
every 1 to (\A[2] | 100000)\1 do {
s_of_n := s_of_n_creator(\A[1] | 3)
every sample := s_of_n(0 to 9)
every freq[!sample] +:= 1
}
every write(i := 0 to 9,": ",right(freq[i],6))
end
 
procedure s_of_n_creator(n)
items := []
itemCnt := 0.0
return makeProc {
repeat {
item := (items@&source)[1]
itemCnt +:= 1
if *items < n then put(items, item)
else if ?0 < (n/itemCnt) then ?items := item
}
}
end</syntaxhighlight>
and a sample run:
<pre>->kas
0: 29941
1: 29963
2: 29941
3: 30005
4: 30087
5: 29895
6: 30075
7: 30059
8: 29962
9: 30072
-></pre>
 
=={{header|J}}==
Line 163 ⟶ 881:
Note that this approach introduces heavy inefficiencies, to achieve information hiding.
 
<syntaxhighlight lang="j">s_of_n_creator=: 1 :0
<lang j>coclass'inefficient'
ctx=: conew&'inefficient' m
s_of_n__ctx
)
 
coclass'inefficient'
create=:3 :0
N=: y
Line 172 ⟶ 895:
s_of_n=:3 :0
K=: K+1
if. N>:#ITEMS do.
ITEMS=: ITEMS,y
else.
if. (N%K)>?0 do.
ITEMS=: (((i.#ITEMS)-.<<<?N){ITEMS),y
else.
ITEMS
Line 182 ⟶ 905:
end.
)
</syntaxhighlight>
 
Explanation: <code>create</code> is the constructor for the class named <code>inefficient</code> and it initializes three properties: <code>N</code> (our initial value), <code>ITEMS</code> (an initially empty list) and <code>K</code> (a counter which is initially 0).
 
Also, we have <code>s_of_n</code> which is a method of that class. It increments K and appends to the list, respecting the random value replacement requirement, once the list has reached the required length.
s_of_n_creator_base_=: 1 :0
 
ctx=: conew&'inefficient' m
Finally, we have <code>s_of_n_creator</code> which is not a method of that class, but which will create an object of that class and return the resulting s_of_n method.
s_of_n__ctx
)</lang>
 
Required example:
 
<langsyntaxhighlight lang="j">run=:3 :0
nl=. conl 1
s3_of_n=. 3 s_of_n_creator
Line 200 ⟶ 924:
 
(~.,._1 + #/.~) (i.10),,D=:run"0 i.1e5
0 3009940119
1 2997340050
2 2979540163
3 2999557996
4 2999642546
5 3028940990
6 2990338680
7 2999336416
8 3021533172
9 29868</syntaxhighlight>
9 29742</lang>
 
Here, we have each of our digits along with how many times each appeared in a result from <code>run</code>.
 
Explanation of <code>run</code>:
 
First, we get a snapshot of the existing objects in <code>nl</code>.
 
Then, we get our s3_of_n which is a method in a new object.
 
Then we run that method on each of the values 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, keeping only the values from the last run, this will be the result of the run.
 
Then we delete any objects which did not previously exist.
 
Finally return our result.
 
=={{header|Java}}==
A class-based solution:
<syntaxhighlight lang="java">import java.util.*;
class SOfN<T> {
private static final Random rand = new Random();
private List<T> sample;
private int i = 0;
private int n;
 
public SOfN(int _n) {
n = _n;
sample = new ArrayList<T>(n);
}
 
public List<T> process(T item) {
if (++i <= n) {
sample.add(item);
} else if (rand.nextInt(i) < n) {
sample.set(rand.nextInt(n), item);
}
return sample;
}
}
public class AlgorithmS {
public static void main(String[] args) {
int[] bin = new int[10];
for (int trial = 0; trial < 100000; trial++) {
SOfN<Integer> s_of_n = new SOfN<Integer>(3);
for (int i = 0; i < 9; i++) s_of_n.process(i);
for (int s : s_of_n.process(9)) bin[s]++;
}
System.out.println(Arrays.toString(bin));
}
}</syntaxhighlight>
 
Sample output:
 
<pre>[29965, 29690, 29911, 29818, 30109, 30250, 30085, 29857, 30191, 30124]</pre>
 
Alternative solution without using an explicitly named type; instead using an anonymous class implementing a generic "function" interface:
<syntaxhighlight lang="java">import java.util.*;
interface Function<S, T> {
public T call(S x);
}
public class AlgorithmS {
private static final Random rand = new Random();
public static <T> Function<T, List<T>> s_of_n_creator(final int n) {
return new Function<T, List<T>>() {
private List<T> sample = new ArrayList<T>(n);
private int i = 0;
public List<T> call(T item) {
if (++i <= n) {
sample.add(item);
} else if (rand.nextInt(i) < n) {
sample.set(rand.nextInt(n), item);
}
return sample;
}
};
}
public static void main(String[] args) {
int[] bin = new int[10];
for (int trial = 0; trial < 100000; trial++) {
Function<Integer, List<Integer>> s_of_n = s_of_n_creator(3);
for (int i = 0; i < 9; i++) s_of_n.call(i);
for (int s : s_of_n.call(9)) bin[s]++;
}
System.out.println(Arrays.toString(bin));
}
}</syntaxhighlight>
 
Sample output:
 
<pre>[29965, 30178, 29956, 29957, 30016, 30114, 29977, 29996, 29982, 29859]</pre>
 
=={{header|jq}}==
'''Adapted from [[#Wren]]'''
{{works with|jq}}
 
'''Also works with gojq, the Go implementation of jq'''.
 
jq does not support functions that return functions,
so we adopt the approach taken for example by the [[#C|C]] entry.
Specifically, following the [[#Wren|Wren]] model, the closure variables
are encapsulated in a JSON object of the form {n, s, next, m},
which is initially
<pre>
{n: $n, s: [range(0;$n)|0], next: 0, m: $n}
</pre>
where $n is the maximum sample size.
 
In the following, /dev/random is used as a source of entropy.
In a bash or bash-like environment, a suitable invocation would
be as follows:
<pre>
< /dev/random tr -cd '0-9' | fold -w 1 | jq -Mcnr algorithm-s.jq
</pre>
 
'''algorithm-s.jq'''
<syntaxhighlight lang=jq>
# Output: a PRN in range(0; .)
def prn:
if . == 1 then 0
else . as $n
| (($n-1)|tostring|length) as $w
| [limit($w; inputs)] | join("") | tonumber
| if . < $n then . else ($n | prn) end
end;
 
# Input and output: {n, s, next, m}
# The initial input should be
# {n: $n, s: [range(0;$n)|0], next: 0, m: $n}
# where $n is the maximum sample size.
def sOfN(items):
if (.next < .n)
then .s[.next] = items
| .next += 1
else .m += 1
| if ((.m | prn) < .n)
then (.n | prn) as $t
| .s[$t] = items
| if .next <= $t
then .next = $t + 1
else .
end
else .
end
end;
 
def task($iterations):
def dim($n): [range(0;$n)|0];
def init($n): {n: $n, s: dim($n), next: 0, m: $n };
 
reduce range(0; $iterations) as $r ( {freq: dim(10) };
reduce range(48; 57) as $d (. + init(3); sOfN($d) )
| reduce sOfN(57).s[] as $d (.;
.freq[$d - 48] += 1) )
| .freq ;
 
task(1e5)
</syntaxhighlight>
{{output}}
<pre>
[30008,29988,29827,30101,30308,30005,29808,29851,30218,29886]
</pre>
 
=={{header|Julia}}==
<syntaxhighlight lang="julia">using Printf
 
function makesofn(n::Integer)
buf = Vector{typeof(n)}(0)
i = 0
return function sofn(item)
i += 1
if i ≤ n
push!(buf, item)
else
j = rand(1:i)
if j ≤ n buf[j] = item end
end
return buf
end
end
 
nhist = zeros(Int, 10)
for _ in 1:10^5
kas = makesofn(3)
for j in 0:8 kas(j) end
for k in kas(9) nhist[k+1] += 1 end
end
 
println("Simulating sof3(0:9) 100000 times:")
for (i, c) in enumerate(nhist)
@printf("%5d → %5d\n", i-1, c)
end</syntaxhighlight>
 
{{out}}
<pre>Simulating sof3(0:9) 100000 times:
0 → 29795
1 → 29947
2 → 30227
3 → 30212
4 → 29763
5 → 29960
6 → 29809
7 → 30215
8 → 29948
9 → 30124</pre>
 
=={{header|Kotlin}}==
{{trans|Java}}
Class based solution:
<syntaxhighlight lang="scala">// version 1.2.51
 
import java.util.Random
 
val rand = Random()
 
class SOfN<T>(val n: Int) {
private val sample = ArrayList<T>(n)
private var i = 0
 
fun process(item: T): List<T> {
if (++i <= n)
sample.add(item)
else if (rand.nextInt(i) < n)
sample[rand.nextInt(n)] = item
return sample
}
}
fun main(args: Array<String>) {
val bin = IntArray(10)
(1..100_000).forEach {
val sOfn = SOfN<Int>(3)
for (d in 0..8) sOfn.process(d)
for (s in sOfn.process(9)) bin[s]++
}
println(bin.contentToString())
}</syntaxhighlight>
Sample output:
<pre>
[29981, 29845, 29933, 30139, 30051, 30039, 29702, 30218, 30199, 29893]
</pre>
 
Alternative function based solution:
<syntaxhighlight lang="scala">// version 1.2.51
 
import java.util.Random
 
val rand = Random()
 
fun <T> SOfNCreator(n: Int): (T) -> List<T> {
val sample = ArrayList<T>(n)
var i = 0
return {
if (++i <= n)
sample.add(it)
else if (rand.nextInt(i) < n)
sample[rand.nextInt(n)] = it
sample
}
}
 
fun main(args: Array<String>) {
val bin = IntArray(10)
(1..100_000).forEach {
val sOfn = SOfNCreator<Int>(3)
for (d in 0..8) sOfn(d)
for (s in sOfn(9)) bin[s]++
}
println(bin.contentToString())
}</syntaxhighlight>
 
Sample output:
<pre>
[30172, 29856, 30132, 29884, 29818, 30220, 29900, 30069, 29869, 30080]
</pre>
 
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">ClearAll[sofncreator]
sofncreator[n_] := Module[{sample, i},
sample = {};
i = 0;
Return[
Function[{item},
i++;
If[i <= n,
AppendTo[sample, item]
,
If[RandomInteger[{1, i}] <= n,
sample[[RandomInteger[{1, n}]]] = item
]
];
sample
]
]
]
bin = ConstantArray[0, 10];
items = Range[10];
sofn = sofncreator[3];
Do[
sample = sofn[item];
Print[" Item: ", item, " -> sample: " , sample]
,
{item, items}
]
Do[
sofn = sofncreator[3];
Do[
sample = sofn[item]
,
{item, items}
];
Do[
bin[[s]] += 1
,
{s, sample}
]
,
{trial, 100000}
];
{Range[Length[bin]], bin} // Transpose // Grid</syntaxhighlight>
{{out}}
<pre> Item: 1 -> sample: {1}
Item: 2 -> sample: {1,2}
Item: 3 -> sample: {1,2,3}
Item: 4 -> sample: {4,2,3}
Item: 5 -> sample: {5,2,3}
Item: 6 -> sample: {5,6,3}
Item: 7 -> sample: {7,6,3}
Item: 8 -> sample: {7,6,3}
Item: 9 -> sample: {7,6,3}
Item: 10 -> sample: {7,10,3}
 
1 29732
2 30055
3 30059
4 29787
5 30067
6 30123
7 30136
8 30056
9 29949
10 30036</pre>
 
=={{header|Nim}}==
 
<syntaxhighlight lang="nim">import random
 
func sOfNCreator[T](n: Positive): proc(item: T): seq[T] =
var sample = newSeqOfCap[T](n)
var i = 0
 
result = proc(item: T): seq[T] =
inc i
if i <= n:
sample.add(item)
elif rand(1..i) <= n:
sample[rand(n - 1)] = item
sample
 
when isMainModule:
 
randomize()
 
echo "Digits counts for 100_000 runs:"
var hist: array[10, Natural]
for _ in 1..100_000:
let sOfN = sOfNCreator[Natural](3)
for i in 0..8:
discard sOfN(i)
for val in sOfN(9):
inc hist[val]
 
for n, count in hist:
echo n, ": ", count</syntaxhighlight>
 
{{out}}
<pre>Digits counts for 100_000 runs:
0: 30092
1: 29906
2: 29956
3: 29896
4: 30151
5: 30000
6: 30267
7: 29853
8: 30186
9: 29693</pre>
 
=={{header|Objective-C}}==
{{works with|Mac OS X|10.6+}}
Uses blocks
<syntaxhighlight lang="objc">#import <Foundation/Foundation.h>
 
typedef NSArray *(^SOfN)(id);
 
SOfN s_of_n_creator(int n) {
NSMutableArray *sample = [[NSMutableArray alloc] initWithCapacity:n];
__block int i = 0;
return [^(id item) {
i++;
if (i <= n) {
[sample addObject:item];
} else if (rand() % i < n) {
sample[rand() % n] = item;
}
return sample;
} copy];
}
 
int main(int argc, const char *argv[]) {
@autoreleasepool {
 
NSCountedSet *bin = [[NSCountedSet alloc] init];
for (int trial = 0; trial < 100000; trial++) {
SOfN s_of_n = s_of_n_creator(3);
NSArray *sample;
for (int i = 0; i < 10; i++)
sample = s_of_n(@(i));
[bin addObjectsFromArray:sample];
}
NSLog(@"%@", bin);
}
return 0;
}</syntaxhighlight>
 
Log:
 
<pre>
<NSCountedSet: 0x100114120> (0 [29934], 9 [30211], 5 [29926], 1 [30067], 6 [30001], 2 [29972], 7 [30126], 3 [29944], 8 [29910], 4 [29909])
</pre>
 
=={{header|OCaml}}==
 
<langsyntaxhighlight lang="ocaml">let s_of_n_creator n =
let i = ref 0
and sample = ref [| |] in
functionfun item ->
incr i;
if !i <= n then sample := Array.append [| item |] !sample
Line 227 ⟶ 1,386:
 
let () =
Random.self_init ();
let n = 3 in
let num_items = 10 in
let items_set = Array.init num_items (fun i -> i) in
let results = Array.createmake num_items 0 in
for i = 1 to 100_000 do
let res = test n items_set in
Line 237 ⟶ 1,396:
done;
Array.iter (Printf.printf " %d") results;
print_newline ()</langsyntaxhighlight>
 
Output:
 
<pre> 30051 29899 30249 30058 30012 29836 29998 29882 30148 29867</pre>
 
=={{header|PARI/GP}}==
{{improve|PARI/GP|Does not return a function.}}
<syntaxhighlight lang="parigp">KnuthS(v,n)={
my(u=vector(n,i,i));
for(i=n+1,#v,
if(random(i)<n,u[random(n)+1]=i)
);
vecextract(v,u)
};
test()={
my(v=vector(10),t);
for(i=1,1e5,
t=KnuthS([0,1,2,3,4,5,6,7,8,9],3);
v[t[1]+1]++;v[t[2]+1]++;v[t[3]+1]++
);
v
};</syntaxhighlight>
 
Output:
<pre>%1 = [30067, 30053, 29888, 30161, 30204, 29990, 30175, 29980, 29622, 29860]</pre>
 
=={{header|Perl}}==
<syntaxhighlight lang="perl">use strict;
 
sub s_of_n_creator {
my $n = shift;
my @sample;
my $i = 0;
sub {
my $item = shift;
$i++;
if ($i <= $n) {
# Keep first n items
push @sample, $item;
} elsif (rand() < $n / $i) {
# Keep item
@sample[rand $n] = $item;
}
@sample
}
}
 
my @items = (0..9);
my @bin;
 
foreach my $trial (1 .. 100000) {
my $s_of_n = s_of_n_creator(3);
my @sample;
foreach my $item (@items) {
@sample = $s_of_n->($item);
}
foreach my $s (@sample) {
$bin[$s]++;
}
}
print "@bin\n";
</syntaxhighlight>
 
;Sample output:
<pre>30003 29923 30192 30164 29994 29976 29935 29860 30040 29913</pre>
 
=={{header|Phix}}==
{{trans|C}}
Phix does not support closures, but they are easy enough to emulate using {routine_id,environment}.<br>
Obviously the direct call (as commented out) is inevitably going to be marginally faster, and<br>
of course an s_of_n() that operated directly on local vars rather than elements of env, would be faster still.<br>
Not that a mere 100,000 samples takes any method more than a tiny fraction of a second, you understand.
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">enum</span> <span style="color: #000000;">RID</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">I</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">SAMPLE</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">s_of_n</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">env</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">item</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">i</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">env</span><span style="color: #0000FF;">[</span><span style="color: #000000;">I</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">env</span><span style="color: #0000FF;">[</span><span style="color: #000000;">SAMPLE</span><span style="color: #0000FF;">])</span>
<span style="color: #000000;">env</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">env</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">env</span><span style="color: #0000FF;">[</span><span style="color: #000000;">I</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">i</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">n</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">env</span><span style="color: #0000FF;">[</span><span style="color: #000000;">SAMPLE</span><span style="color: #0000FF;">][</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">item</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">/</span><span style="color: #000000;">i</span><span style="color: #0000FF;">></span><span style="color: #7060A8;">rnd</span><span style="color: #0000FF;">()</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">env</span><span style="color: #0000FF;">[</span><span style="color: #000000;">SAMPLE</span><span style="color: #0000FF;">][</span><span style="color: #7060A8;">rand</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">item</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">env</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">s_of_n_creator</span><span style="color: #0000FF;">(</span><span style="color: #004080;">int</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">s_of_n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">invoke</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">env</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">args</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">env</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">call_func</span><span style="color: #0000FF;">(</span><span style="color: #000000;">env</span><span style="color: #0000FF;">[</span><span style="color: #000000;">RID</span><span style="color: #0000FF;">],</span><span style="color: #7060A8;">prepend</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">args</span><span style="color: #0000FF;">),</span><span style="color: #000000;">env</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">env</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">items</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">env</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s_of_n_creator</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">items</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000080;font-style:italic;">-- env = s_of_n(env,items[i])</span>
<span style="color: #000000;">env</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">invoke</span><span style="color: #0000FF;">(</span><span style="color: #000000;">env</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">items</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">env</span><span style="color: #0000FF;">[</span><span style="color: #000000;">SAMPLE</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">items_set</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">frequencies</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">items_set</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">100000</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">items_set</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">fdx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">1</span>
<span style="color: #000000;">frequencies</span><span style="color: #0000FF;">[</span><span style="color: #000000;">fdx</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #0000FF;">?</span><span style="color: #000000;">frequencies</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
{29631,30097,29737,30252,29774,30147,29901,30042,30204,30215}
</pre>
Note that s_of_n_creator() must match {RID, I, SAMPLE}. You might instead prefer (taking the appropriate care not to miss any!):
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">enum</span> <span style="color: #000000;">RID</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">I</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">SAMPLE</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">CLOSURE_LEN</span><span style="color: #0000FF;">=$</span>
<span style="color: #0000FF;">...</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">s_of_n_creator</span><span style="color: #0000FF;">(</span><span style="color: #004080;">int</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">closure</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">CLOSURE_LEN</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">closure</span><span style="color: #0000FF;">[</span><span style="color: #000000;">RID</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">routine_id</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"s_of_n"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">closure</span><span style="color: #0000FF;">[</span><span style="color: #000000;">I</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #000000;">closure</span><span style="color: #0000FF;">[</span><span style="color: #000000;">SAMPLE</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">closure</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<!--</syntaxhighlight>-->
 
=={{header|PHP}}==
{{works with|PHP|5.3+}}
<syntaxhighlight lang="php"><?php
function s_of_n_creator($n) {
$sample = array();
$i = 0;
return function($item) use (&$sample, &$i, $n) {
$i++;
if ($i <= $n) {
// Keep first n items
$sample[] = $item;
} else if (rand(0, $i-1) < $n) {
// Keep item
$sample[rand(0, $n-1)] = $item;
}
return $sample;
};
}
 
$items = range(0, 9);
 
for ($trial = 0; $trial < 100000; $trial++) {
$s_of_n = s_of_n_creator(3);
foreach ($items as $item)
$sample = $s_of_n($item);
foreach ($sample as $s)
$bin[$s]++;
}
print_r($bin);
?></syntaxhighlight>
 
;Sample output:
<pre>Array
(
[3] => 30158
[8] => 29859
[9] => 29984
[6] => 29937
[7] => 30361
[4] => 29994
[5] => 29849
[0] => 29724
[1] => 29997
[2] => 30137
)</pre>
 
=={{header|PicoLisp}}==
<langsyntaxhighlight PicoLisplang="picolisp">(de s_of_n_creator (@N)
(curry (@N (I . 0) (Res)) (Item)
(cond
Line 256 ⟶ 1,594:
(for I (mapc S_of_n (0 1 2 3 4 5 6 7 8 9))
(inc (nth Freq (inc I))) ) ) )
Freq )</langsyntaxhighlight>
Output:
<pre>-> (30003 29941 29918 30255 29848 29875 30056 29839 30174 30091)</pre>
 
=={{header|Python}}==
{{works with|Python|3.x}}
<lang python>from random import random, randrange
<syntaxhighlight lang="python">from random import randrange
 
def s_of_n_creator(n):
Line 272 ⟶ 1,611:
# Keep first n items
sample.append(item)
elif randomrandrange(i) < n / i:
# Keep item
del sample[randrange(n)] = item
sample.append(item)
return sample
return s_of_n
Line 295 ⟶ 1,633:
bin[s] += 1
print("\nTest item frequencies for 100000 runs:\n ",
'\n '.join("%i:%i" % x for x in enumerate(bin)))</langsyntaxhighlight>
 
;Sample output:
Line 324 ⟶ 1,662:
===Python Class based version===
Only a slight change creates the following class-based implementation:
<langsyntaxhighlight lang="python">class S_of_n_creator():
def __init__(self, n):
self.n = n
Line 336 ⟶ 1,674:
# Keep first n items
sample.append(item)
elif randomrandrange(i) < n / i:
# Keep item
del sample[randrange(n)] = item
return sample.append(item)</syntaxhighlight>
return sample</lang>
The above can be instantiated as follows after which <code>s_of_n</code> can be called in the same way as it is in the first example where it is a function instead of an instance.
<langsyntaxhighlight lang="python">s_of_n = S_of_n_creator(3)</langsyntaxhighlight>
 
=={{header|Racket}}==
<syntaxhighlight lang="racket">#lang racket/base
 
(define (s-of-n-creator n)
(define i 0)
(define sample (make-vector n)) ; the sample of n items
(lambda (item)
(set! i (add1 i))
(cond [(<= i n) ; we're not full, so kind of boring
(vector-set! sample (sub1 i) item)]
[(< (random i) n) ; we've already seen n items; swap one?
(vector-set! sample (random n) item)])
sample))
 
(define counts (make-vector 10 0))
 
(for ([i 100000])
(define s-of-n (s-of-n-creator 3))
(define sample (for/last ([digit 10]) (s-of-n digit)))
(for ([d sample]) (vector-set! counts d (add1 (vector-ref counts d)))))
 
(for ([d 10]) (printf "~a ~a\n" d (vector-ref counts d)))</syntaxhighlight>
Output:
<pre>0 30117
1 29955
2 30020
3 29906
4 30146
5 29871
6 30045
7 30223
8 29940
9 29777</pre>
 
=={{header|Raku}}==
(formerly Perl 6)
<syntaxhighlight lang="raku" line>sub s_of_n_creator($n) {
my (@sample, $i);
-> $item {
if ++$i <= $n { @sample.push: $item }
elsif $i.rand < $n { @sample[$n.rand] = $item }
@sample
}
}
 
my @bin;
for ^100000 {
my &s_of_n = s_of_n_creator 3;
sink .&s_of_n for ^9;
@bin[$_]++ for s_of_n 9;
}
 
say @bin;</syntaxhighlight>
Output:
<pre>29975 30028 30246 30056 30004 29983 29836 29967 29924 29981</pre>
 
=={{header|REXX}}==
<syntaxhighlight lang="rexx">/*REXX program using Knuth's algorithm S (a random sampling N of M items). */
parse arg trials size . /*obtain optional arguments from the CL*/
if trials=='' | trials=="," then trials= 100000 /*Not specified? Then use the default.*/
if size=='' | size=="," then size= 3 /* " " " " " " */
#.= 0 /*initialize frequency counter array. */
do trials /*OK, now let's light this candle. */
call s_of_n_creator size /*create an initial list of N items. */
 
do gen=0 for 10; call s_of_n gen /*call s_of_n with a single decimal dig*/
end /*gen*/
/* [↓] examine what SofN generated. */
do count=1 for size; _= !.count /*get a dec. digit from the Nth item. */
#._= #._ + 1 /*bump counter for the decimal digit. */
end /*count*/
end /*trials*/
@= ' trials, and with a size of '
hdr= " Using Knuth's algorithm S for " commas(trials) @ || commas(size)": "
say hdr; say copies("═", length(hdr) ) /*display the header and its separator.*/
 
do dig=0 to 9 /* [↓] display the frequency of a dig.*/
say right("frequency of the", 37) dig 'digit is: ' commas(#.dig)
end /*dig*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
commas: parse arg _; do jc=length(_)-3 to 1 by -3; _=insert(',', _, jc); end; return _
/*──────────────────────────────────────────────────────────────────────────────────────*/
s_of_n: parse arg item; items= items + 1 /*get "item", bump the items counter.*/
if random(1, items)>size then return /*probability isn't good, so skip it. */
_= random(1, size); !._= item /*now, figure out which previous ··· */
return /* ··· item to replace with ITEM.*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
s_of_n_creator: parse arg item 1 items /*generate ITEM number of items. */
do k=1 for item /*traipse through the first N items. */
!.k= random(0, 9) /*set the Kth item with random digit.*/
end /*k*/
return /*the piddly stuff is done (for now). */</syntaxhighlight>
{{out|output|text=&nbsp; when using the default input of: &nbsp; &nbsp; <tt> 100000 &nbsp; 2 </tt>}}
<pre>
Using Knuth's algorithm S for 100,000 trials, and with a size of 3:
═══════════════════════════════════════════════════════════════════════════
frequency of the 0 digit is: 29,879
frequency of the 1 digit is: 30,259
frequency of the 2 digit is: 30,254
frequency of the 3 digit is: 29,929
frequency of the 4 digit is: 30,022
frequency of the 5 digit is: 30,010
frequency of the 6 digit is: 29,692
frequency of the 7 digit is: 30,108
frequency of the 8 digit is: 29,976
frequency of the 9 digit is: 29,871
</pre>
 
=={{header|RPL}}==
This is an idiomatic adaptation of the algorithm: SCREA initializes 2 persistent variables: S contains the sample and SPAR the algorithm parameters (n and i)
{{works with|RPL|HP49-C}}
« 0 2 →LIST '<span style="color:green">SPAR</span>' STO { } '<span style="color:green">S</span>' STO
» '<span style="color:blue">SCREA</span>' STO
« <span style="color:green">SPAR</span> EVAL
'''CASE'''
DUP2 > '''THEN''' DROP2 '<span style="color:green">S</span>' STO+ '''END'''
/ →NUM RAND ≥ '''THEN''' <span style="color:green">S</span> DUP SIZE RAND * CEIL ROT PUT '<span style="color:green">S</span>' STO '''END'''
DROP '''END'''
'<span style="color:green">SPAR</span>' 2 DUP2 GET 1 + PUT <span style="color:green">S</span>
» '<span style="color:blue">SOFN</span>' STO
« { } → sample
« { 10 } 0 CON
1 1000 '''START'''
3 <span style="color:blue">SCREA</span>
0
0 9 '''FOR''' k
DROP k <span style="color:blue">SOFN</span>
'''NEXT'''
'sample' STO
« sample k POS » 'k' 0 9 1 SEQ
NOT NOT AXL +
'''NEXT'''
» » '<span style="color:blue">TASK</span>' STO
{{out}}
<pre>
1: [ 206. 218. 235. 309. 359. 329. 327. 324. 359. 334. ]
</pre>
 
=={{header|Ruby}}==
Using a closure
<syntaxhighlight lang="ruby">def s_of_n_creator(n)
sample = []
i = 0
Proc.new do |item|
i += 1
if i <= n
sample << item
elsif rand(i) < n
sample[rand(n)] = item
end
sample
end
end
 
frequency = Array.new(10,0)
100_000.times do
s_of_n = s_of_n_creator(3)
sample = nil
(0..9).each {|digit| sample = s_of_n[digit]}
sample.each {|digit| frequency[digit] += 1}
end
 
(0..9).each {|digit| puts "#{digit}\t#{frequency[digit]}"}</syntaxhighlight>
Example
<pre>0 29850
1 30015
2 29970
3 29789
4 29841
5 30075
6 30281
7 30374
8 29953
9 29852</pre>
 
=={{header|Rust}}==
 
{{libheader|rand 0.3}}
 
<syntaxhighlight lang="rust">use rand::{Rng,weak_rng};
 
struct SofN<R: Rng+Sized, T> {
rng: R,
sample: Vec<T>,
i: usize,
n: usize,
}
 
impl<R: Rng, T> SofN<R, T> {
fn new(rng: R, n: usize) -> Self {
SofN{rng, sample: Vec::new(), i: 0, n}
}
 
fn add(&mut self, item: T) {
self.i += 1;
if self.i <= self.n {
self.sample.push(item);
} else if self.rng.gen_range(0, self.i) < self.n {
self.sample[self.rng.gen_range(0, self.n)] = item;
}
}
 
fn sample(&self) -> &Vec<T> {
&self.sample
}
}
 
 
pub fn main() {
const MAX: usize = 10;
let mut bin: [i32; MAX] = Default::default();
for _ in 0..100000 {
let mut s_of_n = SofN::new(weak_rng(), 3);
for i in 0..MAX { s_of_n.add(i); }
 
for s in s_of_n.sample() {
bin[*s] += 1;
}
}
for (i, x) in bin.iter().enumerate() {
println!("frequency of {}: {}", i, x);
}
}</syntaxhighlight>
 
{{out}}
<pre>
frequency of 0: 29883
frequency of 1: 29901
frequency of 2: 29896
frequency of 3: 30029
frequency of 4: 30017
frequency of 5: 29850
frequency of 6: 30139
frequency of 7: 30252
frequency of 8: 30030
frequency of 9: 30003
</pre>
 
=={{header|Scala}}==
===Imperative (Ugly and side effects)===
{{trans|Java}}
<syntaxhighlight lang="scala">import java.util
import scala.util.Random
 
object KnuthsAlgorithmS extends App {
 
import scala.collection.JavaConverters._
 
val (n, rand, bin) = (3, Random, new Array[Int](10))
 
for (_ <- 0 until 100000) {
val sample = new util.ArrayList[Int](n)
for (item <- 0 until 10) {
if (item < n) sample.add(item)
else if (rand.nextInt(item + 1) < n)
sample.asScala(rand.nextInt(n)) = item
}
for (s <- sample.asScala.toList) bin(s) += 1
}
 
println(bin.mkString("[", ", ", "]"))
}</syntaxhighlight>
{{Out}}See it running in your browser by [https://scalafiddle.io/sf/nlldfXD/0 ScalaFiddle (JavaScript, non JVM)] or by [https://scastie.scala-lang.org/WLaee5H9T72cximqK9gECA Scastie (JVM)].
 
=={{header|Sidef}}==
{{trans|Raku}}
<syntaxhighlight lang="ruby">func s_of_n_creator(n) {
var i = 0
var sample = []
{ |item|
if (++i <= n) {
sample << item;
}
elsif (i.rand < n) {
sample[n.rand] = item;
}
sample;
}
}
 
var items = 0..9;
var bin = [];
 
100000.times {
var s_of_n = s_of_n_creator(3);
var sample = []
for item in items {
sample = s_of_n(item);
}
for s in sample {
bin[s] := 0 ++;
}
}
 
say bin;</syntaxhighlight>
{{out}}
<pre>
[30056, 29906, 30058, 29986, 30062, 29748, 29989, 29985, 30126, 30084]
</pre>
 
=={{header|Swift}}==
<syntaxhighlight lang="swift">import Darwin
 
func s_of_n_creator<T>(n: Int) -> T -> [T] {
var sample = [T]()
var i = 0
return {(item: T) in
i++
if (i <= n) {
sample.append(item)
} else if (Int(arc4random_uniform(UInt32(i))) < n) {
sample[Int(arc4random_uniform(UInt32(n)))] = item
}
return sample
}
}
 
var bin = [Int](count:10, repeatedValue:0)
for trial in 0..<100000 {
let s_of_n: Int -> [Int] = s_of_n_creator(3)
var sample: [Int] = []
for i in 0..<10 {
sample = s_of_n(i)
}
for s in sample {
bin[s]++
}
}
println(bin)</syntaxhighlight>
{{out}}
<pre>
[30038, 29913, 30047, 30069, 30159, 30079, 29773, 29962, 30000, 29960]
</pre>
 
=={{header|Tcl}}==
<langsyntaxhighlight lang="tcl">package require Tcl 8.6
 
oo::class create SofN {
Line 373 ⟶ 2,049:
}
}
parray freq</langsyntaxhighlight>
Sample output:<pre>
freq(0) = 29812
Line 386 ⟶ 2,062:
freq(9) = 29824
</pre>
 
=={{header|V (Vlang)}}==
{{trans|go}}
<syntaxhighlight lang="v (vlang)">import rand
import rand.seed
fn s_of_ncreator(n int) fn(u8) []u8 {
mut s := []u8{len: 0, cap:n}
mut m := n
return fn[mut s, mut m, n](item u8) []u8 {
if s.len < n {
s << item
} else {
m++
if rand.intn(m) or {0} < n {
s[rand.intn(n) or {0}] = item
}
}
return s
}
}
fn main() {
rand.seed(seed.time_seed_array(2))
mut freq := [10]int{}
for _ in 0..int(1e5) {
s_of_n := s_of_ncreator(3)
for d := '0'[0]; d < '9'[0]; d++ {
s_of_n(d)
}
for d in s_of_n('9'[0]) {
freq[d-'0'[0]]++
}
}
println(freq)
}</syntaxhighlight>
Output:
<pre>
[30131, 30045, 29880, 30178, 29745, 29890, 30150, 30014, 30068, 29899]
</pre>
 
=={{header|Wren}}==
{{trans|Go}}
<syntaxhighlight lang="wren">import "random" for Random
 
var r = Random.new()
 
var sOfNCreator = Fn.new { |n|
var s = List.filled(n, 0)
var next = 0
var m = n
return Fn.new { |item|
if (next < n) {
s[next] = item
next = next + 1
} else {
m = m + 1
if (r.int(m) < n) {
var t = r.int(n)
s[t] = item
if (next <= t) next = t + 1
}
}
return s
}
}
 
var freq = List.filled(10, 0)
for (r in 0...1e5) {
var sOfN = sOfNCreator.call(3)
for (d in 48...57) sOfN.call(d)
for (d in sOfN.call(57)) {
freq[d - 48] = freq[d - 48] + 1
}
}
System.print(freq)</syntaxhighlight>
 
{{out}}
Sample run:
<pre>
[29842, 30051, 29878, 30178, 29731, 30089, 30070, 29939, 30058, 30164]
</pre>
 
=={{header|zkl}}==
<syntaxhighlight lang="zkl">fcn s_of_n_creator(n){
fcn(item,ri,N,samples){
i:=ri.inc(); // 1,2,3,4,...
if(i<=N) samples.append(item);
else if ((0).random(i) < N) samples[(0).random(N)] = item;
samples
}.fp1(Ref(1),n,L())
}</syntaxhighlight>
One run:
<syntaxhighlight lang="zkl">s3:=s_of_n_creator(3);
[0..9].pump(List,s3,"copy").println();</syntaxhighlight>
{{out}}
<pre>
L(L(0),L(0,1),L(0,1,2),L(0,1,2),L(0,4,2),L(5,4,2),L(5,6,2),L(5,6,2),L(5,6,2),L(9,6,2))
</pre>
100,000 runs:
<syntaxhighlight lang="zkl">dist:=L(0,0,0,0,0,0,0,0,0,0);
do(0d100_000){
(0).pump(10,Void,s_of_n_creator(3)).apply2('wrap(n){dist[n]=dist[n]+1})
}
N:=dist.sum();
dist.apply('wrap(n){"%.2f%%".fmt(n.toFloat()/N*100)}).println();</syntaxhighlight>
{{out}}
<pre>L("10.00%","9.98%","10.00%","9.99%","10.00%","9.98%","10.01%","10.04%","9.98%","10.02%")</pre>
Aerobar
1,151

edits

Retrieved from "https://rosettacode.org/wiki/Special:MobileDiff/203051...362074"