Knuth's algorithm S

From Rosetta Code
Task
Knuth's algorithm S
You are encouraged to solve this task according to the task description, using any language you may know.

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
  1. Select the first n items as the sample as they become available;
  2. 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.
  3. Repeat #2 for any subsequent items.
The Task
  1. Create a function s_of_n_creator that given the maximum sample size, returns a function s_of_n that takes one parameter, item.
  2. Function s_of_n 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.
  3. Test your functions by printing and showing the frequency of occurrences of the selected digits from 100,000 repetitions of:
  1. Use the s_of_n_creator with n == 3 to generate an s_of_n.
  2. 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.

Ada[edit]

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:

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;

Here is the implementation of that package:

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;

The main program:

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;

A sample output:

 0: 30008;    1: 30056;    2: 30080;    3: 29633;    4: 29910;    5: 30293;    6: 30105;    7: 29924;    8: 29871;    9: 30120; 

BBC BASIC[edit]

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.

      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$(a$)) + "]"

Output:

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

C[edit]

Instead of returning a closure we set the environment in a structure:

#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;
}

C++[edit]

Works with: C++11
#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;
}
Output:
30052
29740
30197
30223
29857
29688
30095
29803
30098
30247

Class-based version:

#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;
}

Clojure[edit]

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.

(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)
 

Sample output:

([0 29924] [1 30053] [2 30018] [3 29765] [4 29974] [5 30225] [6 30082] [7 29996] [8 30128] [9 29835])

If we really need a stateful (thread safe!) function for some reason, we can get it like this:

(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)))))

CoffeeScript[edit]

 
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]
 

output

 
> coffee knuth_sample.coffee
0 29899
1 29841
2 29930
3 30058
4 29932
5 29948
6 30047
7 30114
8 29976
9 30255
 


Common Lisp[edit]

(defun s-n-creator (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 algorithm-s ()
(let ((*random-state* (make-random-state t))
(frequency (make-array '(10) :initial-element 0)))
(loop repeat 100000
for s-of-n = (s-n-creator 3)
do (flet ((s-of-n (item)
(funcall s-of-n item)))
(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))
 
output
#(30026 30023 29754 30017 30267 29997 29932 29990 29965 30029)

D[edit]

import std.stdio, std.random;
 
auto sofN_creator(in int n) {
size_t i;
int[] sample;
 
return (in int item) {
i++;
if (i <= n)
sample ~= item;
else if (uniform01 < (double(n) / i))
sample[uniform(0, n)] = item;
return sample;
};
}
 
void main() {
enum nRuns = 100_000;
size_t[10] bin;
 
foreach (immutable trial; 0 .. nRuns) {
immutable sofn = sofN_creator(3);
int[] sample;
foreach (immutable item; 0 .. bin.length)
sample = sofn(item);
foreach (immutable s; sample)
bin[s]++;
}
writefln("Item counts for %d runs:\n%s", nRuns, bin);
}
Output:
Item counts for 100000 runs:
[30191, 29886, 29988, 30149, 30251, 29997, 29748, 29909, 30041, 29840]

Faster Version[edit]

import std.stdio, std.random, std.algorithm;
 
struct SOfN(size_t n) {
size_t i;
int[n] sample = void;
 
int[] next(in size_t item, ref Xorshift rng) {
i++;
if (i <= n)
sample[i - 1] = item;
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);
}

Elena[edit]

#import system.
#import system'dynamic.
#import extensions.
#import system'routines.
#import system'collections.
 
#class(extension)algorithmOp
{
#method s_of_n
[
#var counter := Integer new.
 
^ ArrayList new mix &into:
{
eval : n
[
counter += 1.
 
(this length < self)
 ? [ this += n. ]
 ! [
(randomGenerator eval:counter < self)
 ? [ this@(randomGenerator eval:self) := n. ].
].
 
^ this array.
]
}.
]
}
 
#symbol program =
[
#var bin := Array new:10 set &every:(&index:n) [ Integer new ].
0 till:10000 &doEach: trial
[
#var s_of_n := 3 s_of_n.
 
0 till:10 &doEach:n
[
#var sample := s_of_n eval:n.
 
(n == 9)
 ? [ sample run &each: i [ [email protected] += 1. ]. ].
].
].
 
console writeLine:bin.
].
Output:
3050,3029,3041,2931,3040,2952,2901,2984,3069,3003

Elixir[edit]

 
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
 

Output:

%{1 => 30138, 2 => 29980, 3 => 29992, 4 => 29975, 5 => 30110, 6 => 29825,
  7 => 29896, 8 => 30188, 9 => 29898, 10 => 29998}

Go[edit]

package main
 
import (
"fmt"
"math/rand"
"time"
)
 
func sOfNCreator(n int) func(byte) []byte {
s := make([]byte, 0, n)
m := n
return func(item byte) []byte {
if len(s) < n {
s = append(s, item)
} else {
m++
if rand.Intn(m) < n {
s[rand.Intn(n)] = item
}
}
return s
}
}
 
func main() {
rand.Seed(time.Now().UnixNano())
var freq [10]int
for r := 0; r < 1e5; r++ {
sOfN := sOfNCreator(3)
for d := byte('0'); d < '9'; d++ {
sOfN(d)
}
for _, d := range sOfN('9') {
freq[d-'0']++
}
}
fmt.Println(freq)
}

Output:

[30075 29955 30024 30095 30031 30018 29973 29642 30156 30031]

Icon and Unicon[edit]

The following solution makes use of the makeProc procedure defined in the UniLib library and so is Unicon specific. However, the solution can be modified to work in Icon as well.

Technically, s_of_n_creator returns a co-expression, not a function. In Unicon, the calling syntax for this co-expression is indistinguishable from that of a function.

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

and a sample run:

->kas    
0:  29941
1:  29963
2:  29941
3:  30005
4:  30087
5:  29895
6:  30075
7:  30059
8:  29962
9:  30072
->

J[edit]

Note that this approach introduces heavy inefficiencies, to achieve information hiding.

s_of_n_creator=: 1 :0
ctx=: conew&'inefficient' m
s_of_n__ctx
)
 
coclass'inefficient'
create=:3 :0
N=: y
ITEMS=: ''
K=:0
)
 
s_of_n=:3 :0
K=: K+1
if. N>:#ITEMS do.
ITEMS=: ITEMS,y
else.
if. (N%K)>?0 do.
ITEMS=: ((<<<?N){ITEMS),y
else.
ITEMS
end.
end.
)
 

Explanation: create is the constructor for the class named inefficient and it initializes three properties: N (our initial value), ITEMS (an initially empty list) and K (a counter which is initially 0).

Also, we have s_of_n 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.

Finally, we have s_of_n_creator 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.

Required example:

run=:3 :0
nl=. conl 1
s3_of_n=. 3 s_of_n_creator
r=. {: s3_of_n"0 i.10
coerase (conl 1)-.nl
r
)
 
(~.,._1 + #/.~) (i.10),,D=:run"0 i.1e5
0 40119
1 40050
2 40163
3 57996
4 42546
5 40990
6 38680
7 36416
8 33172
9 29868

Here, we have each of our digits along with how many times each appeared in a result from run.

Explanation of run:

First, we get a snapshot of the existing objects in nl.

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.

Java[edit]

A class-based solution:

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) {
i++;
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);
List<Integer> sample = null;
for (int i = 0; i < 10; i++)
sample = s_of_n.process(i);
for (int s : sample)
bin[s]++;
}
System.out.println(Arrays.toString(bin));
}
}

Output:

[30115, 30141, 30050, 29887, 29765, 30132, 29767, 30114, 30079, 29950]

Alternative solution without using an explicitly named type; instead using an anonymous class implementing a generic "function" interface:

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) {
i++;
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);
List<Integer> sample = null;
for (int i = 0; i < 10; i++)
sample = s_of_n.call(i);
for (int s : sample)
bin[s]++;
}
System.out.println(Arrays.toString(bin));
}
}

Julia[edit]

 
function makesofn(n::Int)
buf = Any[]
i = 0
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
return sofn
end
 
 
nhist = zeros(Int, 10)
 
for i 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)
println(@sprintf "  %2d => %5d" i-1 c)
end
 
Output:
Simulating sof3(0:9) 100000 times:
    0 => 29994
    1 => 30026
    2 => 30173
    3 => 29590
    4 => 29967
    5 => 30104
    6 => 30185
    7 => 29761
    8 => 30147
    9 => 30053

Objective-C[edit]

Works with: Mac OS X version 10.6+

Uses blocks

#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;
}

Log:

<NSCountedSet: 0x100114120> (0 [29934], 9 [30211], 5 [29926], 1 [30067], 6 [30001], 2 [29972], 7 [30126], 3 [29944], 8 [29910], 4 [29909])

OCaml[edit]

let s_of_n_creator n =
let i = ref 0
and sample = ref [| |] in
fun item ->
incr i;
if !i <= n then sample := Array.append [| item |] !sample
else if Random.int !i < n then !sample.(Random.int n) <- item;
!sample
 
let test n items_set =
let s_of_n = s_of_n_creator n in
Array.fold_left (fun _ v -> s_of_n v) [| |] items_set
 
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.create num_items 0 in
for i = 1 to 100_000 do
let res = test n items_set in
Array.iter (fun j -> results.(j) <- succ results.(j)) res
done;
Array.iter (Printf.printf " %d") results;
print_newline()

Output:

 30051 29899 30249 30058 30012 29836 29998 29882 30148 29867

PARI/GP[edit]

This example is in need of improvement:
Does not return a function.
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
};

Output:

%1 = [30067, 30053, 29888, 30161, 30204, 29990, 30175, 29980, 29622, 29860]

Perl[edit]

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";
 
Sample output
30003 29923 30192 30164 29994 29976 29935 29860 30040 29913

Perl 6[edit]

sub s_of_n_creator($n) {
my @sample;
my $i = 0;
-> $item {
if ++$i <= $n {
push @sample, $item;
}
elsif $i.rand < $n {
@sample[$n.rand] = $item;
}
@sample;
}
}
 
my @items = 0..9;
my @bin;
 
for ^100000 {
my &s_of_n = s_of_n_creator(3);
my @sample;
for @items -> $item {
@sample = s_of_n($item);
}
for @sample -> $s {
@bin[$s]++;
}
}
say @bin;

Output:

29975 30028 30246 30056 30004 29983 29836 29967 29924 29981

PHP[edit]

Works with: PHP version 5.3+
<?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);
?>
Sample output
Array
(
    [3] => 30158
    [8] => 29859
    [9] => 29984
    [6] => 29937
    [7] => 30361
    [4] => 29994
    [5] => 29849
    [0] => 29724
    [1] => 29997
    [2] => 30137
)

PicoLisp[edit]

(de s_of_n_creator (@N)
(curry (@N (I . 0) (Res)) (Item)
(cond
((>= @N (inc 'I)) (push 'Res Item))
((>= @N (rand 1 I)) (set (nth Res (rand 1 @N)) Item)) )
Res ) )
 
(let Freq (need 10 0)
(do 100000
(let S_of_n (s_of_n_creator 3)
(for I (mapc S_of_n (0 1 2 3 4 5 6 7 8 9))
(inc (nth Freq (inc I))) ) ) )
Freq )

Output:

-> (30003 29941 29918 30255 29848 29875 30056 29839 30174 30091)

Python[edit]

Works with: Python version 3.x
from random import randrange
 
def s_of_n_creator(n):
sample, i = [], 0
def s_of_n(item):
nonlocal i
 
i += 1
if i <= n:
# Keep first n items
sample.append(item)
elif randrange(i) < n:
# Keep item
sample[randrange(n)] = item
return sample
return s_of_n
 
if __name__ == '__main__':
bin = [0]* 10
items = range(10)
print("Single run samples for n = 3:")
s_of_n = s_of_n_creator(3)
for item in items:
sample = s_of_n(item)
print(" Item: %i -> sample: %s" % (item, sample))
#
for trial in range(100000):
s_of_n = s_of_n_creator(3)
for item in items:
sample = s_of_n(item)
for s in sample:
bin[s] += 1
print("\nTest item frequencies for 100000 runs:\n ",
'\n '.join("%i:%i" % x for x in enumerate(bin)))
Sample output
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, 3]
  Item: 4 -> sample: [0, 1, 3]
  Item: 5 -> sample: [0, 1, 3]
  Item: 6 -> sample: [0, 1, 3]
  Item: 7 -> sample: [0, 3, 7]
  Item: 8 -> sample: [0, 3, 7]
  Item: 9 -> sample: [0, 3, 7]

Test item frequencies for 100000 runs:
  0:29983
  1:30240
  2:29779
  3:29921
  4:30224
  5:29967
  6:30036
  7:30050
  8:29758
  9:30042

Python Class based version[edit]

Only a slight change creates the following class-based implementation:

class S_of_n_creator():
def __init__(self, n):
self.n = n
self.i = 0
self.sample = []
 
def __call__(self, item):
self.i += 1
n, i, sample = self.n, self.i, self.sample
if i <= n:
# Keep first n items
sample.append(item)
elif randrange(i) < n:
# Keep item
sample[randrange(n)] = item
return sample

The above can be instantiated as follows after which s_of_n can be called in the same way as it is in the first example where it is a function instead of an instance.

s_of_n = S_of_n_creator(3)

Racket[edit]

#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)))

Output:

0 30117
1 29955
2 30020
3 29906
4 30146
5 29871
6 30045
7 30223
8 29940
9 29777

REXX[edit]

/*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=='' then trials=100000 /*Not specified? Then use the default.*/
if 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 gener=0 for 10
call s_of_n gener /*call s_of_n with a single decimal dig*/
end /*gener*/
 
do count=1 for size /*let's examine what SofN generated. */
_=!.count /*get a decimal digit from the Nth */
#._=#._+1 /* ··· item, and count it, of course.*/
end /*count*/
end /*trials*/
@='trials, and with size='
say "Using Knuth's algorithm S for" commas(trials) @ || commas(size)":"
say
do dig=0 to 9 /* [↓] display the frequency of a dig.*/
say left('',20) "frequency of the" dig 'digit is:' commas(#.dig)
end /*dig*/
exit /*stick a fork in it, we're all done. */
/*────────────────────────────────────────────────────────────────────────────*/
commas: procedure; parse arg _; n=_'.9'; #=123456789; b=verify(n,#,"M")
e=verify(n, #'0', , verify(n, #"0.", 'M')) - 4
do j=e to b by -3; _=insert(',',_,j); end /*j*/; return _
/*────────────────────────────────────────────────────────────────────────────*/
s_of_n: parse arg item; items=items+1 /*get "item", bump the items counter.*/
c=random(1, items) /* [↓] should replace a previous item?*/
if c>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). */

output   when using the default input of:   100000   2

Using Knuth's algorithm  S  for 100,000 trials, and with size=3:

                     frequency of the 0 digit is: 29,843
                     frequency of the 1 digit is: 30,083
                     frequency of the 2 digit is: 29,966
                     frequency of the 3 digit is: 30,006
                     frequency of the 4 digit is: 30,137
                     frequency of the 5 digit is: 29,833
                     frequency of the 6 digit is: 30,160
                     frequency of the 7 digit is: 30,182
                     frequency of the 8 digit is: 29,941
                     frequency of the 9 digit is: 29,849

Ruby[edit]

Using a closure

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]}"}

Example

0       29850
1       30015
2       29970
3       29789
4       29841
5       30075
6       30281
7       30374
8       29953
9       29852

Sidef[edit]

Translation of: Perl 6
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;
Output:
[30056, 29906, 30058, 29986, 30062, 29748, 29989, 29985, 30126, 30084]

Swift[edit]

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)
Output:
[30038, 29913, 30047, 30069, 30159, 30079, 29773, 29962, 30000, 29960]

Tcl[edit]

package require Tcl 8.6
 
oo::class create SofN {
variable items size count
constructor {n} {
set size $n
}
method item {item} {
if {[incr count] <= $size} {
lappend items $item
} elseif {rand()*$count < $size} {
lset items [expr {int($size * rand())}] $item
}
return $items
}
}
 
# Test code
for {set i 0} {$i < 100000} {incr i} {
set sOf3 [SofN new 3]
foreach digit {0 1 2 3 4 5 6 7 8 9} {
set digs [$sOf3 item $digit]
}
$sOf3 destroy
foreach digit $digs {
incr freq($digit)
}
}
parray freq
Sample output:
freq(0) = 29812
freq(1) = 30099
freq(2) = 29927
freq(3) = 30106
freq(4) = 30048
freq(5) = 29993
freq(6) = 29912
freq(7) = 30219
freq(8) = 30060
freq(9) = 29824

zkl[edit]

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())
}

One run:

s3:=s_of_n_creator(3);
[0..9].pump(List,s3,"copy").println();
Output:
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))

100,000 runs:

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();
Output:
L("10.00%","9.98%","10.00%","9.99%","10.00%","9.98%","10.01%","10.04%","9.98%","10.02%")