**Reservoir sampling** is a randomized algorithm that is used to select $k$ out of $n$ samples; $n$ is usually very large or unknown. For example, reservoir sampling can be used to obtain a sample of size $k$ from a population of people with brown hair. This algorithm takes $O(n)$ to select $k$ elements with uniform probability.

# Algorithm

1. Copy the first $k$ elements from the input array to the output array.

2. Iterate from $k$ to $n-1$ (both inclusive). In each iteration $j$:

   2.1 Generate a random number $num$ from 0 to $j$.

   2.2 If $num$ is less than $k$, replace the element at index $num$ in the output array with the item at index $j$ in the input array.

# Code

// Including dependancies
#include <iostream>
#include <stdlib.h>
#include <time.h>
using namespace std;

int main() {
  // Defining the parameters
  int k = 4;
  int n = 8;
  // The array to be sampled
  int input[] = {1, 7, 4, 8, 2, 6, 5, 9};
  int output[k];
  // Getting a random seed everytime
  srand (time(NULL));
  int i;
  // Initializing the output array to the first k elements
  // of the input array.
  for(i = 0; i < k; i++){
    output[i] = input[i];
  }
  int j;
  // Iterating over k to n-1 
  for(j = i; j < n; j++){
    // Generating a random number from 0 to j
    int index = rand() % (j + 1);
    // Replacing an element in the  output with an element
    // in the input if the randomly generated number is less
    // than k.
    if(index < k){
      output[index] = input[j];
    }
  }
  cout<<"Input array:"<<endl;
  for( i = 0; i < n; i++){
    cout<<input[i]<<" ";
  }
  cout<<endl;
  cout<<"Output array:"<<endl;
  for(i = 0; i < k; i++){
    cout<<output[i]<<" ";
  }
  cout<<endl;
  return 0;
}

# Including dependancies
import random
# Defining the parameters
n = 8
k = 4
# The array to be sampled
input_array = [1, 7, 4, 8, 2, 6, 5, 9]
output = []
# Initializing the output array to the first k elements
# of the input array
for i in range(k):
  output.append(input_array[i])
# Iterating over k to n-1
for j in range(k,n):
  # Generating a random number
  index = random.randint(0, j)
  # Replacing an element in the  output with an element
  # in the input if the randomly generated number is less
  # than k.
  if index < k:
    output[index] = input_array[j]
print("Input array:")
print(input_array)
print("Output array:")
print(output)

Python3

// Importing dependancies
import java.util.Random;
import java.util.Arrays; 
class HelloWorld {
    public static void main( String args[] ) {
      // Defining the parameters
      int n = 8;
      int k = 4;
      // The array to be smaples
      int input[] = {1, 7, 4, 8, 2, 6, 5, 9};
      int output[] = new int[k];
      int i;
      // Initialzing the output array to the first k
      // elements of the input array
      for(i = 0; i < k; i++){
        output[i] = input[i];
      }
      int j;
      Random num = new Random();
      // Iterating from k to n-1
      for(j = i; j < n; j++){
        // Generating a randon number from 0 to j
        int index = num.nextInt(j + 1);
        // Replacing an element in the  output with an element
        // in the input if the randomly generated number is less
        // than k.
        if(index < k){
          output[index] = input[j];
        }
      }
      System.out.println("Input array:");
      System.out.println(Arrays.toString(input));
      System.out.println("Output array:");
      System.out.println(Arrays.toString(output));
        
    }
}

Java

What is reservoir sampling?

Reservoir sampling selects k elements from n samples using a randomized algorithm in O(n) time.