Print all subsets of given size of a set

24 Nov, 2021
Generate all possible subsets of size r of the given array with distinct elements. 
Examples:  
Input  : arr[] = {1, 2, 3, 4}
         r = 2
Output :  1 2
          1 3
          1 4
          2 3
          2 4
          3 4

Input  : arr[] = {10, 20, 30, 40, 50}
         r = 3
Output : 10 20 30 
         10 20 40 
         10 20 50 
         10 30 40 
         10 30 50 
         10 40 50 
         20 30 40 
         20 30 50 
         20 40 50 
         30 40 50 
This problem is the same Print all possible combinations of r elements in a given array of size n.The idea here is similar to Subset Sum Problem. We, one by one, consider every element of the input array, and recur for two cases:1) The element is included in the current combination (We put the element in data[] and increase the next available index in data[]) 2) The element is excluded in the current combination (We do not put the element in and do not change the index)When the number of elements in data[] becomes equal to r (size of a combination), we print it.This method is mainly based on Pascal’s Identity, i.e. ncr = n-1cr + n-1cr-1
C++
C
Java
Python3
C#
PHP
Javascript
// C++ Program to print all combination of size r in// an array of size n#include <iostream>using namespace std; void combinationUtil(int arr[], int n, int r,                     int index, int data[], int i);  // The main function that prints all combinations of// size r in arr[] of size n. This function mainly// uses combinationUtil()void printCombination(int arr[], int n, int r){       // A temporary array to store all combination    // one by one    int data[r];      // Print all combination using temporary array 'data[]'    combinationUtil(arr, n, r, 0, data, 0);}  /* arr[]  ---> Input Array   n      ---> Size of input array   r      ---> Size of a combination to be printed   index  ---> Current index in data[]   data[] ---> Temporary array to store current combination   i      ---> index of current element in arr[]     */void combinationUtil(int arr[], int n, int r, int index,                     int data[], int i){    // Current combination is ready, print it    if (index == r) {        for (int j = 0; j < r; j++)            cout <<" "<< data[j];        cout <<"\n";        return;    }      // When no more elements are there to put in data[]    if (i >= n)        return;      // current is included, put next at next location    data[index] = arr[i];    combinationUtil(arr, n, r, index + 1, data, i + 1);      // current is excluded, replace it with next    // (Note that i+1 is passed, but index is not    // changed)    combinationUtil(arr, n, r, index, data, i + 1);}  // Driver program to test above functionsint main(){    int arr[] = { 10, 20, 30, 40, 50 };    int r = 3;    int n = sizeof(arr) / sizeof(arr[0]);    printCombination(arr, n, r);    return 0;} // This code is contributed by shivanisinghss2110
// C++ Program to print all combination of size r in// an array of size n#include <stdio.h>void combinationUtil(int arr[], int n, int r,                     int index, int data[], int i); // The main function that prints all combinations of// size r in arr[] of size n. This function mainly// uses combinationUtil()void printCombination(int arr[], int n, int r){    // A temporary array to store all combination    // one by one    int data[r];     // Print all combination using temporary array 'data[]'    combinationUtil(arr, n, r, 0, data, 0);} /* arr[]  ---> Input Array   n      ---> Size of input array   r      ---> Size of a combination to be printed   index  ---> Current index in data[]   data[] ---> Temporary array to store current combination   i      ---> index of current element in arr[]     */void combinationUtil(int arr[], int n, int r, int index,                     int data[], int i){    // Current combination is ready, print it    if (index == r) {        for (int j = 0; j < r; j++)            printf("%d ", data[j]);        printf("\n");        return;    }     // When no more elements are there to put in data[]    if (i >= n)        return;     // current is included, put next at next location    data[index] = arr[i];    combinationUtil(arr, n, r, index + 1, data, i + 1);     // current is excluded, replace it with next    // (Note that i+1 is passed, but index is not    // changed)    combinationUtil(arr, n, r, index, data, i + 1);} // Driver program to test above functionsint main(){    int arr[] = { 10, 20, 30, 40, 50 };    int r = 3;    int n = sizeof(arr) / sizeof(arr[0]);    printCombination(arr, n, r);    return 0;}
// Java program to print all combination of size// r in an array of size nimport java.io.*; class Permutation {     /* arr[]  ---> Input Array    data[] ---> Temporary array to store current combination    start & end ---> Starting and Ending indexes in arr[]    index  ---> Current index in data[]    r ---> Size of a combination to be printed */    static void combinationUtil(int arr[], int n, int r,                          int index, int data[], int i)    {        // Current combination is ready to be printed,        // print it        if (index == r) {            for (int j = 0; j < r; j++)                System.out.print(data[j] + " ");            System.out.println("");            return;        }         // When no more elements are there to put in data[]        if (i >= n)            return;         // current is included, put next at next        // location        data[index] = arr[i];        combinationUtil(arr, n, r, index + 1,                               data, i + 1);         // current is excluded, replace it with        // next (Note that i+1 is passed, but        // index is not changed)        combinationUtil(arr, n, r, index, data, i + 1);    }     // The main function that prints all combinations    // of size r in arr[] of size n. This function    // mainly uses combinationUtil()    static void printCombination(int arr[], int n, int r)    {        // A temporary array to store all combination        // one by one        int data[] = new int[r];         // Print all combination using temporary        // array 'data[]'        combinationUtil(arr, n, r, 0, data, 0);    }     /* Driver function to check for above function */    public static void main(String[] args)    {        int arr[] = { 10, 20, 30, 40, 50 };        int r = 3;        int n = arr.length;        printCombination(arr, n, r);    }}/* This code is contributed by Devesh Agrawal */
# Python3 program to print all# subset combination of n# element in given set of r element . # arr[] ---> Input Array# data[] ---> Temporary array to#             store current combination# start & end ---> Starting and Ending#                  indexes in arr[]# index ---> Current index in data[]# r ---> Size of a combination#        to be printeddef combinationUtil(arr, n, r,                    index, data, i):    # Current combination is    # ready to be printed,    # print it    if(index == r):        for j in range(r):            print(data[j], end = " ")        print(" ")        return     # When no more elements    # are there to put in data[]    if(i >= n):        return     # current is included,    # put next at next    # location    data[index] = arr[i]    combinationUtil(arr, n, r,                    index + 1, data, i + 1)         # current is excluded,    # replace it with    # next (Note that i+1    # is passed, but index    # is not changed)    combinationUtil(arr, n, r, index,                    data, i + 1)  # The main function that# prints all combinations# of size r in arr[] of# size n. This function# mainly uses combinationUtil()def printcombination(arr, n, r):     # A temporary array to    # store all combination    # one by one    data = list(range(r))         # Print all combination    # using temporary    # array 'data[]'    combinationUtil(arr, n, r,                    0, data, 0)  # Driver Codearr = [10, 20, 30, 40, 50] r = 3n = len(arr)printcombination(arr, n, r) # This code is contributed# by Ambuj sahu
// C# program to print all combination// of size r in an array of size nusing System; class GFG {     /* arr[] ---> Input Array    data[] ---> Temporary array to store    current combination start & end --->    Starting and Ending indexes in arr[]    index ---> Current index in data[]    r ---> Size of a combination to be    printed */    static void combinationUtil(int []arr,                  int n, int r, int index,                          int []data, int i)    {                 // Current combination is ready to        // be printed, print it        if (index == r)        {            for (int j = 0; j < r; j++)                Console.Write(data[j] + " ");                             Console.WriteLine("");                         return;        }         // When no more elements are there        // to put in data[]        if (i >= n)            return;         // current is included, put next        // at next location        data[index] = arr[i];        combinationUtil(arr, n, r, index + 1,                                data, i + 1);         // current is excluded, replace        // it with next (Note that i+1        // is passed, but index is not        // changed)        combinationUtil(arr, n, r, index,                                data, i + 1);    }     // The main function that prints all    // combinations of size r in arr[] of    // size n. This function mainly uses    // combinationUtil()    static void printCombination(int []arr,                                int n, int r)    {                 // A temporary array to store all        // combination one by one        int []data = new int[r];         // Print all combination using        // temporary array 'data[]'        combinationUtil(arr, n, r, 0, data, 0);    }     /* Driver function to check for    above function */    public static void Main()    {        int []arr = { 10, 20, 30, 40, 50 };        int r = 3;        int n = arr.Length;                 printCombination(arr, n, r);    }} // This code is contributed by vt_m.
<?php// Program to print all combination of// size r in an array of size n // The main function that prints all// combinations of size r in arr[] of// size n. This function mainly uses// combinationUtil()function printCombination( $arr, $n, $r){    // A temporary array to store all    // combination one by one    $data = array();     // Print all combination using    // temporary array 'data[]'    combinationUtil($arr, $n, $r, 0, $data, 0);} /* arr[] ---> Input Arrayn ---> Size of input arrayr ---> Size of a combination to be printedindex ---> Current index in data[]data[] ---> Temporary array to storecurrent combinationi ---> index of current element in arr[] */function combinationUtil( $arr, $n, $r, $index,                    $data, $i){    // Current combination is ready, print it    if ($index == $r) {        for ( $j = 0; $j < $r; $j++)            echo $data[$j]," ";        echo "\n";        return;    }     // When no more elements are there to    // put in data[]    if ($i >= $n)        return;     // current is included, put next at    // next location    $data[$index] = $arr[$i];    combinationUtil($arr, $n, $r, $index + 1,                              $data, $i + 1);     // current is excluded, replace it with    // next (Note that i+1 is passed, but    // index is not changed)    combinationUtil($arr, $n, $r, $index,                            $data, $i + 1);} // Driver program to test above functions    $arr = array( 10, 20, 30, 40, 50 );    $r = 3;    $n = count($arr);    printCombination($arr, $n, $r); // This code is contributed by anuj_67.?>
<script>    // Javascript program to print all combination    // of size r in an array of size n         /* arr[] ---> Input Array    data[] ---> Temporary array to store    current combination start & end --->    Starting and Ending indexes in arr[]    index ---> Current index in data[]    r ---> Size of a combination to be    printed */    function combinationUtil(arr, n, r, index, data, i)    {                  // Current combination is ready to        // be printed, print it        if (index == r)        {            for (let j = 0; j < r; j++)                document.write(data[j] + " ");                              document.write("</br>");                          return;        }          // When no more elements are there        // to put in data[]        if (i >= n)            return;          // current is included, put next        // at next location        data[index] = arr[i];        combinationUtil(arr, n, r, index + 1,                                data, i + 1);          // current is excluded, replace        // it with next (Note that i+1        // is passed, but index is not        // changed)        combinationUtil(arr, n, r, index,                                data, i + 1);    }      // The main function that prints all    // combinations of size r in arr[] of    // size n. This function mainly uses    // combinationUtil()    function printCombination(arr, n, r)    {                  // A temporary array to store all        // combination one by one        let data = new Array(r);        data.fill(0);          // Print all combination using        // temporary array 'data[]'        combinationUtil(arr, n, r, 0, data, 0);    }         let arr = [ 10, 20, 30, 40, 50 ];    let r = 3;    let n = arr.length;     printCombination(arr, n, r);     </script>
Output: 
10 20 30 
10 20 40 
10 20 50 
10 30 40 
10 30 50 
10 40 50 
20 30 40 
20 30 50 
20 40 50 
30 40 50 
Refer to the post below for more solutions and ideas to handle duplicates in the input array. Print all possible combinations of r elements in a given array of size n.
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