Print all subsets of given size of a set

Difficulty Level : Hard
Last Updated : 06 Jul, 2018

Generate all possible subset of size r of 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

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

This problem is same as 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 input array, and recur for two cases:

1) The element is included in current combination (We put the element in data[] and increment next available index in data[])
2) The element is excluded in current combination (We do not put the element and do not change index)

When number of elements in data[] become equal to r (size of a combination), we print it.

This method is mainly based on Pascal’s Identity, i.e. n_c_{_r} = n-1_c_{_r} + n-1_c_{_r-1}

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 temprary 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 cobination 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 functions 
int 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

// Java program to print all combination of size 
// r in an array of size n 
import java.io.*; 
  
class Permutation { 
  
    /* arr[]  ---> Input Array 
    data[] ---> Temporary array to store current combination 
    start & end ---> Staring 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 temprary 
        // 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

# Python 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 ---> Staring and Ending  
#                  indexes in arr[] 
# index ---> Current index in data[] 
# r ---> Size of a combination  
#        to be printed  
def 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 Code 
arr = [10, 20, 30, 40, 50] 
  
r = 3
n = len(arr) 
printcombination(arr, n, r) 
  
# This code is contributed 
# by Ambuj sahu 

C#

// C# program to print all combination 
// of size r in an array of size n 
using System; 
  
class GFG { 
  
    /* arr[] ---> Input Array 
    data[] ---> Temporary array to store 
    current combination start & end ---> 
    Staring 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 
        // temprary 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

<?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  
    // temprary 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[] */
function combinationUtil( $arr, $n, $r, $index, 
                    $data, $i) 
{ 
    // Current cobination is ready, print it 
    if ($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. 
?> 

Output:

Refer below post for more solutions and ideas to handle duplicates in input array.
Print all possible combinations of r elements in a given array of size n.

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Related Articles

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python3

C#

PHP