Print all subsets of given size of a set

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. n_cr = n-1_cr + n-1_cr-1

Implementation:

C++

// 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 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;
}

// This code is contributed by shivanisinghss2110

C

// 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 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 ---> 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

# 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 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 --->
    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

<?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 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, $i)
{
    // Current combination is ready, print it
    if ($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.
?>

Javascript

<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

Time complexity of this algorithm is O(n*r). The outer loop runs n times and the inner loop runs r times.
Auxiliary Space: O(r), the space complexity is O(r) because we are creating a temporary array of size r and storing the combinations 
in it.

Approach 2: Using DP

The given program generates combinations of size r from an array of size n using a recursive approach. It does not use dynamic programming (DP) explicitly. However, dynamic programming can be applied to optimize the solution by avoiding redundant computations.

To implement a DP approach, we can use a 2D table to store the intermediate results and avoid recomputing the same combinations. Here’s an updated version of the program that incorporates dynamic programming:

C++

#include <iostream>
#include <vector>
using namespace std;

// Function to print all combinations of size r
// using a dynamic programming approach
void printCombination(int arr[], int n, int r)
{
    vector<vector<int>> dp(n + 1, vector<int>(r + 1, 0));

    // Calculate the combinations using dynamic programming
    for (int i = 0; i <= n; i++) {
        for (int j = 0; j <= min(i, r); j++) {
            if (j == 0 || j == i)
                dp[i][j] = 1;
            else
                dp[i][j] = dp[i - 1][j - 1] + dp[i - 1][j];
        }
    }

    // Print the combinations
    for (int i = 0; i < dp[n].size(); i++) {
        if (dp[n][i] == 0)
            break;
        for (int j = 0; j < dp[n][i]; j++) {
            cout << arr[i] << " ";
        }
        cout << endl;
    }
}

// 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;
}

Output

10 
20 20 20 20 20 
30 30 30 30 30 30 30 30 30 30 
40 40 40 40 40 40 40 40 40 40 

Time complexity of this algorithm is O(n*r).The outer loop runs n times and the inner loop runs r times.

Auxiliary Space: O(n*r).

Another Approach(using BitMasking):

Follow the below steps to solve the above problem:

1) Generate all possible binary numbers with a length equal to the number of elements in the set. Each binary number will represent a potential subset.
2) Iterate through each binary number from 0 to 2^N – 1, where N is the number of elements in the set. This represents all possible subsets of the set.
3) For each binary number, check the number of set bits(1s). If the count of set bits is equal to the desired subset size, consider it as a valid subset.
4) To extract the elements of the subset, iterate through the bits of the binary number. If a bit is set (1), include the corresponding element from the set in the subset.
5) Print the desired output.

Below is the implementation of above approach:

C++

#include <bits/stdc++.h>
using namespace std;

void printSubset(int arr[], int subset[], int r) {
    for (int i = 0; i < r; i++)
        cout << subset[i] << " ";
    cout << endl;
}

void printCombination(int arr[], int n, int r) {
    int totalSubsets = 1 << n;  // Total number of subsets is 2^n
    for (int bitmask = 0; bitmask < totalSubsets; bitmask++) {
        // Count the number of set bits in the bitmask
        int count = 0;
        int temp = bitmask;
        while (temp > 0) {
            count += temp & 1;
            temp >>= 1;
        }

        if (count == r) {
            int subset[r];
            int index = 0;
            for (int i = 0; i < n; i++) {
                if (bitmask & (1 << i))
                    subset[index++] = arr[i];
            }
            printSubset(arr, subset, r);
        }
    }
}

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;
}
// This code is contributed by Yash Agarwal(yashagarwal2852002)

Output

10 20 30 
10 20 40 
10 30 40 
20 30 40 
10 20 50 
10 30 50 
20 30 50 
10 40 50 
20 40 50 
30 40 50 

Time Complexity: O(2^n), where n is the number of elements in the given array.

Auxiliary Space: O(n+r)

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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