Print all subsets of given size of a set

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. ncr = n-1cr + n-1cr-1

C++

 // Program to print all combination of size r in // an array of size n #include 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);     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

 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:

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 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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Improved By : vt_m, AmbujSahu

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