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
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 <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:
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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