Perfect Sum Problem
Given an array arr[] of integers and an integer K, the task is to print all subsets of the given array with the sum equal to the given target K.
Examples:
Input: arr[] = {5, 10, 12, 13, 15, 18}, K = 30
Output: {12, 18}, {5, 12, 13}, {5, 10, 15}
Explanation:
Subsets with sum 30 are:
12 + 18 = 30
5 + 12 + 13 = 30
5 + 10 + 15 = 30
Input: arr[] = {1, 2, 3, 4}, K = 5
Output: {2, 3}, {1, 4}
Approach: The idea is to find out all the subsets using the Power Set concept. For every set, check if the sum of the set is equal to K or not. If it is equal, then the set is printed.
Below is the implementation of the above approach:
C++
// C++ implementation of the above approach#include <bits/stdc++.h> using namespace std; // Function to print the subsets whose// sum is equal to the given target Kvoid sumSubsets(vector<int> set, int n, int target){ // Create the new array with size // equal to array set[] to create // binary array as per n(decimal number) int x[set.size()]; int j = set.size() - 1; // Convert the array into binary array while (n > 0) { x[j] = n % 2; n = n / 2; j--; } int sum = 0; // Calculate the sum of this subset for (int i = 0; i < set.size(); i++) if (x[i] == 1) sum = sum + set[i]; // Check whether sum is equal to target // if it is equal, then print the subset if (sum == target) { cout<<("{"); for (int i = 0; i < set.size(); i++) if (x[i] == 1) cout << set[i] << ", "; cout << ("}, "); }} // Function to find the subsets with sum Kvoid findSubsets(vector<int> arr, int K){ // Calculate the total no. of subsets int x = pow(2, arr.size()); // Run loop till total no. of subsets // and call the function for each subset for (int i = 1; i < x; i++) sumSubsets(arr, i, K);} // Driver codeint main(){ vector<int> arr = { 5, 10, 12, 13, 15, 18 }; int K = 30; findSubsets(arr, K); return 0;} // This code is contributed by mohit kumar 29 |
Java
// Java implementation of the above approachimport java.util.*; class GFG { // Function to print the subsets whose // sum is equal to the given target K public static void sumSubsets( int set[], int n, int target) { // Create the new array with size // equal to array set[] to create // binary array as per n(decimal number) int x[] = new int[set.length]; int j = set.length - 1; // Convert the array into binary array while (n > 0) { x[j] = n % 2; n = n / 2; j--; } int sum = 0; // Calculate the sum of this subset for (int i = 0; i < set.length; i++) if (x[i] == 1) sum = sum + set[i]; // Check whether sum is equal to target // if it is equal, then print the subset if (sum == target) { System.out.print("{"); for (int i = 0; i < set.length; i++) if (x[i] == 1) System.out.print(set[i] + ", "); System.out.print("}, "); } } // Function to find the subsets with sum K public static void findSubsets(int[] arr, int K) { // Calculate the total no. of subsets int x = (int)Math.pow(2, arr.length); // Run loop till total no. of subsets // and call the function for each subset for (int i = 1; i < x; i++) sumSubsets(arr, i, K); } // Driver code public static void main(String args[]) { int arr[] = { 5, 10, 12, 13, 15, 18 }; int K = 30; findSubsets(arr, K); }} |
Python3
# Python3 implementation of the above approach # Function to print the subsets whose # sum is equal to the given target K def sumSubsets(sets, n, target) : # Create the new array with size # equal to array set[] to create # binary array as per n(decimal number) x = [0]*len(sets); j = len(sets) - 1; # Convert the array into binary array while (n > 0) : x[j] = n % 2; n = n // 2; j -= 1; sum = 0; # Calculate the sum of this subset for i in range(len(sets)) : if (x[i] == 1) : sum += sets[i]; # Check whether sum is equal to target # if it is equal, then print the subset if (sum == target) : print("{",end=""); for i in range(len(sets)) : if (x[i] == 1) : print(sets[i],end= ", "); print("}, ",end=""); # Function to find the subsets with sum K def findSubsets(arr, K) : # Calculate the total no. of subsets x = pow(2, len(arr)); # Run loop till total no. of subsets # and call the function for each subset for i in range(1, x) : sumSubsets(arr, i, K); # Driver code if __name__ == "__main__" : arr = [ 5, 10, 12, 13, 15, 18 ]; K = 30; findSubsets(arr, K); # This code is contributed by Yash_R |
C#
// C# implementation of the above approachusing System; class GFG { // Function to print the subsets whose // sum is equal to the given target K public static void sumSubsets( int []set, int n, int target) { // Create the new array with size // equal to array set[] to create // binary array as per n(decimal number) int []x = new int[set.Length]; int j = set.Length - 1; // Convert the array into binary array while (n > 0) { x[j] = n % 2; n = n / 2; j--; } int sum = 0; // Calculate the sum of this subset for (int i = 0; i < set.Length; i++) if (x[i] == 1) sum = sum + set[i]; // Check whether sum is equal to target // if it is equal, then print the subset if (sum == target) { Console.Write("{"); for (int i = 0; i < set.Length; i++) if (x[i] == 1) Console.Write(set[i] + ", "); Console.Write("}, "); } } // Function to find the subsets with sum K public static void findSubsets(int[] arr, int K) { // Calculate the total no. of subsets int x = (int)Math.Pow(2, arr.Length); // Run loop till total no. of subsets // and call the function for each subset for (int i = 1; i < x; i++) sumSubsets(arr, i, K); } // Driver code public static void Main(String []args) { int []arr = { 5, 10, 12, 13, 15, 18 }; int K = 30; findSubsets(arr, K); }} // This code is contributed by 29AjayKumar |
Output:
{12, 18, }, {5, 12, 13, }, {5, 10, 15, },
Time Complexity: 2N
Efficient Approach:
This problem can also be solved using Dynamic Programming. Refer to this article.
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