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++

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// 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 K
void 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 K
void 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 code
int 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

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Java














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// Java implementation of the above approach 


import 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); 


    } 


} 



















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Python3














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# 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 



















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C#














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// C# implementation of the above approach 


using 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 



















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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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