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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