You are given a set of positive integers. You need to find whether or not, the set can be divided into to partitions of equal sum.

**Sample Input: **{ 7, 3, 1, 5, 4, 8 }.**Expected Output: **True.**Explanation: **One possible solution is that the set can be divided into two subsets { 7, 3, 4} and { 1, 5, 8 } which has equal sum 14. There might exist other solutions as well.

**Algorithm:**

This problem is a special case of the ** subset sum problem** which is a special case of

*0-1 knapsack problem.*- If the total sum of the array is odd, then the array cannot be divided into two partitions of equal sum.
- If the total sum is even, then we can apply the same technique as used in subset sum problem with given sum = (total_sum) / 2
- Please refer to the
for further details.*subset sum problem*

/* Author => Raunak Jain */ #include <bits/stdc++.h> using namespace std; int helper(vector<int> nums, int sum){ int n = nums.size(); vector<vector<bool>>dp(n+1, vector<bool>(sum+1, false)); for(int i=0; i<=n; i++){ dp[i][0]=true; } for(int i=1; i<=n; i++){ for(int j=1; j<=sum; j++){ if(j<nums[i-1]){ dp[i][j]=dp[i-1][j]; }else{ dp[i][j]=dp[i-1][j] || dp[i-1][j-nums[i-1]]; } } } return dp[n][sum]; } int main(){ int sum=0; vector<int> nums = { 7, 3, 1, 5, 4, 8 }; for(auto i:nums){ sum+=i; } if(!(sum&1) && helper(nums, sum/2)){ cout<<"True"; }else{ cout<<"False"; } return 0; }

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