<p>You are given an integer array <code>matchsticks</code> where <code>matchsticks[i]</code> is the length of the <code>i<sup>th</sup></code> matchstick. You want to use <strong>all the matchsticks</strong> to make one square. You <strong>should not break</strong> any stick, but you can link them up, and each matchstick must be used <strong>exactly one time</strong>.</p>

<p>Return <code>true</code> if you can make this square and <code>false</code> otherwise.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/09/matchsticks1-grid.jpg" style="width: 253px; height: 253px;" />
<pre>
<strong>Input:</strong> matchsticks = [1,1,2,2,2]
<strong>Output:</strong> true
<strong>Explanation:</strong> You can form a square with length 2, one side of the square came two sticks with length 1.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> matchsticks = [3,3,3,3,4]
<strong>Output:</strong> false
<strong>Explanation:</strong> You cannot find a way to form a square with all the matchsticks.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= matchsticks.length &lt;= 15</code></li>
	<li><code>1 &lt;= matchsticks[i] &lt;= 10<sup>8</sup></code></li>
</ul>

class Solution {
public:

   vector<vector<int>>dp;
   bool solve(vector<int>&nums, int k, int currSum,int mask,int target)
   {   
       if(k<0 || currSum<0)return false;
       if(currSum == 0)
       {   
           return solve(nums,k-1,target,mask,target);
       }
       if(mask == (1<<nums.size())-1 && k==0)return true;
       
       if(dp[k][mask] != -1)return dp[k][mask];
       
       bool ans = false;
       for(int i=0;i<nums.size();i++)
       {
           if((mask & (1<<i)) == 0)
           {
               ans = ans || solve(nums,k,currSum-nums[i],mask|(1<<i),target);
           }
       }

       return dp[k][mask]=ans;
    
   }


    bool makesquare(vector<int>& nums) {
        
        int  sum=0;
        for(int i =0;i<nums.size();i++)
        {
            sum+= (nums[i]);
        }
        cout<<"Sum:"<<sum<<endl;
        if(sum%4)return false;

        int target = sum/4;
        cout<<"Target"<<target<<endl;
        int n = nums.size();
        dp.resize(5,vector<int>(1<<(n+1), -1));
        return solve(nums,4,target,0,target);
    }
};
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