<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<int> dp;
    bool rec(int submask , vector<int> & matchsticks , int req){
        int n = matchsticks.size();
        if(submask == (1 << n) - 1){
            return true;
        }
        if(dp[submask] != -1){
            return dp[submask];
        }
        for(int i = 0 ; i < (1 << n) ; i++){
            if((submask & (i)) != submask){
                continue;
            }
            else{
                int sum = 0;
                for(int j = 0 ; j < n ; j++){
                    if(((1 << j) & submask) == 0){
                        if(((1 << j) & i) != 0){
                            sum += matchsticks[j];
                        }
                    }
                }
                if(sum == req){
                    dp[submask] = rec(i , matchsticks , req);
                    if(dp[submask] == 1){
                        return true;
                    }
                }
            }    
        }
        dp[submask] = 0;
        return false;
    }
    bool makesquare(vector<int>& matchsticks) {
        
        int n = matchsticks.size();
        int sum = 0;
        for(int i = 0 ; i < n ; i++){
            sum += matchsticks[i];
        }
        if(sum % 4 != 0){
            return false;
        }
        int req = sum/4;
        int num = (1 << 15) + 1;
        dp = vector<int>(num , -1);
        bool ans = rec(0 , matchsticks , req);
        return ans;
    }
};
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