<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:
    int side;
    vector<int> dp;
    bool solve(vector<int> &a, int k, int curr, int mask, int i){
        if(k == 1) return true;
        if(i>=a.size()) return false;

        if(dp[mask] != -1) return false;

        if(curr == side) return dp[mask] = solve(a, k-1, 0, mask, 0);
        
        for(int j = i; j<a.size(); j++){
            if(!(mask&(1<<j)) && a[j]+curr<=side && solve(a, k, a[j]+curr, mask | (1<<j), j+1)) return dp[mask] = true;
        }
        return dp[mask] = false;
    }

    bool makesquare(vector<int>& a) {
        int sum = accumulate(a.begin(), a.end(), 0);
        side = sum/4;
        if(sum%4 != 0) return false;
        dp.resize(1<<(a.size()+1), -1);
        return solve(a, 4, 0, 0, 0);
    }
};
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