<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:
    bool solve(vector<int>& matchsticks, int idx, int n, vector<int>& sides) {
        if (idx == n) return true;
        bool ans = false;
        int a = matchsticks[idx];
        for(int i = 0; i < 4; i++) {
            if (sides[i] >= a) {
                sides[i] -= a;
                ans = ans || solve(matchsticks, idx + 1, n, sides);
                sides[i] += a;
            }
        }
        return ans;
    }
    bool makesquare(vector<int>& matchsticks) {
        int m = 0, n = matchsticks.size();
        if (n < 4) return false;
        for(int a: matchsticks) m += a;
        if (m % 4 != 0) return false;
        sort(matchsticks.begin(), matchsticks.end(), greater<>());
        int l = m / 4;
        vector<int> sides(4, l);
        return solve(matchsticks, 0, n, sides);
    }
};
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