<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 makesquare(vector<int>& matchsticks) {
        int len = 0;
        int sum = 0;
        sort(matchsticks.begin(), matchsticks.end(), greater<int>());
        for(int& stick: matchsticks)
        {
            sum += stick;
        }
        len = sum / 4;
        if (len * 4 != sum)
        {
            return false;
        }
        for(int stick: matchsticks)
        {
            if (stick > len)
            {
                return false;
            }
        }
        // cout << "yyyyyyyy" << endl;
        vector<int> edges(4, 0);
        unordered_set<string> vis;
        function<string(vector<int>)> hash = [&](vector<int> egs) -> string {
            sort(egs.begin(), egs.end());
            return to_string(egs[0]) + "_" + to_string(egs[1]) + "_" + to_string(egs[2]) + "_" + to_string(egs[3]);
        };
        function<bool(int)> dfs = [&](int pos) -> bool {
            for(int i = 0; i < 4; i++)
                {
                    if (edges[i] > len)
                    {
                        return false;
                    }
                }
            if (pos == matchsticks.size())
            {
                for(int i = 0; i < 3; i++)
                {
                    if (edges[i] != len)
                    {
                        return false;
                    }
                }
                return true;
            }
            for(int i = 0; i < 4; i++)
            {
                edges[i] += matchsticks[pos];
                auto h = hash(edges);
                // cout << h << endl;
                if (vis.find(h) != vis.end())
                {
                    edges[i] -= matchsticks[pos];
                    // return false;
                    continue;
                }
                if (dfs(pos + 1))
                {
                    return true;
                }
                vis.insert(h);
                edges[i] -= matchsticks[pos];
            }
            return false;
        };
        return dfs(0);
    }
};
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