<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:
    struct SetHash {
        std::size_t operator()(const std::set<int>& s) const {
            std::size_t hash = 0;
            for (const int& i : s) {
                hash ^= std::hash<int>{}(i) + 0x9e3779b9 + (hash << 6) + (hash >> 2);
            }
            return hash;
        }
    };

    bool recur(int i, vector<int>& matchsticks, int a, int b, int c, int d, map<set<int>, bool>& dp) {
        if (a < 0 || b < 0 || c < 0 || d < 0) return false;
        if (i >= matchsticks.size()) {
            // cout << a << " " << b << " " << c << " " << d << " : " << (a == b && b == c && c == d) << endl;
            return (a == 0 && a == b && b == c && c == d);
        }
        int count = 0;
        if (a == 0) count++;
        if (b == 0) count++;
        if (c == 0) count++;
        if (d == 0) count++;
        if (count >= 3) return true;
        
        if (dp.find({a, b, c, d}) != dp.end()) return dp[{a, b, c, d}];
        dp[{a, b, c, d}] = {
            recur(i+1, matchsticks, a-matchsticks[i], b, c, d, dp) ||
            recur(i+1, matchsticks, a, b-matchsticks[i], c, d, dp) || 
            recur(i+1, matchsticks, a, b, c-matchsticks[i], d, dp) ||
            recur(i+1, matchsticks, a, b, c, d-matchsticks[i], dp)
        };
        // cout << a << " " << b << " " << c << " " << d << " = " << dp[{a, b, c, d}] << endl;
        return dp[{a, b, c, d}];
    }
    bool makesquare(vector<int>& matchsticks) {
        map<set<int>, bool> dp;
        sort(matchsticks.begin(), matchsticks.end(), std::greater<int>());
        int s = std::accumulate(matchsticks.begin(), matchsticks.end(), 0);
        if (s % 4 != 0) return false;
        return recur(0, matchsticks, s/4, s/4, s/4, s/4, dp);
    }
};
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