<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>& matc) {
        sort(matc.begin(), matc.end(), greater<int>());  
        int summ = 0;
        for (int i = 0; i < matc.size(); i++) {
            summ += matc[i];
        }
        if (summ % 4 != 0)
            return false;

        int sle = summ / 4;
        vector<vector<vector<int>>> dp(matc.size() + 1);
        dp[0].push_back({0, 0, 0, 0});

        for (int i = 0; i < matc.size(); i++) {
            set<vector<int>> see;
            for (int j = 0; j < dp[i].size(); j++) { 
                for (int k = 0; k < 4; k++) {
                    vector<int> r(dp[i][j]);
                    r[k] += matc[i];
                    if (r[k] > sle)
                        continue;  
                    sort(r.begin(), r.end());
                    see.insert(r);
                }
            }
            dp[i + 1].assign(see.begin(), see.end());
        }
        // for(int i=0;i<dp[matc.size()].size();i++){
        //     for(int j=0;j<4;j++){
        //         cout<<dp[matc.size()][i][j]<<", ";
        //     }
        // }
        // cout<<endl;
        for (int i = 0; i < dp[matc.size()].size(); i++) {
            bool valid = true;
            for (int j = 0; j < 4; j++) {
                if (dp[matc.size()][i][j] != sle) {
                    valid = false;
                    break;
                }
            }
            if (valid)
                return true;
        }
        return false;
    }
};
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