<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 {
    vector<vector<int>> dp;
    bool check(int side, vector<int>& m, int mask, int curr, int count) {
        if (count == 4) {
            return true;
        }

        if (dp[count][mask] != -1) {
            return dp[count][mask];
        }

        bool ans = false;
        for (int i = 0; i < m.size(); i++) {
            int cmask = 1 << i;
            if ((cmask & mask) == 0) {
                if (curr + m[i] == side) {
                    ans = ans || check(side, m, cmask | mask, 0, count + 1);
                } else if (curr + m[i] < side) {
                    ans =
                        ans || check(side, m, cmask | mask, curr + m[i], count);
                }
            }
        }

        return dp[count][mask] = ans;
    }

public:
    bool makesquare(vector<int>& matchsticks) {
        int perm = 0;
        unordered_map<int, int> mp;

        for (const auto matchStick : matchsticks) {
            mp[matchStick]++;
            perm += matchStick;
        }

        if (perm % 4 > 0) {
            return false;
        }

        int side = perm / 4;

        dp = vector<vector<int>>(4, vector<int>(1 << matchsticks.size(), -1));

        return check(side, matchsticks, 0, 0, 0);
    }
};
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