<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:
    map<vector<int>, bool> memo;
    bool helper(vector<int>& matchsticks, int a, int b, int c, int d, int res, int i) {
        vector<int> temp = {a, b, c, d};
        sort(temp.begin(), temp.end());

        if (i == matchsticks.size()) {
            if (a == b && b == c && c == d && d == res) {
                memo[temp] = true;
            } else {
                memo[temp] = false;
            }
        }

        if (a > res || b > res || c > res || d > res) {
            memo[temp] = false;
        }

        if (memo.find(temp) != memo.end()) {
            return memo[temp];
        }

        memo[temp] = helper(matchsticks, a + matchsticks[i], b, c, d, res, i + 1) ||
            helper(matchsticks, a, b + matchsticks[i], c, d, res, i + 1) ||
            helper(matchsticks, a, b, c + matchsticks[i], d, res, i + 1) ||
            helper(matchsticks, a, b, c, d + matchsticks[i], res, i + 1); 
        return memo[temp];
    }

    bool makesquare(vector<int>& matchsticks) {
        int sum = 0;
        for (int i = 0; i < matchsticks.size(); i++) {
            sum += matchsticks[i];
        }

        if (sum % 4 != 0) {
            return false;
        } sum /= 4;

        for (int i = 0; i < matchsticks.size(); i++) {
            if (matchsticks[i] > sum) {
                return false;
            }
        }

        sort(matchsticks.begin(), matchsticks.end(), [](int a, int b) {
            return a > b;
        });
        
        return helper(matchsticks, 0, 0, 0, 0, sum, 0);
    }
};
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