<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 f(vector<int>& a, int pos, long long c1, long long c2, long long c3, long long c4, long long s, unordered_map<int, int>& b) {
        if (pos < 0) {
            return c1 == c2 && c2 == c3 && c3 == c4;
        }
        if (c1 > s | c2 > s | c3 > s | c4 > s) {
            return false;
        }
        int d = (c1 << 25) | (c2 << 16) | (c3 << 8) | c4;
        if (b.count(d)!=0) {
            return b[d];
        }
        bool t1 = f(a, pos - 1, c1 + a[pos], c2, c3, c4, s, b);
        if(t1) return b[d]=true;
        bool t2 = f(a, pos - 1, c1, c2 + a[pos], c3, c4, s, b);
        if(t2) return b[d]=true;
        bool t3 = f(a, pos - 1, c1, c2, c3 + a[pos], c4, s, b);
        if(t3) return b[d]=true;
        bool t4 = f(a, pos - 1, c1, c2, c3, c4 + a[pos], s, b);
        return b[d] = t4;
    }

    bool makesquare(vector<int>& matchsticks) {
        sort(matchsticks.begin(),matchsticks.end());
        unordered_map<int,int> b;
        int n = matchsticks.size() - 1;
        long long c1 = 0;
        long long c2 = 0;
        long long c3 = 0;
        long long c4 = 0;
        long long sum = 0;
        for (int i = 0; i < matchsticks.size(); i++) {
            sum += matchsticks[i];
        }
        if (sum % 4 != 0) {
            return false;
        }
        return f(matchsticks, n, c1, c2, c3, c4, sum / 4, b);
    }
};

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