<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 {
    unordered_map<string, int> mp;
    int sl = 0;

public:
    bool makesquare(vector<int>& m) {
        int totalLength = accumulate(m.begin(), m.end(), 0);
        if (totalLength % 4 != 0) return false;
        sl = totalLength / 4;
        sort(m.rbegin(), m.rend());
        vector<int> ans(4, 0);
        return f(0, m, ans);
    }

    bool f(int i, vector<int>& m, vector<int> ans) {
        if (i == m.size()) {
           return ans[0] == sl && ans[1] == sl &&
                   ans[2] == sl && ans[3] == sl;
        }

        string state = getState(ans);
        if (mp.find(state) != mp.end()) {
            return mp[state];
        }

        for (int j = 0; j < 4; j++) {
            if (ans[j] + m[i] <= sl) {
                ans[j] += m[i];
                if (f(i + 1, m, ans)) {
                    return mp[state] = true;
                }
                ans[j] -= m[i];
            }
            if (ans[j] == 0) break;
        }

        return mp[state] =false;
    }

    string getState(vector<int>& sides) {
        return to_string(sides[0]) + "-" + to_string(sides[1]) + "-" +
               to_string(sides[2]) + "-" + to_string(sides[3]);
    }
};
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