<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:
    typedef vector<int> I;
    int target;

    bool bt(I m, I s, int idx) {
        if (idx == m.size()) {
            for (int i : s) {
                if (i != target) {
                    return false;
                }
            }
            return true;
        }
        for (int i = 0 ; i < 4; i++) {
            if (i > 0 && s[i] == s[i-1]) {
                continue;
            }
            if (s[i] + m[idx] > target) {
                continue;
            }
            s[i] += m[idx];
            if (bt(m,s,idx + 1)) {
                return true;
            }
            s[i] -= m[idx];
        }
        return false;
    }
    bool makesquare(vector<int>& matchsticks) {
        ios_base :: sync_with_stdio(0);
        cin.tie(NULL);
        cout.tie(NULL);
        int sum = accumulate(matchsticks.begin(), matchsticks.end(), 0);
        if (sum % 4 != 0) {
            return false;
        }
        target = sum / 4;
        I sides(4, 0);
        sort(matchsticks.begin(), matchsticks.end(), greater<int>());
        return bt(matchsticks, sides, 0);
    }
};
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