Matchsticks to Square
<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://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0400-0499/0473.Matchsticks%20to%20Square/images/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>
Bit Manipulation; Array; Dynamic Programming; Backtracking; Bitmask
func makesquare(matchsticks []int) bool {
	s := 0
	for _, v := range matchsticks {
		s += v
	}
	if s%4 != 0 {
		return false
	}
	sort.Sort(sort.Reverse(sort.IntSlice(matchsticks)))
	edges := make([]int, 4)
	var dfs func(u, x int) bool
	dfs = func(u, x int) bool {
		if u == len(matchsticks) {
			return true
		}
		for i := 0; i < 4; i++ {
			if i > 0 && edges[i-1] == edges[i] {
				continue
			}
			edges[i] += matchsticks[u]
			if edges[i] <= x && dfs(u+1, x) {
				return true
			}
			edges[i] -= matchsticks[u]
		}
		return false
	}
	return dfs(0, s/4)
}