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
class Solution {
    public boolean makesquare(int[] matchsticks) {
        int s = 0, mx = 0;
        for (int v : matchsticks) {
            s += v;
            mx = Math.max(mx, v);
        }
        int x = s / 4, mod = s % 4;
        if (mod != 0 || x < mx) {
            return false;
        }
        Arrays.sort(matchsticks);
        int[] edges = new int[4];
        return dfs(matchsticks.length - 1, x, matchsticks, edges);
    }

    private boolean dfs(int u, int x, int[] matchsticks, int[] edges) {
        if (u < 0) {
            return true;
        }
        for (int 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, matchsticks, edges)) {
                return true;
            }
            edges[i] -= matchsticks[u];
        }
        return false;
    }
}