<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 makesquare(vector<int>& nums) {
if (nums.empty() || nums.size() < 4) return false;
int sum = accumulate(nums.begin(), nums.end(), 0);
if (sum % 4 != 0) return false;
int n = nums.size(), all = (1 << n) - 1, target = sum / 4;
vector<int> masks, validHalf(1 << n, false);
for (int i = 0; i <= all; ++i) {
int curSum = 0;
for (int j = 0; j <= 15; ++j) {
if ((i >> j) & 1) curSum += nums[j];
}
if (curSum == target) {
for (int mask : masks) {
if ((mask & i) != 0) continue;
int half = mask | i;
validHalf[half] = true;
if (validHalf[all ^ half]) return true;
}
masks.push_back(i);
}
}
return false;
}
};
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