<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 solve(std::vector<int> &matchsticks, int n, int k, int curSum, int mask, int target, std::vector<int> &dpTable) {
        if (mask == (1 << n) - 1) return true;

        if (dpTable[mask] != -1) return dpTable[mask];

        bool result = false;
        for (int next = 0; next < n; ++next) {
            if (mask & (1 << next)) continue;

            if (matchsticks[next] + curSum == target) {
                result |= solve(matchsticks, n, k - 1, 0, mask | (1 << next), target, dpTable);
            }
            else if (matchsticks[next] + curSum < target) {
                result |= solve(matchsticks, n, k, matchsticks[next] + curSum, mask | (1 << next), target, dpTable);
            }
        }
        return dpTable[mask] = result;
    }
    bool makesquare(vector<int>& matchsticks) {
        int sum = std::accumulate(matchsticks.begin(), matchsticks.end(), 0);
        if (sum % 4 != 0) return false;

        int target = sum / 4;
        auto maxElement = *std::max_element(matchsticks.begin(), matchsticks.end());
        if (maxElement > target) return false;

        int n = static_cast<int>(matchsticks.size());
        std::vector<int> dpTable(1 << n, -1);
        return solve(matchsticks, n, 4, 0, 0, target, dpTable);
    }
};
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