<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:
    unordered_map<int, bool> memo;  
    int target;                   
    
    bool dp(vector<int>& nums, int mask, int currentSum, int sides) {
        if (sides == 4) return true;  
        if (memo.count(mask)) return memo[mask]; 
        
        for (int i = 0; i < nums.size(); ++i) {
            if (!(mask & (1 << i))) {  
                int newSum = currentSum + nums[i];
                if (newSum <= target) {  
                    if (dp(nums, mask | (1 << i), newSum % target, sides + (newSum == target))) {
                        return memo[mask] = true;
                    }
                }
            }
        }
        
        return memo[mask] = false;
    }
    
    bool makesquare(vector<int>& matchsticks) {
        int sum = 0;
        for (int num : matchsticks) sum += num;
        if (sum % 4 != 0) return false;  
        
        target = sum / 4; 
        memo.clear();  
        
        return dp(matchsticks, 0, 0, 0);  
    }
};

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