<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<string, bool> map; 
    bool makesquare(vector<int>& matchsticks) {
        int sum = accumulate(matchsticks.begin(), matchsticks.end(), 0);
        if (sum % 4 != 0) return false;
        int target = sum / 4; 
        //vector<bool> used(matchsticks.size(), false);
        string used(matchsticks.size(), '0');  
        return backtrack(matchsticks, 0, 0, used, target, 0); 
    }


    bool backtrack(vector<int> &matchsticks, int curSum, 
    int edges, string &used, int target, int num_used) {
        if (edges == 4) return true;

        if (map.find(used) != map.end()) return map[used]; 

        if (curSum > target) return false; 

        if (curSum == target) {
            return backtrack(matchsticks, 0, edges+1, used, target, num_used); 
        } 

        if (curSum < target) {
            for (int i = 0; i < used.size(); i++) {
                if (used[i] == '0') {
                    curSum += matchsticks[i]; 
                    used[i] = '1'; 
                    if (backtrack(matchsticks, curSum, edges, used, target, num_used+1)) { 
                    
                        return map[used] = true; 

                    }
                    
                    used[i] = '0'; 
                    curSum -= matchsticks[i]; 
                }
            }
        }

        return map[used] = false; 
    }
};
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