<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:
    def makesquare(self, matchsticks: List[int]) -> bool:
        self.used  = [False] * len(matchsticks)
        total = sum(matchsticks)
        target = total //4
        if total %4 != 0:
            return False
        self.memo ={}

        return self.backtrack(matchsticks, 0,4, 0, target)

    def backtrack(self, matchsticks, start, k,  path, target):
        memo_key= tuple(self.used)

        if memo_key in self.memo:
            return self.memo[memo_key]
        if k ==0: 
            self.memo[memo_key] =True
            return True 

        if path == target :
            return self.backtrack(matchsticks, 0, k-1, 0, target)

        for i in range(start, len(matchsticks)):
            if self.used[i] or path + matchsticks[i] > target:
                continue 
            self.used[i] =True 
            path += matchsticks[i]
            if self.backtrack(matchsticks, i+1, k, path, target):
                self.memo[memo_key] = True
                return True
            self.used[i] =False
            path -= matchsticks[i]

        self.memo[memo_key] =False
        return False


20687