<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:
        total_sum = sum(matchsticks)
        if total_sum % 4 != 0:
            return False
        
        matchsticks.sort(reverse=True)
        sums = [0,0,0,0]
        memo = {}
        return self.helper(0, sums, total_sum // 4, matchsticks, memo)
    
    def helper(self, pos, sums, max_side,matchsticks, memo):
        e1,e2,e3,e4 = sums
        key = (e1,e2,e3,e4)
        #if key in memo:
        #    return memo[key]
        if e1==e2==e3==e4==max_side:
            return True
        if pos >= len(matchsticks):
            return False
        for i,s in enumerate(sums):
            if s + matchsticks[pos] > max_side:
                continue
            sums[i] += matchsticks[pos]
            if self.helper(pos+1, sums, max_side,matchsticks,memo):
                memo[key] = True
                return True
            sums[i] -= matchsticks[pos]
        memo[key] = False
        return False

        #helper(pos+1, e1+)
        # for i in range()
        # for i, n in enumerate(matchsticks):
        #     without = matchsticks[:i] + matchsticks[i+1:]
        #     for j in range(len(sums)):
        #         if sums[j] + n > max_side:
        #             continue
        #         sums[j] += n
        #         if self.helper(without, sums, max_side):
        #             return True
        #         sums[j] -= n
        # memo[key] = False
        # return False
        
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