<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:
        # HMM, TLE, so our method is inefficient
        # How to speed up?


        # find a way to put matchsticks into 4 buckets of equal length
        total = sum(matchsticks)
        quarter = total//4
        if total % 4 != 0 or len(matchsticks) < 4:
            return False
        for val in matchsticks:
            if val > quarter:
                return False
        
        # Now, we need a way to create buckets using these matchsticks
        buckets = [matchsticks[0],0,0,0]
        square = False
        #matchsticks = sorted(matchsticks,reverse=True)
        def add_to_bucket(ind,buckets):
            nonlocal square
            # for val in buckets:
            #     if val > quarter:
            #         return
            # check end:
            if ind == len(matchsticks):
                count = 0
                for val in buckets:
                    if val == quarter:
                        count += 1
                if count == 4:
                    square = True
                return

            # arrange into buckets:
            if square:
                return
            
            if buckets[0] + matchsticks[ind] <= quarter:
                buckets[0] += matchsticks[ind]
                add_to_bucket(ind+1,buckets)
                buckets[0] -= matchsticks[ind]
            
            if buckets[1] + matchsticks[ind] <= quarter and buckets[1] != buckets[0]:
                buckets[1] += matchsticks[ind]
                add_to_bucket(ind+1,buckets)
                buckets[1] -= matchsticks[ind]
            
            if buckets[2] + matchsticks[ind] <= quarter and buckets[2] != buckets[1]:
                buckets[2] += matchsticks[ind]
                add_to_bucket(ind+1,buckets)
                buckets[2] -= matchsticks[ind]
            
            if buckets[3] + matchsticks[ind] <= quarter and buckets[3] != buckets[2]:
                buckets[3] += matchsticks[ind]
                add_to_bucket(ind+1,buckets)
                buckets[3] -= matchsticks[ind]

        add_to_bucket(1,buckets)
        return square

17097