<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:
        
        totalsum=sum(matchsticks)

        if totalsum%4:
            return False
        sidel= totalsum//4

        used= [0]*len(matchsticks)

        mem={}
        def func(idx, s, n):
            if tuple(used) in mem:
                return mem[tuple(used)]
            if n==4:
                return True
            if s==sidel:
                return func(0, 0,n+1)
            
            if s>sidel or idx==len(matchsticks):
                return False
            
            
            res=False
            for j in range(idx,len(matchsticks)):
                if used[j]==0:
                    used[j]=1
                    res= res or func(j+1,s+matchsticks[j],n)
                    used[j]=0
            mem[tuple(used)]=res
            return res
        return func(0,0,0)
                    

                    




























        totaln=sum(matchsticks)
        if totaln % 4:
            return False
        length=sum(matchsticks)//4

        sides=[0]*4
        matchsticks.sort(reverse=True)

        def func(i):
            if i == len(matchsticks):
                return True
            for j in range(4):
                if sides[j]+matchsticks[i]<=length:
                    sides[j]+=matchsticks[i]
                    if func(i+1):
                        return True
                    sides[j]-=matchsticks[i]
            return False
        return func(0)
       
        
        


        
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