<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:
        def findSolution(i,n,matchSticks, side, a,b,c,d,dp):
            if(i>=n):
                if(a==b and c==d and b==c and a==side):
                    return True
                return False
            if(a>side or b>side or c>side or d>side):
                return False
            key = str(a) + "-" + str(b) + "-" + str(c) + "-" + str(d)
            if(key in dp):
                return dp[key]
            curr = matchSticks[i]
            dp[key] =  (findSolution(i+1,n,matchsticks, side, a + curr,b,c,d,dp) or
             findSolution(i+1,n,matchsticks, side, a,b + curr,c,d,dp) or 
             findSolution(i+1,n,matchsticks, side, a,b,c+curr,d,dp) or 
             findSolution(i+1,n,matchsticks, side, a,b,c,d+curr,dp))
            return dp[key]
        matchsticks.sort(reverse = True)
        side = sum(matchsticks)
        if(side%4!=0):
            return False
        n = len(matchsticks)
        side = side/4
        dp = {}
        return findSolution(0, n, matchsticks, side, 0,0,0,0,dp)

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