<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 {
public:
    bool func(int ind, vector<int>& side, vector<int> matchsticks){
        if(ind==matchsticks.size()){
            if(side[1]==side[2] && side[2]==side[3] && side[3]==side[4] && side[4]==sum/4) return true;
            return false;
        }
        
        if(side[1]>sum/4 || side[2]>sum/4 || side[3]>sum/4 || side[4]>sum/4 ) return false;
        for(int i=1; i<=4 ;i++)
        {
            if(side[i]+matchsticks[ind]>sum/4) continue;
            int j = i;
            while (--j >= 1)
                if (side[i] == side[j]) 
                    break;
            if (j != 0) continue;
            side[i]+=matchsticks[ind];
            if(func(ind+1, side,matchsticks)) return true;
            side[i]-=matchsticks[ind];
        }


        return false;
    }
    int sum = 0;
    bool makesquare(vector<int>& matchsticks) {
        vector<int> sides(5,0);
        for(auto it: matchsticks) sum+=it;
        sort(matchsticks.begin(), matchsticks.end(), [](int a, int b){
            return a>b;
        });
        return func(0, sides, matchsticks);
    }
};
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