<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 isPossible(vector<int> matchsticks, int target,vector<int> &res, int idx){
        
        if(idx == matchsticks.size()){
            return (res[0] == res[1] && res[1] == res[2] && res[2] == res[3]);
        }
        
        for(int i=0;i<4;i++){
            
            if(res[i] + matchsticks[idx] > target){
                continue;
            }
            
            int j = i-1;
            
            while(j>=0){
                
                if(res[i] == res[j]) break;
                
                j--;
                
            }
            
            if(j != -1)
                continue;
            
            
            res[i] += matchsticks[idx];
            
            if(isPossible(matchsticks,target,res,idx+1)) return true;
            
            res[i] -= matchsticks[idx];
            
        }
        return false;
    }
    
    
    
    bool makesquare(vector<int>& matchsticks) {
        
        //Edge Case
        if(matchsticks.size() == 0)
            return 0;
        
        int sum = accumulate(matchsticks.begin(),matchsticks.end(),0);
        
        int target = sum/4;
            
        vector<int> sides(4,0);
        
        sort(matchsticks.begin(),matchsticks.end(),greater<int>());
        
        return isPossible(matchsticks,target,sides,0);
        
    }
};
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