<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:
map<pair<int,int>,bool> ma;
int s=0;
int format(vector<int> mat){
    int k =1;
    for(int i=0;i<mat.size();i++){
        k=k<<1;
        k = k|(mat[i]!=0);
    }
    // cout<<k<<" ";
    return k;
}
bool cal(int k,vector<int> &mat,int c){
   // cout<<"\n";
    if(k<2){
        return true;
    }
    bool ans =false;
    int key = format(mat);
    //   cout<<c<<" "<<k<<"**";
    if(ma.find({key,k})!=ma.end()){
        return ma[{key,k}];
    }
   
    for(int i =0 ;i <mat.size();i++){
        if(mat[i]!=0){
            int y =mat[i];
            if(mat[i]>c){
                continue;
            }
            mat[i]=0;
            if(c-y==0){
                ans = ans||cal(k-1,mat,s);
            }else{
                ans=ans||cal(k,mat,c-y);
            }
            mat[i]=y;
        }
    }
    ma[{key,k}]=ans;
    return ans;
}
bool makesquare(vector<int>& matchsticks) {
    int sum=0;
    for(int i=0;i<matchsticks.size();i++){
        sum+=matchsticks[i];
    }
    if(sum%4!=0){
        return false;
    }
    s=sum/4;
    return cal(4,matchsticks,sum/4);
}
};
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