<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 solve(vector<int> &arr,int n,int k,vector<int> ref,
    int ind,int s){
        //base case:
        if(ind==n){
            for(int i=1;i<=k;i++){
                if(ref[i]!=s){
                    return false;
                }
            }
            return true;
        }
        //assign matchsticks to the sides:
        bool ans=false;
        for(int j=1;j<=k;j++){
            int given=0;
            // if(ref[j]==0){
            //     given=1;
            // }
            if(ref[j]+arr[ind]>s){
                continue;
            }
            // if(ref[j]==0){
            //     given=1;
            // }
            //given ind-th stick to jth side:
            ref[j]=ref[j]+arr[ind];
            bool temp=solve(arr,n,k,ref,ind+1,s);
            if(temp==true){
                return true;
            }
            //ans=ans|temp;
            //backtrack:
            ref[j]=ref[j]-arr[ind];
            if(ref[j]==0){
                break;
            }
        }
        return ans;
    }
    bool makesquare(vector<int>& arr) {
        int n=arr.size();
        int k=4;
        int sum=0;
        for(int i=0;i<n;i++){
            sum=sum+arr[i];
        }
        if(n<k||sum%k>0){
            return false;
        }
        int s=sum/k;
        if(*max_element(arr.begin(),arr.end())>s){
            return false;
        }
        sort(arr.begin(),arr.end(),greater<int>());
        //int s=sum/k;
        vector<int> ref(k+1,0);
        int ind=0;
        bool ans=solve(arr,n,k,ref,ind,s);
        return ans;
    }
};
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