<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:
    vector<vector<int>>dp;
    int solve(int cur,int idx,int mask,vector<int>&arr,int n,int l){
        if(idx==4) return true;
        if(dp[idx][mask]!=-1) return dp[idx][mask];
        bool ans = false;
        for(int i = 0; i < n; i++){
            if((mask&(1<<i))==0){
                if(cur+arr[i]==l){
                    bool chk = solve(0,idx+1,mask|(1<<i),arr,n,l);
                    if(chk==true){
                        ans = true;
                        break;
                    }
                }else if(cur+arr[i] < l){
                    bool chk = solve(cur+arr[i],idx,mask|(1<<i),arr,n,l);
                    if(chk==true){
                        ans = true;
                        break;
                    }
                }
            }
        }

        return dp[idx][mask] = ans;
    }
    bool makesquare(vector<int>& arr) {
        int n = arr.size();
        long long sum = 0;
        for(int i:arr) sum+=i;
        if(sum%4!=0) return false;
        int l = sum/4;
        for(int i:arr){
            if(i>l) return false;
        }
        dp.resize(4,vector<int>(1<<n,-1));
        bool ans = solve(0,0,0,arr,n,l);

        return ans;
    }
};
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