<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 helper(vector<int>matchsticks,int sum, int target, int k, vector<int> &visited, int mask, vector<int> &dp) {
        if(k==0) {
            bool ans = 1;
            for(auto x : visited) {
                ans = ans & x;
            }
            return ans;
        }
        if(sum == target) {
            // cout<<sum<<" "<<target<<" "<<k<<"\n";
            // for(auto x : visited) {
            //     cout<<x<<" ";
            // }
            // cout<<"\n";
            return helper(matchsticks,0,target,k-1,visited,mask,dp);
        }
        if(dp[mask] != -1)
            return dp[mask];
        bool ans = false;
        for(int i =0 ;i<matchsticks.size();i++) {
            if(visited[i])
                continue;
            if(sum + matchsticks[i] <= target) {
            mask = mask | (1<<i);
                visited[i] += 1;
                // cout<<i<<" "<<sum + matchsticks[i]<<"<-\n";
                ans = ans || helper(matchsticks,sum + matchsticks[i],target,k,visited,mask,dp);
                visited[i] -= 1;
                mask = mask ^ (1<<i);
            }
        }
        return dp[mask]=ans;
    }
    bool makesquare(vector<int>& matchsticks) {
        int sum=0,i,n=matchsticks.size();
        for(auto x : matchsticks)
            sum+=x;
        if(sum%4 != 0)
            return false;
        vector<int> visited(n,0);
        vector<int> dp((1 << n) -1, -1);
        int ans = helper(matchsticks,0,sum/4,4,visited,0,dp);
        return ans;
    }
};
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