<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(int bits,int sum, int num,vector<int>& a,int req,unordered_map<int,int>& dp) {
        int n = a.size();
        if(bits==0) {
            //cout<<sum<<" "<<num<<"\n";
            return sum==req and num==4;
        }
        if(dp.find(bits)!=dp.end()) {
            return dp[bits];
        }
        bool ans = false;
        for(int i=0;i<n;i++) {
            if(((bits>>i) & 1) == 1 and sum-a[i]>=0) {
                ans |= solve(bits^(1<<i),sum-a[i]>0?sum-a[i]:req,sum-a[i]>0?num:num+1,a,req,dp);
            }
        }
        return dp[bits] = ans;
    }

    bool makesquare(vector<int>& matchsticks) {
        int sum = accumulate(matchsticks.begin(),matchsticks.end(),0);
        if(sum%4!=0) {
            return false;
        }
        cout<<sum<<"\n";
        int n = matchsticks.size();
        int bits = (1<<n)-1;
        cout<<bits<<"\n";
        unordered_map<int,int> dp;
        return solve(bits,sum/4,0,matchsticks,sum/4,dp);
    }
};
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