<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 mask, vector<int>& matchsticks, int index, int sum, int targetSum, vector<int> powerOf2, vector<int> &dp){
        if(sum > targetSum){
            return dp[mask] = false;
        }
        if(index == matchsticks.size()){
            return sum == targetSum;
        }
        if(dp[mask] != -1){
            return dp[mask];
        }
        if(sum == targetSum){
            sum = 0;
        }
        for(int i = 0; i < matchsticks.size(); i++){
            if(!(powerOf2[i] & mask)){
                if(solve(powerOf2[i] | mask, matchsticks, index + 1, sum + matchsticks[i], targetSum, powerOf2, dp)){
                    return dp[mask] = true;
                }
            }
        }
        return dp[mask] = false;
    }
    
    bool makesquare(vector<int>& matchsticks) {
        int sum = 0;
        for(int stick : matchsticks){
            sum += stick;
        }
        if(sum % 4 != 0){
            return false;
        }
        vector<int> mp(matchsticks.size());
        vector<int> dp(1<<matchsticks.size(), -1);
        sort(matchsticks.rbegin(), matchsticks.rend());
        int pow = 1;
        for(int i=0;i<matchsticks.size();i++){
            if(matchsticks[i] > sum/4)  return false;
            mp[i] = pow;
            pow *= 2;
        }
        return solve(0, matchsticks, 0, 0, sum/4, mp, dp);
    }
};
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