<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(int sum, int bitmask, int tar, int cnt, vector<int>& matchsticks, vector<int>& dp) {
        if (cnt == 4) {
            return true;
        }
        if (dp[bitmask] != -1) {
            return dp[bitmask];
        }
        if (sum == tar) {
            return dp[bitmask] = helper(0, bitmask, tar, cnt + 1, matchsticks, dp);
        }
        
        bool ans = false;
        for (int i = 0; i < matchsticks.size(); i++) {
            if ((bitmask & (1 << i)) == 0 && sum + matchsticks[i] <= tar) {
                int temp = bitmask;
                temp |= (1 << i);
                ans = ans| helper(sum + matchsticks[i], temp, tar, cnt, matchsticks, dp);
             
            }
        }
        
        return dp[bitmask] = ans;
    }

    bool makesquare(vector<int>& matchsticks) {
        int sum = accumulate(matchsticks.begin(), matchsticks.end(), 0);
        int maxi = *max_element(matchsticks.begin(), matchsticks.end());
        if (sum % 4 != 0) {
            return false;
        }
        if (sum / 4 < maxi) {
            return false;
        }

        int n = matchsticks.size();
        vector<int> dp(1 << n, -1);
        return helper(0, 0, sum / 4, 0, matchsticks, dp);
    }
};

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