<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>

const int SIDES = 4;
const int MAX_LENGTH = 15;
int SIZE;
int SIDE_SIZE;


class Solution {
public:
      bool dfs(const std::vector<int>& xs, std::bitset<MAX_LENGTH> mask, int side, int c, std::unordered_map<int, bool>& memo)
    {  

        if(c == 4)
          return true;

        if(side > SIDE_SIZE)
           return false;
         
        if(auto i = memo.find((int)mask.to_ulong()); i != memo.end())
          return (*i).second; 

         bool ans = false;
         for(int i = 0; i < SIZE && !mask.all() && !ans; i++)
         {
             if(mask.test(i)) continue;
             mask.set(i);
             if(side + xs[i] == SIDE_SIZE)
                ans |= memo[(int)mask.to_ulong()] = dfs(xs, mask, 0, c + 1, memo);
             ans |= memo[(int)mask.to_ulong()] = dfs(xs, mask, side + xs[i], c, memo);
             mask.set(i, false);
         }
         return ans;
    }
    bool makesquare(vector<int>& matchsticks) {
           SIZE = matchsticks.size();
        int perimeter = std::reduce(matchsticks.begin(), matchsticks.end());
        if(SIZE < 4 || (perimeter % SIDES))
          return false;
        SIDE_SIZE = perimeter / SIDES;
        std::sort(matchsticks.begin(), matchsticks.end(), std::greater<int>());
        std::bitset<MAX_LENGTH> mask;
        std::unordered_map<int, bool> memo;
        return dfs(matchsticks, mask, 0, 0, memo);
    }
};
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