<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>


// //tle
// class Solution {
// public:
//     bool f(int i,vector<int> &d, int side, vector<int>& stick){
//         if(i==stick.size() && (d[0] == d[1] && d[1] == d[2] && d[2] == d[3])) return true;
//         if(i==stick.size()) return false;

//             for(int j=0;j<4;j++){               
//                 if(d[j]+stick[i]>side)continue;
//                 d[j]+=stick[i];
//                 if (f(i+1,d,side,stick)) return true;
//                 d[j]-=stick[i];
//             }
        
//         return false;
//     }

//     bool makesquare(vector<int>& stick) {
//         int sum=0;
//         for(auto it: stick) sum+=it;
//         if(sum%4 !=0) return false;
//         int side=sum/4;
//         vector<int>d(4,0);
        
//         return f(0,d,side,stick);
//     }
// };


//
class Solution {
public:
    unordered_map<int, bool> memo;

    bool f(int mask, int sides, int currSum, int sideLength, vector<int>& stick) {
        if (sides == 0) return true; // All sides are filled
        if (currSum == sideLength) return f(mask, sides - 1, 0, sideLength, stick); // Start a new side

        if (memo.find(mask) != memo.end()) return memo[mask];

        for (int i = 0; i < stick.size(); i++) {
            if (!(mask & (1 << i)) && currSum + stick[i] <= sideLength) {
                if (f(mask | (1 << i), sides, currSum + stick[i], sideLength, stick)) {
                    return memo[mask] = true;
                }
            }
        }

        return memo[mask] = false;
    }

    bool makesquare(vector<int>& stick) {
        int totalLength = accumulate(stick.begin(), stick.end(), 0);
        if (totalLength % 4 != 0) return false;

        int sideLength = totalLength / 4;
        sort(stick.rbegin(), stick.rend());

        return f(0, 4, 0, sideLength, stick);
    }
};

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