<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 makesquare(vector<int>& matchsticks) {
        long totalLength = 0;
        for(int &len : matchsticks){
            totalLength += len;
        }
        if(totalLength%4 != 0) return false;

        int sideLength = totalLength/4;
        long state = 0;
        unordered_set<long> combos;
        unordered_set<long> visited;
        createAllPossibleCombos(matchsticks, sideLength, state, combos, visited);

        bool ans = false;
        long targetState = (1 << matchsticks.size()) - 1;
        vector<unordered_set<long>> visitedCombo(4);
        checkPossibility(combos, visitedCombo, 0, targetState, 0, ans);
        return ans;
    }

    void checkPossibility(
        unordered_set<long> &combos, 
        vector<unordered_set<long>> &visited,
        long state, 
        long &targetState, 
        int level, 
        bool &ans
    ){

        //cout<<"level: "<<level<<" state: "<<state<<" target: "<<targetState<<endl;
        if(level > 3){
            if(level == 4 && state == targetState) ans = true;
            return;
        }

        if(visited[level].find(state) != visited[level].end()) return;
        visited[level].insert(state);

        auto itr = combos.begin();
        while(itr != combos.end()){
            if((state^(*itr)) > state){
                //cout<<"adding "<<(*itr)<<" "<<(state | (*itr))<<endl;
                checkPossibility(combos, visited, state | (*itr), targetState, level+1, ans);
                if(ans) break;
            }

            itr++;
        }
    }

    void createAllPossibleCombos(
        vector<int> &matchsticks, 
        int target, 
        long state, 
        unordered_set<long> &combos,
        unordered_set<long> &visited
    ){
        if(visited.find(state) != visited.end()) return;
        visited.insert(state);

        if(target == 0){
            // cout<<"inserting "<<state<<endl;
            combos.insert(state);
            return;
        }
        if(target < 0) return;

        for(int i=0;i<matchsticks.size();i++){
            if(target < matchsticks[i]) continue;
            createAllPossibleCombos(matchsticks, target - matchsticks[i], state | (1<<i), combos, visited);
        }
    }
};
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