<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 index, int curr_k, int k, int currSum, int targetSum, string &picked, vector<int> &matchsticks, unordered_map<string, bool> &dp) {
        if(curr_k == k - 1) {
            return true;
        }
        if(currSum > targetSum) {
            return false;
        }
        if(dp.find(picked) != dp.end()) {
            return dp[picked];
        }
        if(currSum == targetSum) {
            return dp[picked] = helper(0, curr_k+1, k, 0, targetSum, picked, matchsticks, dp);
        }

        for(int i=index;i<matchsticks.size();i++) {
            if(picked[i] == '0') {
                picked[i] = '1';
                if(helper(i+1, curr_k, k, currSum + matchsticks[i], targetSum, picked, matchsticks, dp)) {
                    return dp[picked] = true;
                }
                picked[i] = '0';
  
            }
        }

        return dp[picked] = false;
    }

    bool makesquare(vector<int>& matchsticks) {
        int totalSum = 0;
        for(int i=0;i<matchsticks.size();i++) {
            totalSum += matchsticks[i];
        }
        if(totalSum % 4 != 0) {
            return false;
        }
        int targetSum = totalSum/4;
        string picked(matchsticks.size(), '0');
        unordered_map<string, bool> dp;
        sort(matchsticks.begin(), matchsticks.end(), greater<int>());
        return helper(0, 0, 4, 0, targetSum, picked, matchsticks, dp);
    }
};
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