<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 solve(int i, int n, int sum, int target, int k, vector<int>&v, vector<int>&vis) {
    //     if (k == 0) return true;
    //     if (sum == target) return solve(0, n, 0, target, k - 1, v, vis);

    //     for (int j = i; j < n; ++j) {
    //         if (vis[j] && sum + v[j] <= target ) {
    //             vis[i] = 0;
    //             if (solve(i + 1, n, sum + v[j], target, k, v, vis)) {
    //                 return true;
    //             }
    //             vis[i] = 1;
    //             if (sum == 0) {
    //                 return false;
    //             }
    //         }
    //     }
    //     return false;
    // }

    bool solve(int start,int sum,int target,int n,int k,vector<int>nums,vector<int>&vis){
        if(k==0) return true;

        if(sum==target){
            return solve(0,0,target,n,k-1,nums,vis);
        }

        for(int i=start;i<n;++i){
            if(vis[i] && sum+nums[i]<=target){
                vis[i]=0;
                if(solve(i+1,sum+nums[i],target,n,k,nums,vis)){
                    return true;
                }
                vis[i]=1;
                if(sum==0){
                    return false;
                }
            }
        }

        return false;
    }

    bool canPartitionKSubsets(vector<int>& nums, int k) {
        int n=nums.size();
        int sum=0;
        for(int i:nums) sum+=i;
        if(sum%k!=0){
            return false;
        }
        for(int i:nums) {
            if(i>sum/k) return false;
        }
        int val=sum/k;
        vector<int>vis(n,1);
        bool ans=solve(0,0,val,n,k,nums,vis);
        return ans;
    }

    bool makesquare(vector<int>& matchsticks) {
        return canPartitionKSubsets(matchsticks,4);
        // int side = 0;
        // for (int i : matchsticks) side += i;
    	// for (int i : matchsticks) if (i > side / 4) return false ;
        // if (side % 4 != 0) return false;
        // vector<int>vis(matchsticks.size(), 1);
        // return solve(0, matchsticks.size(), 0, side / 4, 4, matchsticks, vis);
    }

};
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