<p>Given an array <code>arr</code> of positive integers, consider all binary trees such that:</p>

<ul>
	<li>Each node has either <code>0</code> or <code>2</code> children;</li>
	<li>The values of <code>arr</code> correspond to the values of each <strong>leaf</strong> in an in-order traversal of the tree.</li>
	<li>The value of each non-leaf node is equal to the product of the largest leaf value in its left and right subtree, respectively.</li>
</ul>

<p>Among all possible binary trees considered, return <em>the smallest possible sum of the values of each non-leaf node</em>. It is guaranteed this sum fits into a <strong>32-bit</strong> integer.</p>

<p>A node is a <strong>leaf</strong> if and only if it has zero children.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/10/tree1.jpg" style="width: 500px; height: 169px;" />
<pre>
<strong>Input:</strong> arr = [6,2,4]
<strong>Output:</strong> 32
<strong>Explanation:</strong> There are two possible trees shown.
The first has a non-leaf node sum 36, and the second has non-leaf node sum 32.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/10/tree2.jpg" style="width: 224px; height: 145px;" />
<pre>
<strong>Input:</strong> arr = [4,11]
<strong>Output:</strong> 44
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= arr.length &lt;= 40</code></li>
	<li><code>1 &lt;= arr[i] &lt;= 15</code></li>
	<li>It is guaranteed that the answer fits into a <strong>32-bit</strong> signed integer (i.e., it is less than 2<sup>31</sup>).</li>
</ul>

class Solution {
public:

    int solver(vector<int>&arr, map<pair<int,int>,int>&mp,int left,int right, vector<vector<int>>&dp){
        if(left==right) return 0;
        if(dp[left][right]!=-1) return dp[left][right];
        int ans = INT_MAX;
        for(int i=left; i<right;i++){
            ans = min(ans,mp[{left,i}] * mp[{i+1,right}] + solver(arr,mp,left,i,dp)+solver(arr,mp,i+1,right,dp));
        }
        return dp[left][right] = ans;
    }

    // int tab(vector<int>&arr, map<pair<int,int>,int>&mp){
    //     int n = arr.size();
    //     vector<vector<int>>&dp(n+1,)
    // }


    int mctFromLeafValues(vector<int>& arr) {
        //from i to j maxi map
     map<pair<int,int>,int>maxi;
        for(int i=0;i<arr.size();i++){
            maxi.insert({{i, i}, arr[i]});
            for(int j=i+1; j<arr.size();j++){
                int val =  max(arr[j], maxi[{i,j-1}]);
               maxi.insert({{i, j}, val});
            }
        }


        int n = arr.size();
        

        vector<vector<int>>dp(n,vector<int>(n,-1));
        return solver(arr,maxi,0,n-1,dp);
    }
};
13800