<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 solve(vector<int>& arr, int s, int e, map<pair<int,int>,int>& m, vector<vector<int>>& dp)
    {
        // if(s>e)
        //     return 0;
        if(s==e)
            return 0;
        if(dp[s][e]!=-1)
            return dp[s][e];
        int sum=1e9;
        for(int i=s;i<e;i++)
        {
            sum=min(sum,m[{s,i}]*m[{i+1,e}]+solve(arr,s,i,m,dp)+solve(arr,i+1,e,m,dp));
        }
        return dp[s][e]=sum;
    }
    int mctFromLeafValues(vector<int>& arr) {
        int n = arr.size();
        map<pair<int,int>,int> m;
        vector<vector<int>> dp(n,vector<int>(n,-1));
        int max_val;
        for(int i=0;i<n;i++)
        {
            m[{i,i}]=arr[i];
            max_val=arr[i];
            for(int j=i+1;j<n;j++)
            {
                max_val=max(max_val,arr[j]);
                m[{i,j}]=max_val;
            }
        }
        return solve(arr,0,n-1,m,dp);
    }
};
14800