<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 n= 50;
int v[43][43];
vector<vector<int>>dp;
    int mctFromLeafValues(vector<int>& a) {
        int n=a.size();
        dp=vector<vector<int>>(n+10, vector<int>(n+10, -1));
        for(int i=0;i<n;i++){
            v[i][i] = a[i];
            for(int j=i+1;j<n;j++){
                v[i][j] = max(v[i][j-1], a[j]);
            }
        }
        return sol(0, n-1, a);
    }

    int sol(int i, int j, vector<int>& a){
        if(i==j) return 0;
        if(dp[i][j]!=-1) return dp[i][j];
        int res= 100000;
        for(int ind=i;ind<=j-1;ind++){
            res = min(res, sol(i, ind, a)+v[i][ind]*v[ind+1][j]+sol(ind+1,j, a));
        }
        return dp[i][j] = res;

    }
};
12000