<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 findanswer(vector<int>&arr,int lb,int ub,vector<vector<int>>&dp)
{
    if(lb==ub)
    {
        return 0;
    }
    if(dp[lb][ub]!=-1)
    {
        return dp[lb][ub];
    }
    
    int ans=INT_MAX;
    int maxi1=INT_MIN;
    int maxi2=INT_MIN;
    for(int j=lb;j<=ub-1;j++)
    {
        if(arr[j]>maxi1)
        {
            maxi1=arr[j];
        }
        int ans1=findanswer(arr,lb,j,dp);
        int ans2=findanswer(arr,j+1,ub,dp);
        for(int x=j+1;x<=ub;x++)
        {
            maxi2=max(maxi2,arr[x]);
        }
         ans=min(ans,ans1+ans2+maxi1*maxi2);
        



        

    }
    return dp[lb][ub]=ans;

}
    int mctFromLeafValues(vector<int>& arr) {
        int lb=0;
        vector<vector<int>>dp(arr.size()+1,vector<int>(arr.size()+1,-1));
        int ub=arr.size()-1;
        return findanswer(arr, lb, ub,dp);
        
    }
};
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