public class Solution
extends Object
1130 - Minimum Cost Tree From Leaf Values\.
Medium
Given an array `arr` of positive integers, consider all binary trees such that:
* Each node has either `0` or `2` children;
* The values of `arr` correspond to the values of each **leaf** in an in-order traversal of the tree.
* The value of each non-leaf node is equal to the product of the largest leaf value in its left and right subtree, respectively.
Among all possible binary trees considered, return _the smallest possible sum of the values of each non-leaf node_. It is guaranteed this sum fits into a **32-bit** integer.
A node is a **leaf** if and only if it has zero children.
**Example 1:**
**Input:** arr = [6,2,4]
**Output:** 32
**Explanation:** There are two possible trees shown. The first has a non-leaf node sum 36, and the second has non-leaf node sum 32.
**Example 2:**
**Input:** arr = [4,11]
**Output:** 44
**Constraints:**
* `2 <= arr.length <= 40`
* `1 <= arr[i] <= 15`
* It is guaranteed that the answer fits into a **32-bit** signed integer (i.e., it is less than 231).