Minimum Cost Tree From Leaf Values
Given an array arr of positive integers, consider all binary trees such that:
- Each node has either
0or2children. - The values of
arrcorrespond 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
32There are two possible trees; the first has a non-leaf node sum of 36, and the second has a non-leaf node sum of 32.
Example 2
Input
arr = [4,11]Output
44With leaves 4 and 11, the only non-leaf node has value 4 * 11 = 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 2^31).