Minimum Cost Tree From Leaf Values — LeetCode 1130 Python Solution

The problem

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.

Example

Input

arr = [6,2,4]

Output

32

Explanation

There are two possible trees shown.

Python solution

class Solution:
    def mctFromLeafValues(self, arr: List[int]) -> int:
        @cache
        def dfs(i: int, j: int) -> Tuple:
            if i == j:
                return 0, arr[i]
            s, mx = inf, -1
            for k in range(i, j):
                s1, mx1 = dfs(i, k)
                s2, mx2 = dfs(k + 1, j)
                t = s1 + s2 + mx1 * mx2
                if s > t:
                    s = t
                    mx = max(mx1, mx2)
            return s, mx

        return dfs(0, len(arr) - 1)[0]

Complexity

Pattern: Stack

When the most recent unresolved thing is the one that matters, use a stack. LeetCode 1130. Minimum Cost Tree From Leaf Values is filed here because LeetCode tags it Stack, which is the vocabulary this hub collects.

The stack guide has the Python template for the pattern and the 194 LeetCode problems that use it.

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