花花酱 LeetCode 1339. Maximum Product of Splitted Binary Tree

Given a binary tree root. Split the binary tree into two subtrees by removing 1 edge such that the product of the sums of the subtrees are maximized.

Since the answer may be too large, return it modulo 10^9 + 7.

Example 1:

Input: root = [1,2,3,4,5,6]
Output: 110
Explanation: Remove the red edge and get 2 binary trees with sum 11 and 10. Their product is 110 (11*10)

Example 2:

Input: root = [1,null,2,3,4,null,null,5,6]
Output: 90
Explanation:  Remove the red edge and get 2 binary trees with sum 15 and 6.Their product is 90 (15*6)

Example 3:

Input: root = [2,3,9,10,7,8,6,5,4,11,1]
Output: 1025

Example 4:

Input: root = [1,1]
Output: 1

Constraints:

• Each tree has at most 50000 nodes and at least 2 nodes.
• Each node’s value is between [1, 10000].

Solution: Recursion

Two passes:
First pass, compute the sum of the entire tree S.
Second pass, for each node, compute the sum of left/right subtree S_l, S_r.
ans = max{(S – S_l) * S_l, (S – S_r) * S_r}

Time complexity: O(n)
Space complexity: O(n)