Leetcode #1339: Maximum Product of Splitted Binary Tree
In this guide, we solve Leetcode #1339 Maximum Product of Splitted Binary Tree in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
Given the root of a binary tree, split the binary tree into two subtrees by removing one edge such that the product of the sums of the subtrees is maximized. Return the maximum product of the sums of the two subtrees.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Tree, Depth-First Search, Binary Tree
Intuition
We need to explore a structure deeply before backing up, which suits DFS.
DFS keeps local context on the call stack and is easy to implement recursively.
Approach
Define a recursive DFS that carries the necessary state.
Combine child results as the recursion unwinds.
Steps:
- Define a recursive DFS with state.
- Visit children and combine results.
- Return the final aggregation.
Example
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)
Python Solution
# Definition for a binary tree node.
# class TreeNode:
# def __init__(self, val=0, left=None, right=None):
# self.val = val
# self.left = left
# self.right = right
class Solution:
def maxProduct(self, root: Optional[TreeNode]) -> int:
def sum(root: Optional[TreeNode]) -> int:
if root is None:
return 0
return root.val + sum(root.left) + sum(root.right)
def dfs(root: Optional[TreeNode]) -> int:
if root is None:
return 0
t = root.val + dfs(root.left) + dfs(root.right)
nonlocal ans, s
if t < s:
ans = max(ans, t * (s - t))
return t
mod = 10**9 + 7
s = sum(root)
ans = 0
dfs(root)
return ans % mod
Complexity
The time complexity is , and the space complexity is , where is the number of nodes in the binary tree. The space complexity is , where is the number of nodes in the binary tree.
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.