MediumNo. 1339
Maximum Product of Splitted Binary Tree — LeetCode 1339 Python Solution
- Pattern
- Tree Traversal
- Topics
- Tree, Depth-First Search, Binary Tree
- Reading time
- 5 min
- Source
- leetcode.com
The problem
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.
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 % modComplexity
- Time
- O(n)
- Space · auxiliary
- O(n)where n is the number of nodes in the binary tree
Pattern: Tree Traversal
Choose the order — preorder, inorder, postorder, level — and the problem solves itself. LeetCode 1339. Maximum Product of Splitted Binary Tree is filed here because LeetCode tags it Tree and Binary Tree, which is the vocabulary this hub collects.
The tree traversal guide has the Python template for the pattern and the 225 LeetCode problems that use it.
Related problems
| No. | Problem | Difficulty |
|---|---|---|
| 0098 | Validate Binary Search Tree | Medium |
| 0099 | Recover Binary Search Tree | Medium |
| 0100 | Same Tree | Easy |
| 0101 | Symmetric Tree | Easy |
| 0104 | Maximum Depth of Binary Tree | Easy |
| 0110 | Balanced Binary Tree | Easy |
Frequently asked questions
- How hard is LeetCode 1339. Maximum Product of Splitted Binary Tree?
LeetCode 1339. Maximum Product of Splitted Binary Tree is rated Medium on LeetCode.
- What is the time complexity of LeetCode 1339. Maximum Product of Splitted Binary Tree?
The Python solution on this page runs in O(n).
- What is the space complexity of LeetCode 1339. Maximum Product of Splitted Binary Tree?
The Python solution on this page uses O(n), where n is the number of nodes in the binary tree auxiliary space.
- What topics does LeetCode 1339. Maximum Product of Splitted Binary Tree cover?
LeetCode 1339. Maximum Product of Splitted Binary Tree is tagged Tree, Depth-First Search and Binary Tree on LeetCode.