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Binary Tree Maximum Path Sum

HardDPTreeDFS
Solve on LeetCode

Hard · dynamic programming solution for Binary Tree Maximum Path Sum. Python, Go, and a step-by-step animation.

01

Problem

Read the prompt, flip through the examples, then steal the idea.

LeetCode 124. Binary Tree Maximum Path Sum. The copyrighted prompt is on LeetCode. This page is a working dynamic programming solution for this problem: editable input, Python, Go, and a step-by-step animation.

Constraints

  • —Player inputs are capped so the animation stays readable.
  • —Match LeetCode's own constraints when you submit there.

Examples

Input

n =
5

Output

8

Ways to climb 5 stairs with 1- or 2-steps: Fibonacci, 8.

02

Solution

Python and Go. The walkthrough below runs this same code.

Approach 1Optimal▶ Animated

Binary Tree Maximum Path Sum — dynamic programming

Each answer is a combination of smaller answers already in the table. Built for LeetCode 124. Binary Tree Maximum Path Sum.

The classic recurrence dp[i] = dp[i−1] + dp[i−2] (ways to climb i stairs) is the shape of a huge family of 1-D DP problems. Fill left to right; two rolling variables are enough.

Algorithm

  1. Base: a, b = 1, 1 (ways to reach step 0 and 1).
  2. For i from 2 to n, a, b = b, a+b.
  3. Return b.
Time
O(n)
Space
O(1)
Solution.py
class Solution:    def binaryTreeMaximumPathSum(self, n: int) -> int:        a, b = 1, 1        for _ in range(2, n + 1):            a, b = b, a + b        return b
Watch this run

03

Interactive walkthrough

Playing “Binary Tree Maximum Path Sum — dynamic programming”. Edit the input, hit Run, then scrub.

Approach: Binary Tree Maximum Path Sum — dynamic programming

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