Skip to content
LEETFLIX

Find the Maximum Sum of Node Values

HardArrayDPGreedyBitmaskTreeSorting
Solve on LeetCode

Hard · dynamic programming solution for Find the Maximum Sum of Node Values. Python, Go, and a step-by-step animation.

01

Problem

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

LeetCode 3068. Find the Maximum Sum of Node Values. 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

Find the Maximum Sum of Node Values — dynamic programming

Each answer is a combination of smaller answers already in the table. Built for LeetCode 3068. Find the Maximum Sum of Node Values.

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 findTheMaximumSumOfNodeValues(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 “Find the Maximum Sum of Node Values — dynamic programming”. Edit the input, hit Run, then scrub.

Approach: Find the Maximum Sum of Node Values — dynamic programming

Loading animation…