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Maximum Number of Points with Cost

MediumArrayDPMatrix
Solve on LeetCode

Medium · dynamic programming solution for Maximum Number of Points with Cost. Python, Go, and a step-by-step animation.

01

Problem

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

LeetCode 1937. Maximum Number of Points with Cost. 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

Maximum Number of Points with Cost — dynamic programming

Each answer is a combination of smaller answers already in the table. Built for LeetCode 1937. Maximum Number of Points with Cost.

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 maximumNumberOfPointsWithCost(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 “Maximum Number of Points with Cost — dynamic programming”. Edit the input, hit Run, then scrub.

Approach: Maximum Number of Points with Cost — dynamic programming

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