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Number of Ways to Stay in the Same Place After Some Steps

HardDP
Solve on LeetCode

Hard · dynamic programming solution for Number of Ways to Stay in the Same Place After Some Steps. Python, Go, and a step-by-step animation.

01

Problem

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

LeetCode 1269. Number of Ways to Stay in the Same Place After Some Steps. 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

Number of Ways to Stay in the Same Place After Some Steps — dynamic programming

Each answer is a combination of smaller answers already in the table. Built for LeetCode 1269. Number of Ways to Stay in the Same Place After Some Steps.

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 numberOfWaysToStayInTheSamePlaceAfterSomeSteps(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 “Number of Ways to Stay in the Same Place After Some Steps — dynamic programming”. Edit the input, hit Run, then scrub.

Approach: Number of Ways to Stay in the Same Place After Some Steps — dynamic programming

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