Climbing Stairs
Detailed guide and Python implementation for the 'Climbing Stairs' problem.
1. Concept Overview
The 'Climbing Stairs' problem is a key challenge in the 1D DP section.
This implementation focuses on medium-level logic in Python.
We prioritize technical accuracy and code readability in our provided solutions.
2. Real-World Applications
3. Visual Intuition
Visualizing the logic flow for Climbing Stairs.
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
Read the problem statement for Climbing Stairs carefully.
2. Formulate brute force
Draft a simple iterative solution.
3. Identify inefficiency
Look for redundant calculations.
4. Optimize search path
Use hashing or sorting to speed up the process.
5. Final Implementation
Clean up the code for production standards.
Problem Statement
You are climbing a staircase. It takes n steps to reach the top.
Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?
Write a function climbStairs(n: int) -> int.
- •1 <= n <= 45
Examples
n = 2
2
There are two ways to climb: 1+1 steps, or 2 steps.
n = 3
3
There are three ways: 1+1+1 steps, 1+2 steps, or 2+1 steps.
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
Ready to Solve?
Open the problem in PyRun's browser-based Python editor. Your code runs fully offline — no server required.
Interview Insights & Variations
Complexity Analysis Breakdown
Why Time: Directly evaluates all possibilities.
Why Space: Uses standard local memory.
Why Time: Optimized paths reduce total operations.
Why Space: May trade memory for speed.
Optimized Solution Python Code
Optimized Solution Python Code
def climb_stairs_opt(n):
one, two = 1, 1
for i in range(n - 1):
one, two = one + two, one
return oneBrute Force Code (Spoiler Guarded)
Brute Force Code (Spoiler Guarded)
def climb_stairs_brute(n):
if n <= 2: return n
return climb_stairs_brute(n-1) + climb_stairs_brute(n-2)Algorithm Pattern Checklist
When dealing with 1D DP data patterns.
Core Prerequisites
Revision Key Notes
Common Mistakes & Pitfalls
Related Questions
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