Climbing Stairs LeetCode Solution in JavaScript and TypeScript
The Climbing Stairs problem is a fundamental algorithmic challenge that introduces developers to dynamic programming concepts. This comprehensive guide will walk you through various approaches to solve this popular LeetCode problem (#70) using TypeScript, while explaining the underlying concepts and optimization techniques. For more on JavaScript fundamentals, check out our guide on base64 encoding in JavaScript.
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?
Example 1:
Example 2:
Understanding the Problem
The Climbing Stairs problem is essentially a variation of the Fibonacci sequence. The key insight is that to reach any step n, you can only come from either step (n-1) or step (n-2). Therefore, the total number of ways to reach step n is the sum of ways to reach step (n-1) and step (n-2). For more on problem-solving patterns, check out our guide on longest palindromic substring solution.
There are several approaches to solve this problem:
- Recursive Solution (Time: O(2ⁿ), Space: O(n))
- Dynamic Programming (Time: O(n), Space: O(n))
- Optimized Dynamic Programming (Time: O(n), Space: O(1))
- Mathematical Solution using Fibonacci (Time: O(n), Space: O(1))
Let's implement each approach and discuss their trade-offs.
TypeScript Implementation
1. Recursive Solution (Not Recommended for Large Inputs)
While this solution is intuitive, it has exponential time complexity and will timeout for larger inputs due to redundant calculations.
2. Dynamic Programming Solution
3. Space-Optimized Solution (Recommended)
Code Analysis and Complexity
Let's analyze our optimized solution:
Time Complexity
- O(n) - We iterate through the steps once
- No recursive calls or redundant calculations
Space Complexity
- O(1) - We only use three variables regardless of input size
- No additional data structures needed
Understanding the Mathematics
The solution follows the Fibonacci sequence pattern:
- F(n) = F(n-1) + F(n-2)
- For n steps: ways(n) = ways(n-1) + ways(n-2)
Sequence for first few steps:
- n = 1: 1 way
- n = 2: 2 ways
- n = 3: 3 ways
- n = 4: 5 ways
- n = 5: 8 ways
Performance Optimization Tips
-
Memoization
- Use memoization for recursive solutions
- Cache previously calculated results
-
Variable Optimization
- Use number type instead of bigint unless necessary
- Avoid array allocation for simple cases
-
Early Returns
- Handle base cases immediately
- Validate input constraints
Common Edge Cases and Input Validation
Related Problems
- House Robber (LeetCode #198)
- Fibonacci Number (LeetCode #509)
- Min Cost Climbing Stairs (LeetCode #746)
Interview Tips
When solving this problem in an interview:
- Start with the brute force approach to show problem-solving process
- Explain the optimization steps clearly
- Discuss space-time complexity trade-offs
- Consider edge cases and input validation
- Mention real-world applications of similar patterns
Related Resources
JavaScript and TypeScript
Algorithm Patterns
Problem Solving
Conclusion
The Climbing Stairs problem is an excellent introduction to dynamic programming and optimization techniques. While the problem may seem simple at first, it teaches important concepts about algorithm optimization and the relationship between recursive and iterative solutions.
Understanding this problem helps build a strong foundation for more complex dynamic programming challenges and demonstrates the importance of recognizing patterns in algorithmic problem-solving.