EASY NC#99 Blind #16 1-D Dynamic Programming
70. Climbing Stairs
📖 Problem
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?
🧠 Visual Learning Aid
1 Model the input into the right structure
2 Choose the core technique and invariant
3 Execute step-by-step with a sample
4 Validate complexity and edge cases
JS/TS Refreshers
- •Array methods (`push`, `pop`, `shift`, `slice`)
- •Object/Map/Set usage patterns
- •Function parameter and return typing
- •Array DP table updates
- •State transition thinking
- •Base case initialization
Logical Thinking Concepts
- •Define invariants before coding
- •Check edge cases first (`[]`, single element, duplicates)
- •Estimate time/space before implementation
- •Apply Dynamic Programming reasoning pattern
- •Apply DFS reasoning pattern
- •Apply Recursion reasoning pattern
💡 Approach
- → Ways to reach step i = ways to reach step i-1 + ways to reach step i-2
- → Base cases: dp[0] = 1 (1 way to stay), dp[1] = 1 (1 way to take 1 step)
- → Time: O(n), Space: O(n) or O(1) with optimization
- → This is essentially Fibonacci sequence
🛠️ Hints & Pitfalls
Hints
- •Ways to reach step i = ways to reach step i-1 + ways to reach step i-2
- •Base cases: dp[0] = 1 (1 way to stay), dp[1] = 1 (1 way to take 1 step)
- •Time: O(n), Space: O(n) or O(1) with optimization
Common Pitfalls
- •This is essentially Fibonacci sequence
🧪 Test Cases
Hidden tests on submit: 4
Test Case 1
Not run Input:
climbStairs(2); Expected:
2 Test Case 2
Not run Input:
climbStairs(3); Expected:
3 Test Case 3
Not run Input:
climbStairs(5); Expected:
8 📝 Code Editor
📤 Output