MEDIUM NC#100 Dynamic Programming 1D
746. Min Cost Climbing Stairs
📖 Problem
Given an array cost where cost[i] is cost of i-th step, you can start from step 0 or step 1. Find minimum cost to reach top of floor (beyond last step).
🧠 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 Recursion reasoning pattern
💡 Approach
- → dp[i] = min cost to reach step i
- → dp[i] = min(dp[i-1] + cost[i-1], dp[i-2] + cost[i-2])
- → Can start from step 0 or 1 with no initial cost
- → Time: O(n), Space: O(n) or O(1) optimized
🧭 Prerequisites
🛠️ Hints & Pitfalls
Hints
- •dp[i] = min cost to reach step i
- •dp[i] = min(dp[i-1] + cost[i-1], dp[i-2] + cost[i-2])
- •Can start from step 0 or 1 with no initial cost
Common Pitfalls
- •Time: O(n), Space: O(n) or O(1) optimized
🧪 Test Cases
Test Case 1
Not run Input:
minCostClimbingStairs([10,15,20]); Expected:
15 Test Case 2
Not run Input:
minCostClimbingStairs([1,100,1,1,1,100,1,1,100,1]); Expected:
6 Test Case 3
Not run Input:
minCostClimbingStairs(cost: number[]); Expected:
Computed from hidden reference 📝 Code Editor
📤 Output