What is the optimal time complexity of solving Min Cost Climbing Stairs?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Min Cost Climbing Stairs?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Min Cost Climbing Stairs?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Min Cost Climbing Stairs?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Min Cost Climbing Stairs

Learn how to solve the 'Min Cost Climbing Stairs' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Medium

You are given an integer array cost where cost[i] is the cost of ith step on a staircase. Once you pay the cost, you can either climb one or two steps.

You can either start from the step with index 0, or the step with index 1.

Return the minimum cost to reach the top of the floor.

Write a function minCostClimbingStairs(cost: List[int]) -> int.

Constraints

•2 <= len(cost) <= 1000
•0 <= cost[i] <= 999

Examples

Example 1

Input

cost = [10,15,20]

Output

Explanation

Start at index 1, pay 15, and climb to the top. Total is 15.

Example 2

Input

cost = [1,100,1,1,1,100,1,1,100,1]

Output

Explanation

Start at index 0, pay 1, climb to 2, pay 1, climb to 4, pay 1, climb to 6, pay 1, climb to 7, pay 1, climb to 9, pay 1, climb to top. Total is 6.

Need a Hint?

Define subproblem states, establish the recurrence relation, and use memoization (top-down) or tabulation (bottom-up).

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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