What is the optimal time complexity of solving 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 Climbing Stairs?

The space complexity is O(n) 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 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 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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Climbing Stairs

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

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Problem Statement

Medium

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?

Constraints

•1 <= n <= 45

Examples

Example 1

Input

n = 2

Output

Explanation

There are two ways to climb to the top: 1. 1 step + 1 step, 2. 2 steps.

Example 2

Input

n = 3

Output

Explanation

There are three ways to climb to the top: 1. 1 step + 1 step + 1 step, 2. 1 step + 2 steps, 3. 2 steps + 1 step.

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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