What is the optimal time complexity of solving Count ways to reach nth stair?

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 Count ways to reach nth stair?

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 Count ways to reach nth stair?

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 Count ways to reach nth stair?

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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Competitive ProgrammingEasy

Count ways to reach nth stair

Learn how to solve the 'Count ways to reach nth stair' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function count_ways_stair(n) that returns the number of distinct ways to climb n stairs. Each time you can either climb 1 or 2 steps.

Constraints

•1 <= n <= 50

Examples

Example 1

Input

count_ways_stair(3)

Output

Explanation

There are three ways: 1+1+1, 1+2, and 2+1.

Example 2

Input

count_ways_stair(4)

Output

Explanation

There are five ways: 1+1+1+1, 1+1+2, 1+2+1, 2+1+1, 2+2.

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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