What is the optimal time complexity of solving Fibonacci Numbers?

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 Fibonacci Numbers?

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 Fibonacci Numbers?

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 Fibonacci Numbers?

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

Fibonacci Numbers

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

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Problem Statement

Easy

Write a function nth_fibonacci(n) that returns the nth Fibonacci number. Assume F(0) = 0 and F(1) = 1.

Constraints

•0 <= n <= 100

Examples

Example 1

Input

nth_fibonacci(9)

Output

Explanation

F(9) is computed as F(8) + F(7) = 21 + 13 = 34.

Example 2

Input

nth_fibonacci(0)

Output

Explanation

F(0) is 0.

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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