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Fibonacci with Four Approaches is a easy coding interview question covering dynamic programming, recursion — the kind asked at FAANG (Facebook/Meta, Apple, Amazon, Netflix, Google) and AI-first companies like Anthropic, OpenAI, and Nvidia.
Implement the n-th Fibonacci number (F(0)=0, F(1)=1, F(n)=F(n-1)+F(n-2)) using four approaches and analyze each:
1. Naive recursion: O(2^n) time 2. Memoized recursion: O(n) time, O(n) space 3. Bottom-up DP: O(n) time, O(n) space 4. Space-optimized: O(n) time, O(1) space
Example: fib(10) = 55, fib(20) = 6765
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