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Fibonacci Numbers

Explore how to calculate Fibonacci numbers using both naive recursion and efficient iterative methods. Understand the time and space complexity differences and learn dynamic programming techniques to optimize your solutions for coding interviews.

Statement

Implement a function to find the nth^{th} Fibonacci number in the Fibonacci sequence.

Fibonacci numbers form a sequence known as the Fibonacci sequence, where each number is the sum of two preceding ones, starting from 00 and 11.

The Fibonacci numbers are defined as:

  • F0=0F_0= 0
  • F1=1F_1= 1
  • Fn=Fn1+Fn2F_n= F_{n-1} + F_{n-2}, for n2n \geq 2

Based on the definition above, the first 1010 Fibonacci numbers starting, from the ...