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Solution: Fibonacci Number

Explore how to compute Fibonacci numbers efficiently by applying mathematical properties such as Binet’s formula and the golden ratio. Understand the drawbacks of recursive and dynamic programming approaches, and learn to implement a logarithmic time algorithm with constant space that leverages a closed-form expression for fast computation of Fibonacci numbers.

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Statement

The Fibonacci sequence is a famous series of numbers in which each value is created by adding the two preceding numbers. The sequence begins with:

  • F(0)=0F(0) = 0

  • F(1)=1F(1) = 1

From that point on, every term is defined as:

  • F(n)=F(n−1)+F(n−2)F(n) = F(n - 1) + F(n - 2), for any nn greater than 11 ...