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Solution: Fibonacci Number

Explore how to calculate Fibonacci numbers using mathematical concepts such as the golden ratio and Binet’s formula. Learn an optimized approach that runs in logarithmic time with constant space, improving over basic recursive and dynamic programming solutions. This lesson helps you apply math-based optimization to improve algorithm performance in coding interviews.

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(n1)+F(n2)F(n) = F(n - 1) + F(n - 2), for any nn greater than 11 ...