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Problem: Fibonacci Number

Understand how to implement the Fibonacci sequence using recursion combined with memoization to avoid redundant calculations. Explore how this approach improves efficiency from exponential to linear time, while managing space complexity. This lesson helps you write clear and performant recursive solutions in JavaScript by caching intermediate results.

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) ...