Introduction to Fibonacci Numbers

The enigmatic Fibonacci sequence: many of you have crossed paths with this numerical series before, possibly while exploring recursion. Today, we delve into how this seemingly simple sequence can serve as an excellent introduction to the powerhouses of computer science—dynamic programming and memoization.

The Mathematical Definition of Fibonacci Numbers

The Fibonacci sequence is mathematically defined as follows:

Code Snippets in Multiple Languages

To solidify your understanding, let's translate this mathematical definition into several programming languages.

1// Base case for n = 0
2if (n === 0) return 0;
3// Base case for n = 1
4if (n === 1) return 1;
5// Recursive case for n > 1
6return f(n-1) + f(n-2);

Sequence Unveiled

By applying the above code, you'll generate a sequence like so:

10, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

Pseudocode: The Blueprint of Fibonacci

Pseudocode is a programmer's sketchbook. It helps you outline your logic before jumping into the code. For the Fibonacci sequence, our pseudocode would look something like this:

Base Case

1. If $n=0$, return 0.
2. If $n=1$, return 1.

Recursive Case

1. Calculate $f(n-1)$ and store it in temp1.
2. Calculate $f(n-2)$ and store it in temp2.
3. Return temp1 + temp2.

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function f(n) {

   if(n==0) return 0;

   if(n==1) return 1;

   var temp1 = f(n-1);

   var temp2 = f(n-2);

   return temp1 + temp2;

}