Fibonacci Series in Data Structures and Algorithms

What is the Fibonacci sequence?

The Fibonacci sequence creates numbers by adding two numbers in front. Fibonacci series start from two numbers: F0 & F1. The initial value of F0 & F1 may be 0, 1 or 1, 1, respectively.

The condition of the Fibonacci sequence is:

F n = F n-1 + F n-2 

Example of a Fibonacci sequence:

F ₈ = 0 1 1 2 3 5 8 13

Example of another Fibonacci sequence:

F ₈ = 1 1 2 3 5 8 13 21

Below is an illustration of the Fibonacci sequence on:

The algorithm uses a loop for the Fibonacci sequence

First, our algorithm will use the loop to create the Fibonacci sequence:

 B ? t ?? u gi ? i thu ? t Fibonacci ( n ) khai b á o f 0 , f 1 , fib , loop Thi ? t l ? p f 0 l à 0 Thi ? t l ? p f 1 l à 1 hi ? n th ? f 0 , f 1 for loop ? 1 t ? i n fib ? f 0 + f 1 f 0 ? f 1 f 1 ? fib hi ? n th ? d ã y fib k ? t th ú c for K ? t th ú c gi ? i thu ? t 

The algorithm uses recursion for the Fibonacci sequence

Next, based on recursion we will design the algorithm for the Fibonacci sequence as follows:

 B ? t ?? u gi ? i thu ? t Fibonacci ( n ) khai b á o f 0 , f 1 , fib , loop Thi ? t l ? p f 0 l à 0 Thi ? t l ? p f 1 l à 1 hi ? n th ? f 0 , f 1 for loop ? 1 t ? i n fib ? f 0 + f 1 f 0 ? f 1 f 1 ? fib hi ? n th ? d ã y fib k ? t th ú c for K ? t th ú c gi ? i thu ? t