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 ắ t đầ u gi ả i thu ậ t Fibonacci ( n ) khai b á o f 0 , f 1 , fib , loop Thi ế t l ậ p f 0 l à 0 Thi ế t l ậ p f 1 l à 1 hi ể n th ị f 0 , f 1 for loop ← 1 t ớ i n fib ← f 0 + f 1 f 0 ← f 1 f 1 ← fib hi ể n th ị d ã y fib k ế t th ú c for K ế t th ú c gi ả i thu ậ 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 ắ t đầ u gi ả i thu ậ t Fibonacci ( n ) khai b á o f 0 , f 1 , fib , loop Thi ế t l ậ p f 0 l à 0 Thi ế t l ậ p f 1 l à 1 hi ể n th ị f 0 , f 1 for loop ← 1 t ớ i n fib ← f 0 + f 1 f 0 ← f 1 f 1 ← fib hi ể n th ị d ã y fib k ế t th ú c for K ế t th ú c gi ả i thu ậ t 

According to Tutorialspoint

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