Fibonacci series is a number series that contains integers in the following pattern.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ..
In terms of mathematics, the general formula for calculating the Fibonacci series is
fn = fn-1 + fn-2 , where n ≥ 2
Here, f0 = 0 and f1 = 1.
We need to calculate n Fibonacci numbers for any given integer n, where n ≥ 0.
Example:
Input : n = 5
Output : [0, 1, 1, 2, 3]
Input : n = 10
Output : [0, 1, 1, 2, 3, 5, 8, 13, 21, 34]
In this article, we are focusing on two major and common ways for calculating the Fibonacci series.
- Using For loop and While loop
- Using recursion
Using Loop
The method of calculating Fibonacci Series using this method is better as compared to the recursive method. This method makes use of Dynamic Programming which works by storing the number generated so far and then using it for further calculations.
As the number for n=1 and n=2 are fixed, i.e, 0 and 1, then the rest of the numbers in the series can be calculated by the logic,
f3 = f2 + f1
f4 = f3 + f2
f5 = f4 + f3
...
fn = fn-1 + fn-2
This logic can be implemented using for as well as the while loop in JavaScript.
Using for Loop
As the first two values of the series are fixed, we start the loop with i = 2 and iterate until i < n, because array indexing starts at 0, so, n = 1 will technically mean i = 0 in case of arrays.
Javascript
const n = 10;// Create a new array of size 'n'let series = new Array(n);// Fills all places in array with 0series.fill(0);// Seed value for 1st elementseries[0] = 0;// Seed value for 2nd elementseries[1] = 1;for (let i = 2; i < n; i++) { // Apply basic Fibonacci formulae series[i] = series[i - 1] + series[i - 2];}// Print the seriesconsole.log(series); |
[ 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 ]
Using while Loop
Javascript
const n = 10;// Create a new array of size 'n'let series = new Array(n);// Fills all places in array with 0series.fill(0);// Seed value for 1st elementseries[0] = 0;// Seed value for 2nd elementseries[1] = 1;// Initialize the conditional variablelet i = 2;while (i < n) { // Apply basic Fibonacci formulae series[i] = series[i - 1] + series[i - 2]; // Increment the conditional variable i++;}// Print the seriesconsole.log(series); |
[ 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 ]
Using Recursion
The recursion method to print the whole Fibonacci series till a certain number is not recommended because, recursion algorithm itself is costly in terms of time and complexity, and along with fetching a Fibonacci series number at a certain position, we need to store them in an array, which calls the recursive function again and again for each and every element, i.e, n times!
The recursion method can be applied as follows in JavaScript.
Javascript
function fibonacci(n) { // Return value for n = 1 if (n == 1) return 0; // Return value for n = 2 if (n == 2) return 1; // Recursive call return fibonacci(n - 1) + fibonacci(n - 2);}const n = 10;// Create a new array of size 'n'let series = new Array(n);// Fills all places in array with 0series.fill(0);for (let i = 1; i <= n; i++) { // Store i-th Fibonacci number series[i - 1] = fibonacci(i);}// Print the seriesconsole.log(series); |
[ 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 ]
