Fibonacci Series in Java

Fibonacci Series in java is a series of increasing numbers where the first two terms are 0 and 1 respectively. All other subsequent terms are obtained by adding the last two terms before them.

Mathematically,

Let f(n) returns us the nth fibonacci number

$f(0)=0; f(1)=1;$

$f(n)=f(n-1)+f(n-2);$

There are several methods to write the Fibonacci series. In this article, we will discuss the following methods in detail:

1. Fibonacci Series in Java Using for Loop
2. Fibonacci Series in Java Using while Loop
3. Fibonacci Series in Java Using Iterative Approach
4. Fibonacci Series in Java Using recursion
5. Fibonacci Series in Java Using Dynamic Programming

Fibonacci Series in Java Using for Loop

Output:

Explanation:

The Java program calculates the nth number of the Fibonacci sequence, taking n as input from the user.

It initializes an integer array of size $n$ to store the Fibonacci sequence and uses a for loop to calculate the remaining elements. Finally, it prints the nth Fibonacci number to the console.

Time Complexity

O(N) - (Linear Time Complexity)

This is because, for finding the nth Fibonacci number, we move through an array of size n (actually, we are moving $n-2$ indices in the array).

Space Complexity

O(N)

Fibonacci Series in Java Using while Loop

Output:

Explanation:

The Java program calculates the nth number of the Fibonacci sequence using a while loop instead of a for loop.

It takes n as input from the user and initializes an integer array of size n to store the Fibonacci sequence. The loop condition i < n is used to calculate the remaining elements of the sequence. Finally, it prints the nth Fibonacci number to the console.

Time Complexity

O(N) - (Linear Time Complexity)

This is because, to find the nth Fibonacci number, we move through an array of size n (actually, we are moving n-2 indices in the array) using a while loop.

Space Complexity

O(N)

Fibonacci Series in Java Using Iterative Approach

Output:

Explanation: The above program generates and prints the Fibonacci series up to 15 terms using the previous two Fibonacci values iteratively.

Time Complexity

O(N) - (Linear Time Complexity)

Space Complexity

O(1)

Fibonacci Series in Java Using recursion

The function returns the nth Fibonacci number by recursively calling itself for previous values until the input becomes less than or equal to 2. By calling this function to compute each Fibonacci number, we can print the Fibonacci series.

Output:

Explanation: In the above example, we defined a recursive function fib to get nth Fibonacci number and call it repeatedly (for i = 0 to i = 8) to create a Fibonacci series of length 9.

Read to know more about Fibonacci Series Using recursion in Java

Time Complexity

The Time Complexity is $O(2^n)$, i.e. exponential time.

Space Complexity

O(1)

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Fibonacci Series in Java Using Dynamic Programming

Output:

Explanation: In the above program, we use the tabulation method of dynamic programming to calculate the Fibonacci series. It stores the value of the Fibonacci term in the array and calculates further values using the previous two values.

Time Complexity

O(N)

Space Complexity

O(N)