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Fibonacci Series in Java: The Fibonacci sequence is a sequence of numbers where each number is the sum of the two preceding ones, beginning with 0 and 1. This article will demonstrate how to generate the Fibonacci sequence in Java up to a specific term, denoted as N, where N represents the specified number.
In the Fibonacci sequence, each subsequent number is the total of the two preceding numbers. For instance, the sequence starts with 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so on. The sequence begins with the numbers 0 and 1.
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There are two methods to develop a program for the Fibonacci sequence in Java:
- Fibonacci Sequence without recursion
- Fibonacci Sequence with recursion
Fibonacci Series in Java without using recursion
- Initialize variables: Start by initializing the first two numbers of the series. Usually, the first two numbers are 0 and 1.
- Use a loop: Use a loop to calculate the next numbers in the series by adding the last two numbers.
- Update variables: Update the variables to hold the last two numbers for the next iteration.
Here’s a Java program to generate the Fibonacci series without using recursion:
public class Fibonacci {
public static void main(String[] args) {
int n = 10; // Number of terms to display
int first = 0, second = 1;
System.out.println("Fibonacci Series without recursion:");
for (int i = 1; i <= n; ++i) {
System.out.print(first + " ");
// Compute the next term
int next = first + second;
// Update variables
first = second;
second = next;
}
}
}Explanation
Variables Initialization:
int first = 0, second = 1;
first and second are initialized to the first two numbers of the Fibonacci series.
Loop through the series:
for (int i = 1; i <= n; ++i) {
System.out.print(first + " ");
int next = first + second;
first = second;
second = next;
}/code>- The loop runs n times to generate n terms of the series.
- System.out.print(first + ” “); prints the current term.
- int next = first + second; calculates the next term in the series.
- first = second; and second = next; update first and second for the next iteration.
Output:
The program will output the first 10 terms of the Fibonacci series:
0 1 1 2 3 5 8 13 21 34
Fibonacci Series using recursion in java
- Define the Base Cases: The first two numbers in the Fibonacci series are 0 and 1. These are our base cases.
- Define the Recursive Case: For any other number in the series, it is the sum of the two preceding numbers. So, fibonacci(n) = fibonacci(n-1) + fibonacci(n-2).
Here’s a simple Java program to calculate the Fibonacci series using recursion:
public class Fibonacci {
// Method to calculate Fibonacci number
public static int fibonacci(int n) {
// Base cases
if (n == 0) {
return 0;
}
if (n == 1) {
return 1;
}
// Recursive case
return fibonacci(n - 1) + fibonacci(n - 2);
}
public static void main(String[] args) {
int number = 10; // Let's find the first 10 Fibonacci numbers
System.out.println("Fibonacci series up to " + number + " terms:");
// Loop to print the Fibonacci series
for (int i = 0; i < number; i++) {
System.out.print(fibonacci(i) + " ");
}
}
}
Explanation of the Code
Method Definition:
- public static int fibonacci(int n): This method takes an integer n and returns the nth Fibonacci number.
- Base Cases:
If n is 0, return 0.
If n is 1, return 1. - Recursive Case:
For any other value of n, the method calls itself with n-1 and n-2, and adds the results.
Main Method:
- int number = 10;: We want to print the first 10 Fibonacci numbers.
- A for loop iterates from 0 to number – 1 and prints the Fibonacci numbers by calling the fibonacci method.
How the Recursion Works
When fibonacci(n) is called:
- If n is 0 or 1, it returns the base case.
- If n is greater than 1, it breaks the problem into smaller subproblems: fibonacci(n-1) and fibonacci(n-2).
- This process continues until it reaches the base cases, and then it combines the results to give the final output.
Example Execution
For fibonacci(5):
- It calls fibonacci(4) and fibonacci(3).
- fibonacci(4) calls fibonacci(3) and fibonacci(2).
- This continues until the base cases are reached, and then the results are summed up step by step.
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