Find Nth Fibonacci Number()

Step 1: Understanding the Task

The task is to write a Java function to find the nth Fibonacci number. The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones, usually starting with 0 and 1. Therefore, the sequence goes: 0, 1, 1, 2, 3, 5, 8, 13, …

The function should take an integer 'n' as argument and return nth Fibonacci number.

Let's start by writing the function signature as follow:

public static int fibonacci(int n){

}

Step 2: Base Cases

The base cases for the Fibonacci sequence are the first and second number. We know that the first and second number of the series are 0 and 1. Let’s add this base case to our function:

public static int fibonacci(int n) {
  if(n <= 1){
    return n;
  }
}

Step 3: Recursion

For n > 1, we can use a recursive call to calculate the nth Fibonacci number. The nth Fibonacci number is the sum of (n-1)th and (n-2)th Fibonacci number. Hence, we add the following line to our function:

else {
  return fibonacci(n - 1) + fibonacci(n - 2);
}

Step 4: Full Function

Combining all above steps, here is the full function:

public static int fibonacci(int n) {
  if(n <= 1){
    return n;
  }
  else {
    return fibonacci(n - 1) + fibonacci(n - 2);
  }
}

Conclusion

That's it! You just wrote a function to calculate the nth Fibonacci number using recursion in Java. This is a simple example of how recursion works. However, it's important to note that this function is not optimal for large numbers because the same subproblems are solved multiple times. However, for small numbers, this function works perfectly fine.