Recursive Functions

Recursive functions are functions that call themselves. They are an important concept in programming, especially in the context of recursion. By calling themselves, recursive functions create recursive algorithms, which are algorithms that solve a problem by breaking it down into smaller instances of the same problem.

Recursive functions have two main components:

1. Base Case: This is the condition that determines when the recursion should stop. It is the simplest form of the problem that can be solved directly without further recursion.

2. Recursive Case: This is the condition where the function calls itself with a modified input. It represents the step towards the base case, taking the problem closer to its simplest form.

Let's take a look at an example to better understand recursive functions. Consider a function countDown that prints the numbers from a given number down to 1:

1public class Main {
2  public static void countDown(int n) {
3    // Base case: If n is less than or equal to 1, print n and return
4    if (n <= 1) {
5      System.out.println(n);
6      return;
7    }
8
9    // Recursive case: Print n and call the function with n - 1
10    System.out.println(n);
11    countDown(n - 1);
12  }
13
14  public static void main(String[] args) {
15    // Example call to countDown starting from 5
16    countDown(5);
17  }
18}

When we call countDown(5), it will print the numbers 5, 4, 3, 2, and 1 in that order.

Recursive functions can be a powerful tool for solving problems, as they allow us to express complex problems in a more manageable and elegant way. It's important to ensure that recursive functions have a base case that will eventually be reached, to avoid infinite recursion.

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class Main {

  public static void main(String[] args) {

  // replace with your Java logic here

  for(int i = 1; i <= 5; i++) {

    System.out.println(i);

  }

}

}