Java Recursion

Java Recursion

Recursion is the technique of making a function call itself. This technique provides a way to break complicated problems down into simpler problems which are easier to solve.

Recursion may be a bit difficult to understand. The best way to figure out how it works is to experiment with it.

Recursion Example

Adding two numbers together is easy to do, but adding a range of numbers is more complicated. In the following example, recursion is used to add a range of numbers together by breaking it down into the simple task of adding two numbers:

public class Main {
  public static int sum(int k) {
    if (k > 0) {
      return k + sum(k - 1);
    } else {
      return 0;
    }
  }

  public static void main(String[] args) {
    int result = sum(10);
    System.out.println(result);
  }
}

Example Explained

When the sum() method is called, it adds parameter k to the sum of all numbers smaller than k and returns the result. When k becomes 0, the method just returns 0. When running, the program follows these steps:

10 + sum(9)
10 + ( 9 + sum(8) )
10 + ( 9 + ( 8 + sum(7) ) )
...
10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 + sum(0)
10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 + 0

Since the method does not call itself when k is 0, the program stops there and returns the result.

Halting Condition

Just as loops can run into the problem of infinite looping, recursive methods can run into the problem of infinite recursion. Infinite recursion is when the method never stops calling itself. Every recursive method should have a halting condition, which is the condition where the method stops calling itself. In the previous example, the halting condition is when the parameter k becomes 0.

It is helpful to see a variety of different examples to better understand the concept. In this example, the method adds a range of numbers between a start and an end. The halting condition for this recursive method is when end is not greater than start:

public class Main {
  public static int sum(int start, int end) {
    if (end > start) {
      return end + sum(start, end - 1);
    } else {
      return end;
    }
  }

  public static void main(String[] args) {
    int result = sum(5, 10);
    System.out.println(result);
  }
}

Countdown with Recursion

This example demonstrates how to use recursion to create a countdown function:

public class Main {
  static void countdown(int n) {
    if (n > 0) {
      System.out.print(n + " ");
      countdown(n - 1);
    }
  }

  public static void main(String[] args) {
    countdown(5);
  }
}

The method calls itself with n - 1 until n becomes 0.

Calculate Factorial with Recursion

This example uses a recursive method to calculate the factorial of 5:

public class Main {
  static int factorial(int n) {
    if (n > 1) {
      return n * factorial(n - 1);
    } else {
      return 1;
    }
  }

  public static void main(String[] args) {
    System.out.println("Factorial of 5 is " + factorial(5));
  }
}

Factorial means multiplying a number by every number below it, down to 1. For example, the factorial of 5 is: 5 * 4 * 3 * 2 * 1 = 120. By definition, 0! is also 1.