Finite and Infinite Recursion with examples

The process in which a function calls itself directly or indirectly is called Recursion and the corresponding function is called a Recursive function. 
Using Recursion, certain problems can be solved quite easily. Examples of such problems are Towers of Hanoi (TOH), Inorder/Preorder/Postorder Tree Traversals, DFS, etc.

Types of Recursions:

Recursion can be further classified into two kinds, depending on when they terminate:

1. Finite Recursion
2. Infinite Recursion

Finite Recursion:

Finite Recursion occurs when the recursion terminates after a finite number of recursive calls. A recursion terminates only when a base condition is met.

Example:

Below is an implementation to demonstrate Finite Recursion.

// C++ program to demsonstrate Finite Recursion
#include <bits/stdc++.h>
using namespace std;

// Recursive function
void Geek(int N)
{
    // Base condition
    // When this condition is met,
    // the recursion terminates
    if (N == 0)
        return;

    // Print the current value of N
    cout << N << " ";

    // Call itself recursively
    Geek(N - 1);
}

// Driver code
int main()
{

    // Initial value of N
    int N = 5;

    // Call the recursive function
    Geek(N);
    return 0;
}

// Java program for the above approach
class GFG{

// Recursive function
static void Geek(int N)
{
    
    // Base condition
    // When this condition is met,
    // the recursion terminates
    if (N == 0)
        return;

    // Print the current value of N
    System.out.println(N + " ");

    // Call itself recursively
    Geek(N - 1);
}

// Driver code
public static void main(String[] args)
{
    
    // Initial value of N
    int N = 5;

    // Call the recursive function
    Geek(N);
}
}

// This code is contributed by abhinavjain194

# Python program to demsonstrate Finite Recursion
# Recursive function
def Geek( N):

    # Base condition
    # When this condition is met,
    # the recursion terminates
    if (N == 0):
        return

    # Pr the current value of N
    print( N, end =" " )

    # Call itself recursively
    Geek(N - 1)


# Driver code
# Initial value of N
N = 5

# Call the recursive function
Geek(N)

# this code is contributed by shivanisinghss2110

// C# program for the above approach
using System;
using System.Collections.Generic;

class GFG{

// Recursive function
static void Geek(int N)
{
     
    // Base condition
    // When this condition is met,
    // the recursion terminates
    if (N == 0)
        return;
 
    // Print the current value of N
    Console.Write(N + " ");
 
    // Call itself recursively
    Geek(N - 1);
}

// Driver Code
public static void Main(String[] args)
{
  
    // Initial value of N
    int N = 5;
 
    // Call the recursive function
    Geek(N);
}
}

// This code is contributed by target_2.

<script>

// JavaScript program to demsonstrate Finite Recursion
// Recursive function
function Geek(N)
{
    // Base condition
    // When this condition is met,
    // the recursion terminates
    if (N == 0)
        return;

    // Print the current value of N
    document.write(N +" ");

    // Call itself recursively
    Geek(N - 1);
}

// Driver code
// Initial value of N
    var N = 5;

    // Call the recursive function
    Geek(N);
    
 // this code is contributed by shivanisinghss2110
 
</script>

5 4 3 2 1 

Time Complexity: O(n)
Auxiliary Space: O(n)

The recursion tree for the above recursive function looks like this.

When the value of N becomes 0, because of the base condition, the recursion terminates.

Infinite Recursion:

Infinite Recursion occurs when the recursion does not terminate after a finite number of recursive calls. As the base condition is never met, the recursion carries on infinitely.

Example: 

Below is an implementation to demonstrate Infinite Recursion. 

// C++ program to demsonstrate Infinite Recursion
#include <bits/stdc++.h>
using namespace std;

// Recursive function
void Geek(int N)
{
    // Base condition
    // This condition is never met here
    if (N == 0)
        return;

    // Print the current value of N
    cout << N << " ";

    // Call itself recursively
    Geek(N);
}

// Driver code
int main()
{

    // Initial value of N
    int N = 5;

    // Call the recursive function
    Geek(N);
    return 0;
}

// Java program to demsonstrate Infinite Recursion
import java.io.*;
 
class GFG
{
// Recursive function
static void Geek(int N)
{
    // Base condition
    // This condition is never met here
    if (N == 0)
        return;

    // Print the current value of N
    System.out.print( N +" ");

    // Call itself recursively
    Geek(N);
}

// Driver code
public static void main(String[] args)
    {

    // Initial value of N
    int N = 5;

    // Call the recursive function
    Geek(N);
    }
}

// This code is contributed by shivanisinghss2110

# Python3 to demsonstrate Infinite Recursion

# Recursive function
def Geek(N):
    
    # Base condition
    # This condition is never met here
    if (N == 0):
        return

    # Print the current value of N
    print(N, end = " " )

    # Call itself recursively
    Geek(N)

# Driver code

# Initial value of N
N = 5

# Call the recursive function
Geek(N)

# This code is contributed by shivanisinghss2110

// C# program to demsonstrate Infinite Recursion
using System;
 
class GFG
{
// Recursive function
static void Geek(int N)
{
    // Base condition
    // This condition is never met here
    if (N == 0)
        return;

    // Print the current value of N
    Console.Write( N +" ");

    // Call itself recursively
    Geek(N);
}

// Driver code
public static void Main(String[] args)
    {

    // Initial value of N
    int N = 5;

    // Call the recursive function
    Geek(N);
    }
}

// This code is contributed by shivanisinghss2110

<script>
// JavaScript program to demsonstrate Infinite Recursion
// Recursive function
function Geek(N)
{
    // Base condition
    // This condition is never met here
    if (N == 0)
        return;

    // Print the current value of N
    document.write( N +" ");

    // Call itself recursively
    Geek(N);
}

// Driver code
    // Initial value of N
    var N = 5;

    // Call the recursive function
    Geek(N);

// This code is contributed by shivanisinghss2110
</script>

Time Complexity: non finite as this recursion will never end.
Auxiliary Space: non finite

The recursion tree for the above recursive function looks like this.

Since the value of N never becomes 0, so the recursion never terminates. Instead, the recursion continues until the implicit stack becomes full which results in a Stack Overflow. Some compilers directly give the output as Segmentation Fault (Core Dumped), while others may abnormally terminate for some value and then show Segmentation fault.