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Finite and Infinite Recursion with examples

  • Last Updated : 23 Jul, 2021

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:

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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++




// 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




// 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

Python3




# 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#




// 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.

Javascript




<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>
Output
5 4 3 2 1 

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

Recursion Tree

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++




// 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




// 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




# 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#




// 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

Javascript




<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>

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

Recursion Tree

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




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