Mutual Recursion with example of Hofstadter Female and Male sequences

Mutual recursion is a variation recursion. Two functions are called mutually recursive if the first function makes a recursive call to the second function and the second function, in turn, calls the first one.

In software development this concept is used in circular dependency which is a relation between two or more modules which either directly or indirectly depend on each other to function properly. Such modules are also known as mutually recursive.

A great example of mutual recursion would be implementing the Hofstadter Sequence.

Hofstader Sequence

In mathematics, a Hofstadter sequence is a member of a family of related integer sequences defined by non-linear recurrence relations. In this example we are going to focus on Hofstadter Female and Male sequences:

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C

// C program to implement Hofstader Sequence 
// using mutual recursion 
#include <stdio.h> 
  
int hofstaderFemale(int); 
int hofstaderMale(int); 
  
// Female function 
int hofstaderFemale(int n) 
{ 
    if (n < 0) 
        return; 
    else
        return (n == 0) ? 1 : n - hofstaderFemale(n - 1); 
} 
  
// Male function 
int hofstaderMale(int n) 
{ 
    if (n < 0) 
        return; 
    else
        return (n == 0) ? 0 : n - hofstaderMale(n - 1); 
} 
  
// hard coded driver function to run the program 
int main() 
{ 
    int i; 
    printf("F: "); 
    for (i = 0; i < 20; i++)  
        printf("%d ", hofstaderFemale(i)); 
      
    printf("\n"); 
  
    printf("M: "); 
    for (i = 0; i < 20; i++)  
        printf("%d ", hofstaderMale(i));     
  
    return 0; 
} 

Java

// Java program to implement Hofstader  
// Sequence using mutual recursion 
import java .io.*; 
  
class GFG { 
      
    // Female function 
    static int hofstaderFemale(int n) 
    { 
        if (n < 0) 
            return 0; 
        else
            return (n == 0) ? 1 : n -  
            hofstaderFemale(n - 1); 
    } 
      
    // Male function 
    static int hofstaderMale(int n) 
    { 
        if (n < 0) 
            return 0; 
        else
            return (n == 0) ? 0 : n -  
                hofstaderMale(n - 1); 
    } 
  
    // Driver Code 
    static public void main (String[] args) 
    { 
        int i; 
        System.out.print("F: "); 
        for (i = 0; i < 20; i++)  
            System.out.print(hofstaderFemale(i)  
                                        + " "); 
          
        System.out.println(); 
      
        System.out.print("M: "); 
        for (i = 0; i < 20; i++)  
            System.out.print(hofstaderMale(i) 
                                      + " ");  
    } 
} 
  
// This code is contributed by anuj_67. 

Python3

# Python program to implement  
# Hofstader Sequence using  
# mutual recursion 
  
# Female function 
def hofstaderFemale(n): 
    if n < 0: 
        return; 
    else: 
        val = 1 if n == 0 else ( 
                   n - hofstaderFemale(n - 1)) 
        return val 
  
# Male function 
def hofstaderMale(n): 
    if n < 0: 
        return; 
    else: 
        val = 0 if n == 0 else ( 
                   n - hofstaderMale(n - 1)) 
        return val 
  
# Driver code 
print("F:", end = " ") 
for i in range(0, 20): 
    print(hofstaderFemale(i), end = " ") 
  
print("\n") 
print("M:", end = " ") 
for i in range(0, 20): 
    print(hofstaderMale(i), end = " ") 
  
# This code is contributed 
# by Shantanu Sharma 

C#

// C# program to implement Hofstader  
// Sequence using mutual recursion 
using System; 
  
class GFG { 
      
    // Female function 
    static int hofstaderFemale(int n) 
    { 
        if (n < 0) 
            return 0; 
        else
            return (n == 0) ? 1 : n -  
               hofstaderFemale(n - 1); 
    } 
      
    // Male function 
    static int hofstaderMale(int n) 
    { 
        if (n < 0) 
            return 0; 
        else
            return (n == 0) ? 0 : n -  
                 hofstaderMale(n - 1); 
    } 
  
    // Driver Code 
    static public void Main () 
    { 
        int i; 
        Console.WriteLine("F: "); 
        for (i = 0; i < 20; i++)  
            Console.Write(hofstaderFemale(i) + " "); 
          
        Console.WriteLine(); 
      
        Console.WriteLine("M: "); 
        for (i = 0; i < 20; i++)  
            Console.Write(hofstaderMale(i) + " ");  
    } 
} 
  
// This code is contributed by Ajit. 

PHP

<?php 
// PHP program to implement 
// Hofstader Sequence 
// using mutual recursion 
  
//function hofstaderFemale(int); 
//int hofstaderMale(int); 
  
// Female function 
function hofstaderFemale($n) 
{ 
    if ($n < 0) 
        return; 
    else
        return ($n == 0) ? 1 : $n - hofstaderFemale($n - 1); 
} 
  
// Male function 
function hofstaderMale($n) 
{ 
    if ($n < 0) 
        return; 
    else
        return ($n == 0) ? 0 : $n - hofstaderMale($n - 1); 
} 
  
    // Driver Code 
    $i; 
    echo "F: "; 
    for ($i = 0; $i < 20; $i++)  
        echo hofstaderFemale($i), " "; 
      
    echo "\n"; 
  
    echo "M: "; 
    for ($i = 0; $i < 20; $i++)  
        echo hofstaderMale($i), " ";  
  
// This code contribued by Ajit 
?> 

Output:
F: 1 0 2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8 10 9 
M: 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10

Disadvantages of Circular Dependency/Mutual Recursion:

Circular dependencies can cause a domino effect when a small local change in one module spreads into other modules and has unwanted global effects
Circular dependencies can also result in infinite recursions or other unexpected failures.
Circular dependencies may also cause memory leaks by preventing certain very primitive automatic garbage collectors (those that use reference counting) from deallocating unused objects.

References: Wikipedia

This article is contributed by Palash Nigam . If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C

Java

Python3

C#

PHP

Recommended Posts: