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.

Hofstadter 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: 

F ( 0 ) = 1M ( 0 ) = 0 F ( n ) = n - M ( F ( n - 1 ) ), n > 0 M ( n ) = n - F ( M ( n - 1 ) ), n > 0. 

// C++ program to implement Hofstadter Sequence
// using mutual recursion
#include <bits/stdc++.h>
using namespace std;

int hofstadterFemale(int);
int hofstadterMale(int);

// Female function
int hofstadterFemale(int n)
{
    if (n < 0)
        return 0;
    else
        if (n == 0)
            return 1;
        else
            return (n - hofstadterFemale(n - 1));
}

// Male function
int hofstadterMale(int n)
{
    if (n < 0)
        return 0;
    else
        if (n == 0)
            return 0;
        else
            return (n - hofstadterMale(n - 1));
}

// Driver Code
int main()
{
    int i;
    cout << "F: ";
    for (i = 0; i < 20; i++) 
        cout << hofstadterFemale(i) << " ";
    
    cout << "\n";

    cout << "M: ";
    for (i = 0; i < 20; i++) 
        cout << hofstadterMale(i)<< " "; 

    return 0;
}

// This code is contributed by shubhamsingh10

// 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 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.

# 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# 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 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 contributed by Ajit
?>

<script>

// Javascript program to implement Hofstader 
// Sequence using mutual recursion

// Female function
function hofstaderFemale(n)
{
    if (n < 0)
        return 0;
    else
        return (n == 0) ? 1 : 
                n - hofstaderFemale(n - 1);
}
  
// Male function
function hofstaderMale(n)
{
    if (n < 0)
        return 0;
    else
        return (n == 0) ? 0 : 
                n - hofstaderMale(n - 1);
}

// Driver code
let i;
document.write("F: ");
for(i = 0; i < 20; i++) 
    document.write(hofstaderFemale(i) + " ");

document.write("</br>");

document.write("M: ");
for(i = 0; i < 20; i++) 
    document.write(hofstaderMale(i) + " "); 
    
// This code is contributed by rameshtravel07
</script>

 
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:  

1. Circular dependencies can cause a domino effect when a small local change in one module spreads into other modules and has unwanted global effects
2. Circular dependencies can also result in infinite recursions or other unexpected failures.
3. 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