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:
C++
// C++ program to implement Hofstader Sequence // using mutual recursion #include <bits/stdc++.h> using namespace std; int hofstaderFemale(int); int hofstaderMale(int); // Female function int hofstaderFemale(int n) { if (n < 0) return 0; else if (n == 0) return 1; else return (n - hofstaderFemale(n - 1)); } // Male function int hofstaderMale(int n) { if (n < 0) return 0; else if (n == 0) return 0; else return (n - hofstaderMale(n - 1)); } // Driver Code int main() { int i; cout << "F: "; for (i = 0; i < 20; i++) cout << hofstaderFemale(i) << " "; cout << "\n"; cout << "M: "; for (i = 0; i < 20; i++) cout << hofstaderMale(i)<< " "; return 0; } // This code is contributed by shubhamsingh10 |
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
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