以Hofstadter雌雄序列为例的相互递归-yiteyi-C++库

相互递归是一种变体递归 .如果第一个函数对第二个函数进行递归调用，而第二个函数又反过来调用第一个函数，则这两个函数是相互递归调用的。在软件开发中，这个概念被用于循环依赖，循环依赖是两个或多个模块之间的关系，这些模块直接或间接地相互依赖以正常运行。这种模块也称为相互递归模块。相互递归的一个很好的例子是实现Hofstadter序列。

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霍夫斯塔德序列

在数学中，Hofstadter序列是由 非线性 递归关系。在本例中，我们将重点介绍 Hofstadter雌雄序列：

推荐：请尝试你的方法 {IDE} 首先，在进入解决方案之前。

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 <<                                     ""                                     ;                       
           
                                                 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                                     (                                     ""                                     );                       
           
                                                 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                                     (                                     ""                                     )                       
                         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                                     ""                                     ;                       
           
                                                 echo                                     "M: "                                     ;                       
                                                 for                                     (                                     $i                                     = 0;                                     $i                                     < 20;                                     $i                                     ++)                       
                                                 echo                                     hofstaderMale(                                     $i                                     ),                                     " "                                     ;                       
           
                         // This code contributed by Ajit                       
                         ?>                       

Javascript

                         <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>                       

输出：

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

循环依赖/相互递归的缺点：

当一个模块中的一个小的局部更改扩展到其他模块并产生不必要的全局影响时，循环依赖可能会导致多米诺效应
循环依赖还可能导致无限递归或其他意外故障。
循环依赖还可能通过阻止某些非常原始的自动垃圾收集器（使用引用计数的垃圾收集器）释放未使用的对象而导致内存泄漏。

参考资料： 维基百科

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