📜  Golang中不同类型的递归

📅  最后修改于: 2021-05-07 00:42:41             🧑  作者: Mango

递归是函数直接或间接调用自身的概念。每次对递归函数的调用都是一个较小的版本,以便在某个时刻收敛。每个递归函数都有一个基本案例或基本条件,这是递归中的最后一个可执行语句,并停止进一步的调用。

如以下示例中所述,存在不同类型的递归:

1.直接递归

函数直接调用自身而无需其他函数帮助的递归类型称为直接递归。以下示例说明了直接递归的概念:

例子:

// Golang program to illustrate the
// concept of direct recursion
package main
  
import (
    "fmt"
)
  
// recursive function for 
// calculating a factorial 
// of a positive integer
func factorial_calc(number int) int {
  
    // this is the base condition
    // if number is 0 or 1 the
    // function will return 1
    if number == 0 || number == 1 {
        return 1
    }
      
    // if negative argument is 
    // given, it prints error
    // message and returns -1
    if number < 0 {
        fmt.Println("Invalid number")
        return -1
    }
      
    // recursive call to itself
    // with argument decremented 
    // by 1 integer so that it
    // eventually reaches the base case
    return number*factorial_calc(number - 1)
}
  
// the main function
func main() {
  
    // passing 0 as a parameter
    answer1 := factorial_calc(0)
    fmt.Println(answer1, "\n")
      
    // passing a positive integer
    answer2 := factorial_calc(5)
    fmt.Println(answer2, "\n")
      
    // passing a negative integer
    // prints an error message
    // with a return value of -1
    answer3 := factorial_calc(-1)
    fmt.Println(answer3, "\n")
      
    // passing a positive integer
    answer4 := factorial_calc(10)
    fmt.Println(answer4, "\n")
}

输出:

1 

120 

Invalid number
-1 

3628800

2.间接递归

函数调用另一个函数,然后此函数调用调用函数的递归类型称为间接递归。这种类型的递归需要另一个函数的帮助。该函数的确调用了自己,但是间接地(即通过另一个函数)调用了它自己。以下示例说明了间接递归的概念:

例子:

// Golang program to illustrate the
// concept of indirect recursion
package main
  
import (
    "fmt"
)
  
// recursive function for 
// printing all numbers 
// upto the number n
func print_one(n int) {
      
    // if the number is positive
    // print the number and call 
    // the second function
    if n >= 0 {
        fmt.Println("In first function:", n)
        // call to the second function
        // which calls this first
        // function indirectly
        print_two(n - 1)
    }
}
  
func print_two(n int) {
  
    // if the number is positive
    // print the number and call 
    // the second function
    if n >= 0 {
        fmt.Println("In second function:", n)
        // call to the first function
        print_one(n - 1)
    }
}
  
// main function
func main() {
      
    // passing a positive 
    // parameter which prints all 
    // numbers from 1 - 10
    print_one(10)
      
    // this will not print
    // anything as it does not
    // follow the base case
    print_one(-1)
}

输出:

In first function: 10
In second function: 9
In first function: 8
In second function: 7
In first function: 6
In second function: 5
In first function: 4
In second function: 3
In first function: 2
In second function: 1
In first function: 0

注意:仅具有2个函数的间接递归称为相互递归。可以有两个以上的函数来促进间接递归。

3.尾递归

尾部调用是子例程调用,它是函数的最后一个或最后一个调用。当尾部调用执行对同一函数的调用时,该函数被称为尾部递归。在这里,递归调用是该函数执行的最后一件事。

例子:

// Golang program to illustrate the
// concept of tail recursion
package main
  
import (
    "fmt"
)
  
// tail recursive function
// to print all numbers 
// from n to 1
func print_num(n int) {
      
    // if number is still 
    // positive, print it
    // and call the function
    // with decremented value
    if n > 0 {
        fmt.Println(n)
          
        // last statement in 
        // the recursive function
        // tail recursive call
        print_num(n-1)
    }
}
  
// main function
func main() {
      
    // passing a positive 
    // number, prints 5 to 1
    print_num(5)
}

输出:

5
4
3
2
1

4.头递归

在头递归中,递归调用是该函数的第一条语句。调用之前没有其他语句或操作。该函数在调用时不必执行任何操作,并且所有操作都在返回时完成。

例子:

// Golang program to illustrate the
// concept of head recursion
package main
  
import (
    "fmt"
)
  
// head recursive function
// to print all numbers 
// from 1 to n
func print_num(n int) {
      
    // if number is still 
    // less than n, call 
    // the function
    // with decremented value
    if n > 0 {
          
        // first statement in 
        // the function
        print_num(n-1)
          
        // printing is done at
        // returning time
        fmt.Println(n)
    }
}
  
// main function
func main() {
      
    // passing a positive 
    // number, prints 5 to 1
    print_num(5)
}

输出:

1
2
3
4
5

注意:头递归的输出与尾递归的输出完全相反。这是因为尾部递归首先打印数字然后调用自身,而在头部递归中,该函数一直调用自身直到到达基本情况,然后在返回期间开始打印。

5.无限递归

所有的递归函数都是确定的或有限的递归函数,即它们在达到基本条件时就停止了。无限递归是一种递归,这种递归一直持续到无限,并且永远不会收敛到基本情况。这通常会导致系统崩溃或内存溢出。

例子:

// Golang program to illustrate the
// concept of infinite recursion
package main
  
import (
    "fmt"
)
  
// infinite recursion function
func print_hello() {
      
    // printing infinite times
    fmt.Println("GeeksforGeeks")
    print_hello()
}
  
// main function
func main() {
      
    // call to infinite 
    // recursive function
    print_hello()
}

输出:

GeeksforGeeks
GeeksforGeeks
GeeksforGeeks
..... infinite times

6.匿名函数递归

在Golang中,有一个没有名称的函数概念。这些功能称为匿名功能。还可以使用Golang中的匿名函数来执行递归,如下所示:

例子:

// Golang program to illustrate 
// the concept of anonymous 
// function recursion
package main
  
import (
    "fmt"
)
  
// main function
func main() {
      
    // declaring anonymous function
    // that takes an integer value
        var anon_func func(int)
           
    // defining an anonymous
    // function that prints
    // numbers from n to 1
        anon_func = func(number int) {
      
        // base case
            if number == 0 {
                    return 
            } else {
            fmt.Println(number)
              
            // calling anonymous 
            // function recursively
                    anon_func(number-1)
            }
        }
      
    // call to anonymous 
    // recursive function
        anon_func(5)
}

输出:

5
4
3
2
1