有限递归和无限递归的例子

函数直接或间接调用自身的过程称为递归，对应的函数称为递归函数。
使用递归，可以很容易地解决某些问题。此类问题的示例有河内塔 (TOH)、中序/前序/后序树遍历、DFS 等。

递归类型：

递归可以进一步分为两种，取决于它们何时终止：

1. 有限递归
2. 无限递归

有限递归：

当递归在有限次数的递归调用后终止时，就会发生有限递归。递归仅在满足基本条件时终止。

例子：

下面是一个演示有限递归的实现。

C++

// C++ program to demsonstrate Finite Recursion
#include 
using namespace std;
 
// Recursive function
void Geek(int N)
{
    // Base condition
    // When this condition is met,
    // the recursion terminates
    if (N == 0)
        return;
 
    // Print the current value of N
    cout << N << " ";
 
    // Call itself recursively
    Geek(N - 1);
}
 
// Driver code
int main()
{
 
    // Initial value of N
    int N = 5;
 
    // Call the recursive function
    Geek(N);
    return 0;
}

Java

// Java program for the above approach
class GFG{
 
// Recursive function
static void Geek(int N)
{
     
    // Base condition
    // When this condition is met,
    // the recursion terminates
    if (N == 0)
        return;
 
    // Print the current value of N
    System.out.println(N + " ");
 
    // Call itself recursively
    Geek(N - 1);
}
 
// Driver code
public static void main(String[] args)
{
     
    // Initial value of N
    int N = 5;
 
    // Call the recursive function
    Geek(N);
}
}
 
// This code is contributed by abhinavjain194

Python3

# Python program to demsonstrate Finite Recursion
# Recursive function
def Geek( N):
 
    # Base condition
    # When this condition is met,
    # the recursion terminates
    if (N == 0):
        return
 
    # Pr the current value of N
    print( N, end =" " )
 
    # Call itself recursively
    Geek(N - 1)
 
 
# Driver code
# Initial value of N
N = 5
 
# Call the recursive function
Geek(N)
 
# this code is contributed by shivanisinghss2110

C#

// C# program for the above approach
using System;
using System.Collections.Generic;
 
class GFG{
 
// Recursive function
static void Geek(int N)
{
      
    // Base condition
    // When this condition is met,
    // the recursion terminates
    if (N == 0)
        return;
  
    // Print the current value of N
    Console.Write(N + " ");
  
    // Call itself recursively
    Geek(N - 1);
}
 
// Driver Code
public static void Main(String[] args)
{
   
    // Initial value of N
    int N = 5;
  
    // Call the recursive function
    Geek(N);
}
}
 
// This code is contributed by target_2.

Javascript

 
// JavaScript program to demsonstrate Finite Recursion
// Recursive function
function Geek(N)
{
    // Base condition
    // When this condition is met,
    // the recursion terminates
    if (N == 0)
        return;
 
    // Print the current value of N
    document.write(N +" ");
 
    // Call itself recursively
    Geek(N - 1);
}
 
// Driver code
// Initial value of N
    var N = 5;
 
    // Call the recursive function
    Geek(N);
     
 // this code is contributed by shivanisinghss2110
  

输出

5 4 3 2 1 

上述递归函数的递归树如下所示。

递归树

当N的值变为0 时，由于基本条件，递归终止。

无限递归：

当递归在有限次数的递归调用后没有终止时，就会发生无限递归。由于永远不满足基本条件，递归无限进行。

例子：

下面是一个演示无限递归的实现。

C++

// C++ program to demsonstrate Infinite Recursion
#include 
using namespace std;
 
// Recursive function
void Geek(int N)
{
    // Base condition
    // This condition is never met here
    if (N == 0)
        return;
 
    // Print the current value of N
    cout << N << " ";
 
    // Call itself recursively
    Geek(N);
}
 
// Driver code
int main()
{
 
    // Initial value of N
    int N = 5;
 
    // Call the recursive function
    Geek(N);
    return 0;
}

Java

// Java program to demsonstrate Infinite Recursion
import java.io.*;
  
class GFG
{
// Recursive function
static void Geek(int N)
{
    // Base condition
    // This condition is never met here
    if (N == 0)
        return;
 
    // Print the current value of N
    System.out.print( N +" ");
 
    // Call itself recursively
    Geek(N);
}
 
// Driver code
public static void main(String[] args)
    {
 
    // Initial value of N
    int N = 5;
 
    // Call the recursive function
    Geek(N);
    }
}
 
// This code is contributed by shivanisinghss2110

蟒蛇3

# Python3 to demsonstrate Infinite Recursion
 
# Recursive function
def Geek(N):
     
    # Base condition
    # This condition is never met here
    if (N == 0):
        return
 
    # Print the current value of N
    print(N, end = " " )
 
    # Call itself recursively
    Geek(N)
 
# Driver code
 
# Initial value of N
N = 5
 
# Call the recursive function
Geek(N)
 
# This code is contributed by shivanisinghss2110

C＃

// C# program to demsonstrate Infinite Recursion
using System;
  
class GFG
{
// Recursive function
static void Geek(int N)
{
    // Base condition
    // This condition is never met here
    if (N == 0)
        return;
 
    // Print the current value of N
    Console.Write( N +" ");
 
    // Call itself recursively
    Geek(N);
}
 
// Driver code
public static void Main(String[] args)
    {
 
    // Initial value of N
    int N = 5;
 
    // Call the recursive function
    Geek(N);
    }
}
 
// This code is contributed by shivanisinghss2110

Javascript

// JavaScript program to demsonstrate Infinite Recursion
// Recursive function
function Geek(N)
{
    // Base condition
    // This condition is never met here
    if (N == 0)
        return;
 
    // Print the current value of N
    document.write( N +" ");
 
    // Call itself recursively
    Geek(N);
}
 
// Driver code
    // Initial value of N
    var N = 5;
 
    // Call the recursive function
    Geek(N);
 
// This code is contributed by shivanisinghss2110

上述递归函数的递归树如下所示。

递归树

由于N的值永远不会变为0 ，因此递归永远不会终止。相反，递归继续进行，直到隐式堆栈变满，从而导致堆栈溢出。一些编译器直接将输出作为 Segmentation Fault (Core Dumped) 给出，而其他编译器可能会异常终止某些值，然后显示 Segmentation fault。

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