Practice Questions for Recursion | Set 5

Question 1

Predict the output of following program. What does the following fun() do in general?

C++

#include <iostream> 
using namespace std; 
int fun(int a, int b)  
{  
    if (b == 0)  
        return 0;  
    if (b % 2 == 0)  
        return fun(a + a, b/2);  
      
    return fun(a + a, b/2) + a;  
}  
  
int main()  
{  
    cout << fun(4, 3) ;  
    return 0;  
}  
  
// This code is contributed by SHUBHAMSINGH10 

C

#include<stdio.h> 
  
int fun(int a, int b)  
{ 
   if (b == 0) 
       return 0; 
   if (b % 2 == 0) 
       return fun(a+a, b/2); 
  
   return fun(a+a, b/2) + a; 
} 
  
int main() 
{ 
  printf("%d", fun(4, 3)); 
  getchar(); 
  return 0; 
} 

Java

/*package whatever //do not write package name here */
  
import java.io.*; 
  
class GFG { 
    static int fun(int a, int b)  
    {  
        if (b == 0)  
            return 0;  
        if (b % 2 == 0)  
            return fun(a + a, b/2);  
           
        return fun(a + a, b/2) + a;  
    }  
   
    public static void main (String[] args)  
    { 
        System.out.println(fun(4, 3)); 
    } 
} 
// This code is contributed by SHUBHAMSINGH10 

Python3

def fun(a, b): 
    if (b == 0): 
        return 0 
    if (b % 2 == 0): 
        return fun(a + a, b//2)  
      
    return fun(a + a, b//2) + a  
  
# Driver code 
  
print(fun(4, 3)) 
  
# This code is contributed by SHUBHAMSINGH10 

C#

using System; 
  
class GFG{ 
  
    static int fun(int a, int b)  
    {  
        if (b == 0)  
            return 0;  
        if (b % 2 == 0)  
            return fun(a + a, b/2);  
          
        return fun(a + a, b/2) + a;  
    }  
      
    static public void Main ()  
    {  
        Console.Write(fun(4, 3));  
    }  
} 
  
// This code is contributed by SHUBHAMSINGH10 

Output:

It calulates a*b (a multipied b).

Question 2
In question 1, if we replace + with * and replace return 0 with return 1, then what does the changed function do? Following is the changed function.

C++

#include <iostream> 
using namespace std; 
    
int fun(int a, int b)  
{  
   if (b == 0)  
       return 1;  
   if (b % 2 == 0)  
       return fun(a*a, b/2);  
    
   return fun(a*a, b/2)*a;  
}  
    
int main()  
{  
  cout << fun(4, 3) ;  
  getchar();  
  return 0;  
}  
  
//This code is contributed by shubhamsingh10 

C

#include<stdio.h> 
  
int fun(int a, int b) 
{ 
   if (b == 0) 
       return 1; 
   if (b % 2 == 0) 
       return fun(a*a, b/2); 
  
   return fun(a*a, b/2)*a; 
} 
  
int main() 
{ 
  printf("%d", fun(4, 3)); 
  getchar(); 
  return 0; 
} 

Java

import java.io.*; 
   
class GFG { 
    static int fun(int a, int b)  
    {  
        if (b == 0)  
            return 1;  
        if (b % 2 == 0)  
            return fun(a*a, b/2);  
          
        return fun(a*a, b/2)*a;  
    }  
      
    public static void main (String[] args) 
    {  
        System.out.println(fun(4, 3));  
    }  
} 
//This code is contributed by shubhamsingh10 

Python3

def fun(a, b): 
    if (b == 0): 
        return 1 
    if (b % 2 == 0): 
        return fun(a*a, b//2)  
      
    return fun(a*a, b//2)*a  
   
# Driver code 
   
print(fun(4, 3)) 
  
# This code is contributed by shubhamsingh10 

C#

using System; 
  
public class GFG{ 
      
    static int fun(int a, int b)  
    {  
        if (b == 0)  
            return 1;  
        if (b % 2 == 0)  
            return fun(a*a, b/2);  
          
        return fun(a*a, b/2)*a;  
    }  
      
      
    static public void Main () 
    {  
        Console.WriteLine(fun(4, 3));  
    }  
} 
// This code is contributed by shubhamsingh10 

Output:

It calculates a^b (a raised to power b).

Question 3
Predict the output of following program. What does the following fun() do in general?

C++

#include <iostream> 
using namespace std; 
  
int fun(int n) 
{ 
    if (n > 100) 
        return n - 10; 
    return fun(fun(n+11)); 
} 
  
int main() 
{ 
    cout << " " << fun(99) << " "; 
    getchar(); 
    return 0; 
} 
  
// This code is contributed by Shubhamsingh10 

C

#include<stdio.h> 
  
 int fun(int n) 
 { 
   if (n > 100) 
     return n - 10; 
   return fun(fun(n+11)); 
 } 
  
int main() 
{ 
  printf(" %d ", fun(99)); 
  getchar(); 
  return 0; 
}

Java

import java.io.*; 
  
class GFG { 
    static int fun(int n) 
    { 
        if (n > 100) 
            return n - 10; 
        return fun(fun(n+11)); 
    } 
      
    public static void main (String[] args) { 
        System.out.println(" " + fun(99) + " "); 
    } 
} 
// This code is contributed by Shubhamsingh10 

Python3

def fun(n): 
      
    if (n > 100): 
        return n - 10
      
    return fun(fun(n + 11)) 
      
# Driver code 
print(fun(99)) 
  
# This code is contributed by Shubhamsingh10 

C#

using System; 
  
class GFG{ 
      
static int fun(int n) 
{ 
    if (n > 100) 
        return n - 10; 
    return fun(fun(n + 11)); 
} 
  
// Driver code     
static public void Main () 
{  
    Console.WriteLine(fun(99)); 
} 
} 
  
// This code is contributed by Shubhamsingh10 

Output:

fun(99) = fun(fun(110)) since 99 ? 100
           = fun(100)    since 110 > 100
           = fun(fun(111)) since 100 ? 100
           = fun(101)    since 111 > 100
           = 91        since 101 > 100

Returned value of fun() is 91 for all integer rguments n 101. This function is known as McCarthy 91 function.

Please write comments if you find any of the answers/codes incorrect, or you want to share more information/questions about the topics discussed above.

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My Personal Notes

C++

C

Java

Python3

C#

C++

C

Java

Python3

C#

C++

C

Java

Python3

C#

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