Practice Questions for Recursion | Set 5

Question 1

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

C++

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#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

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C

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#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;
}

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Java

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/*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

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Python3

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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) +
  
# Driver code
  
print(fun(4, 3))
  
# This code is contributed by SHUBHAMSINGH10

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C#

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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

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Output:

12

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++

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#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

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C

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#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;
}

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Java

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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

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Python3

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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)*
   
# Driver code
   
print(fun(4, 3))
  
# This code is contributed by shubhamsingh10

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C#

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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

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Output:

64

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++

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#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

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C

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#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;
}

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Java

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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

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Python3

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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

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C#

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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

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Output:

91
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.

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Improved By : SHUBHAMSINGH10

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