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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#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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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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#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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Output: 64
It calulates 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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#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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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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