Practice Questions for Recursion | Set 5

Question 1

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

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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.

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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?

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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, and n - 10 for n > 101. This function is known as McCarthy 91 function.

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