Practice Questions for Recursion | Set 5
Last Updated :
14 Feb, 2025
Question 1
Predict the output of the 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
#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;
}
/*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
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
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
<script>
//Javascript Implementation
function fun(a, b)
{
if (b == 0)
return 0;
if (b % 2 == 0)
return fun(a + a, Math.floor(b/2));
return fun(a + a, Math.floor(b/2)) + a;
}
document.write(fun(4, 3));
// This code is contributed by shubhamsingh10
</script>
It calculates a*b (a multiplied b).
Time Complexity: O(log2(b))
Auxiliary Space: O(log2(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
#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;
}
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
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
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
<script>
//Javascript Implementation
function fun(a, b)
{
if (b == 0)
return 1;
if (b % 2 == 0)
return fun(a * a, Math.floor(b/2));
return fun(a * a, Math.floor(b/2)) * a;
}
document.write(fun(4, 3));
// This code is contributed by shubhamsingh10
</script>
It calculates a^b (a raised to power b).
Time complexity: O(log2b)
Auxiliary Space: O(log2b)
Question 3
Predict the output of the 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
#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;
}
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
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
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
<script>
function fun(n)
{
if (n > 100)
return n - 10
return fun(fun(n + 11))
}
// Driver code
document.write(fun(99))
// This code is contributed by Bobby Gottumukkala
</script>
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 > 100Time complexity: O(n)
Auxiliary Space: O(n), to maintain function call into call stack
The returned value of fun() is 91 for all integer arguments 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.