Preguntas de práctica para la recursividad | conjunto 5

Pregunta 1
Prediga la salida del siguiente programa. ¿Qué hace el siguiente fun() en general?  

#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>

12

Calcula a*b (a multiplicado por b).
 

Pregunta 2 
En la pregunta 1, si reemplazamos + con * y reemplazamos return 0 con return 1, entonces, ¿qué hace la función cambiada? A continuación se muestra la función modificada. 

#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>

64

Calcula a^b (a elevado a la potencia b).
 

Pregunta 3 
Prediga la salida del siguiente programa. ¿Qué hace el siguiente fun() en general?  

#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>

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

Complejidad temporal: O(n)

Complejidad espacial: O(1)

El valor devuelto por fun() es 91 para todos los argumentos enteros n 101. Esta función se conoce como función McCarthy 91. 
Escriba comentarios si encuentra que alguna de las respuestas/códigos es incorrecta, o si desea compartir más información/preguntas sobre los temas discutidos anteriormente.