Dada una función rand50() que devuelve 0 o 1 con la misma probabilidad, escriba una función que devuelva 1 con un 75 % de probabilidad y 0 con un 25 % de probabilidad usando solo rand50(). Minimice el número de llamadas al método rand50(). Además, no se permite el uso de ninguna otra función de biblioteca ni la aritmética de coma flotante.
La idea es usar Bitwise OR . Un OR bit a bit toma dos bits y devuelve 0 si ambos bits son 0, mientras que, de lo contrario, el resultado es 1. Por lo tanto, tiene un 75% de probabilidad de que devuelva 1.
A continuación se muestra la implementación de la idea anterior:
C++
// Program to print 1 with 75% probability and 0
// with 25% probability
#include <iostream>
using namespace std;
// Random Function to that returns 0 or 1 with
// equal probability
int rand50()
{
// rand() function will generate odd or even
// number with equal probability. If rand()
// generates odd number, the function will
// return 1 else it will return 0.
return rand() & 1;
}
// Random Function to that returns 1 with 75%
// probability and 0 with 25% probability using
// Bitwise OR
bool rand75()
{
return rand50() | rand50();
}
// Driver code to test above functions
int main()
{
// Initialize random number generator
srand(time(NULL));
for(int i = 0; i < 50; i++)
cout << rand75();
return 0;
}
Java
// Java program to print 1 with 75% probability and 0
// with 25% probability
class GFG
{
// Random Function to that returns 0 or 1 with
// equal probability
static int rand50()
{
// rand() function will generate odd or even
// number with equal probability. If rand()
// generates odd number, the function will
// return 1 else it will return 0.
return (int) (10 * Math.random()) & 1;
}
// Random Function to that returns 1 with 75%
// probability and 0 with 25% probability using
// Bitwise OR
static int rand75()
{
return rand50() | rand50();
}
// Driver code
public static void main(String[] args)
{
// Initialize random number generator
//srand(time(null));
for (int i = 0; i < 50; i++)
{
System.out.print(rand75());
}
}
}
// This code is contributed by 29AjayKumar
Python3
# Program to print 1 with 75% probability and 0 # with 25% probability from random import randrange # Random Function to that returns 0 or 1 with # equal probability def rand50(): # The randrange function will generate integer # between the half closed interval at end # Here by passing parameter as 0,2 # the function will generate integer between 0 and 1 return (int)(randrange(0, 2)) & 1 # Random Function to that returns 1 with 75% # probability and 0 with 25% probability using # Bitwise OR def rand75(): return rand50() | rand50() # Driver code to test above functions for i in range(0, 50): print(rand75(), end="") # This code is contributed by meetgor.
C#
// C# program to print 1 with 75% probability and 0
// with 25% probability
using System;
public class GFG
{
// Instantiate random number generator
static Random rand = new Random();
// Random Function to that returns 0 or 1 with
// equal probability
static int rand50()
{
// rand() function will generate 1 or 0
// with equal probability
return rand.Next(0, 2);
}
// Random Function to that returns 1 with 75%
// probability and 0 with 25% probability using
// Bitwise OR
static int rand75()
{
return rand50() | rand50();
}
public static void Main(string[] args)
{
for (int i = 0; i < 50; i++)
{
Console.Write(rand75());
}
}
}
//this code is contributed by phasing17
PHP
<?php
// Program to print 1 with 75% probability
// and 0 with 25% probability
// Random Function to that returns 0 or
// 1 with equal probability
function rand50()
{
// rand() function will generate
// odd or even number with equal
// probability. If rand() generates
// odd number, the function will
// return 1 else it will return 0.
return rand() & 1;
}
// Random Function to that returns
// 1 with 75% probability and 0
// with 25% probability using
// Bitwise OR
function rand75()
{
return rand50() | rand50();
}
// Driver Code
// Initialize random
// number generator
srand(time(NULL));
for($i = 0; $i < 50; $i++)
echo rand75();
// This code is contributed m_kit
?>
Javascript
<script>
// Program to print 1 with 75% probability and 0
// with 25% probability
// Random Function to that returns 0 or 1 with
// equal probability
function rand50() {
// rand() function will generate odd or even
// number with equal probability. If rand()
// generates odd number, the function will
// return 1 else it will return 0.
return Math.floor(Math.random() * 10) & 1;
}
// Random Function to that returns 1 with 75%
// probability and 0 with 25% probability using
// Bitwise OR
function rand75() {
return rand50() | rand50();
}
// Driver code to test above functions
// Initialize random number generator
for (let i = 0; i < 50; i++)
document.write(rand75());
// This code is contributed by gfgking
</script>
Producción
11101010110101011010000101011110100010111110101111
Tiempo Complejidad: O(1)
Espacio Auxiliar: O(1)
De manera similar, también podemos usar Bitwise AND . Como devuelve 0 con un 75% de probabilidad, tenemos que invertir el resultado.
// Random Function to that returns 1 with 75%
// probability and 0 with 25% probability using
// Bitwise AND
bool rand75()
{
return !(rand50() & rand50());
}
A continuación se muestra la implementación de la idea anterior:
C++
#include <iostream>
using namespace std;
// Random Function to that returns 0 or 1 with
// equal probability
int rand50()
{
// rand() function will generate odd or even
// number with equal probability. If rand()
// generates odd number, the function will
// return 1 else it will return 0.
return rand() & 1;
}
// Random Function to that returns 1 with 75%
// probability and 0 with 25% probability using
// Bitwise AND
bool rand75()
{
return !(rand50() & rand50());
}
// Driver code to test above functions
int main()
{
// Initialize random number generator
srand(time(NULL));
for(int i = 0; i < 50; i++)
cout << rand75();
return 0;
}
Java
class GFG
{
// Random Function to that returns 0 or 1 with
// equal probability
static int rand50()
{
// rand() function will generate odd or even
// number with equal probability. If rand()
// generates odd number, the function will
// return 1 else it will return 0.
return (int) (10 * Math.random()) & 1;
}
// Random Function to that returns 1 with 75%
// probability and 0 with 25% probability using
// Bitwise AND
static int rand75()
{
return (rand50() & rand50())^1;
}
// Driver code
public static void main(String[] args)
{
// Initialize random number generator
//srand(time(null));
for (int i = 0; i < 50; i++)
{
System.out.print(rand75());
}
}
}
Python3
from random import randrange # Random Function to that returns 0 or 1 with # equal probability def rand50(): return ((int)(randrange(0, 2)) & 1) def rand75(): return (rand50() & rand50())^1 for i in range(0, 50): print(rand75(), end="")
C#
// C# program to implement the approach
using System;
class GFG
{
// Random Function to that returns 0 or 1 with
// equal probability
static int rand50()
{
// Instantiate random number generator using
// system-supplied value as seed.
var rand = new Random();
// rand() function will generate 0 or 1
// number with equal probability.
return rand.Next(0, 2);
}
// Random Function to that returns 1 with 75%
// probability and 0 with 25% probability using
// Bitwise AND
static int rand75()
{
return (rand50() & rand50()) ^ 1;
}
// Driver code
public static void Main(string[] args)
{
// Initialize random number generator
// srand(time(null));
for (int i = 0; i < 50; i++) {
Console.Write(rand75());
}
}
}
// This code is contributed by phasing17
Javascript
// JavaScript program to implement the approach
// Random Function to that returns 0 or 1 with
// equal probability
function rand50()
{
return (Math.floor(Math.random() * 2) & 1);
}
function rand75()
{
return (rand50() & rand50())^1;
}
for (var i = 0; i < 50; i++)
process.stdout.write(rand75().toString());
//This code is contributed by phasing17
Producción
11111111000111101111110011111110011110111111010111
También podemos reemplazar los operadores Bitwise OR y Bitwise AND con operadores OR y AND :
// Random Function to that returns 1 with 75%
// probability and 0 with 25% probability using
// OR or AND operator
int rand75()
{
return !(rand50() && rand50());
// return rand50() || rand50()
}
También podemos lograr el resultado utilizando el operador de desplazamiento a la izquierda y Bitwise XOR :
C++
// Program to print 1 with 75% probability and 0
// with 25% probability
#include <iostream>
using namespace std;
// Random Function to that returns 0 or 1 with
// equal probability
int rand50()
{
// rand() function will generate odd or even
// number with equal probability. If rand()
// generates odd number, the function will
// return 1 else it will return 0.
return rand() & 1;
}
// Random Function to that returns 1 with 75%
// probability and 0 with 25% probability using
// left shift and Bitwise XOR
int rand75()
{
// x is one of {0, 1}
int x = rand50();
x = x << 1;
// x is now one of {00, 10}
x = x ^ rand50();
// x is now one of {00, 01, 10, 11}
return (x > 0) ? 1 : 0;
}
// Driver code to test above functions
int main()
{
// Initialize random number generator
srand(time(NULL));
for (int i = 0; i < 50; i++)
cout << rand75();
return 0;
}
Java
// Java program to print 1 with 75% probability and 0
// with 25% probability
class GFG
{
// Random Function to that returns 0 or 1 with
// equal probability
static int rand50()
{
// rand() function will generate odd or even
// number with equal probability. If rand()
// generates odd number, the function will
// return 1 else it will return 0.
return (int) (10 * Math.random()) & 1;
}
// Random Function to that returns 1 with 75%
// probability and 0 with 25% probability using
// left shift and Bitwise XOR
static int rand75()
{
// x is one of {0, 1}
int x = rand50();
x = x << 1;
// x is now one of {00, 10}
x = x ^ rand50();
// x is now one of {00, 01, 10, 11}
return (x > 0) ? 1 : 0;
}
// Driver code
public static void main(String[] args)
{
for (int i = 0; i < 50; i++)
System.out.print(rand75());
}
}
// This code is contributed by 29AjayKumar
Python3
# Program to print 1 with 75% probability and 0
# with 25% probability
from random import randrange
# Random Function to that returns 0 or 1 with
# equal probability
def rand50():
# rand range function generates a integer between
# the provided ranges which is half closed interval
# It will generate integer 0 or 1 if passed 0,2 as parameter
return (int)(randrange(0, 2)) & 1
# Random Function to that returns 1 with 75%
# probability and 0 with 25% probability using
# left shift and Bitwise XOR
def rand75():
# x is one of {0, 1}
x = rand50()
x = x << 1
# x is now one of {00, 10}
x = x ^ rand50()
# x is now one of {00, 01, 10, 11}
return 1 if (x > 0) else 0
# Driver code to test above functions
for i in range(0, 50):
print(rand75(), end="")
# This code is contributed by meetgor.
C#
// C# program to print 1 with 75% probability and 0
// with 25% probability
using System;
public class GFG
{
// Random Function to that returns 0 or 1 with
// equal probability
static Random rnd = new Random();
static int rand50()
{
// Next(2) will generate 0 or 1 with equal probability
return rnd.Next(2);
}
// Random Function to that returns 1 with 75%
// probability and 0 with 25% probability using
// left shift and Bitwise XOR
static int rand75()
{
// x is one of {0, 1}
int x = rand50();
x = x << 1;
// x is now one of {00, 10}
x = x ^ rand50();
// x is now one of {00, 01, 10, 11}
return (x > 0) ? 1 : 0;
}
static public void Main (){
for (int i = 0; i < 50; i++)
Console.Write(rand75());
}
}
// This code is contributed by shruti456rawal
PHP
<?php
// Program to print 1 with
// 75% probability and 0
// with 25% probability
// Random Function to that
// returns 0 or 1 with
// equal probability
function rand50()
{
// rand() function will
// generate odd or even
// number with equal
// probability. If rand()
// generates odd number,
// the function will return
// 1 else it will return 0.
return rand() & 1;
}
// Random Function to that
// returns 1 with 75%
// probability and 0 with
// 25% probability using
// left shift and Bitwise XOR
function rand75()
{
// x is one of {0, 1}
$x = rand50();
$x = $x << 1;
// x is now one
// of {00, 10}
$x = $x ^ rand50();
// x is now one of
// {00, 01, 10, 11}
return ($x > 0) ? 1 : 0;
}
// Driver code
// Initialize random
// number generator
srand(time(NULL));
for ($i = 0; $i < 50; $i++)
echo rand75();
// This code is contributed
// by ajit
?>
Javascript
<script>
// Javascript program to print 1 with 75% probability and 0
// with 25% probability
// Random Function to that returns 0 or 1 with
// equal probability
function rand50()
{
// rand() function will generate odd or even
// number with equal probability. If rand()
// generates odd number, the function will
// return 1 else it will return 0.
return Math.floor((10 * Math.random())) & 1;
}
// Random Function to that returns 1 with 75%
// probability and 0 with 25% probability using
// Bitwise OR
function rand75()
{
// x is one of {0, 1}
let x = rand50();
x = x << 1;
// x is now one of {00, 10}
x = x ^ rand50();
// x is now one of {00, 01, 10, 11}
return (x > 0) ? 1 : 0;
}
// Driver code
for (let i = 0; i < 50; i++)
{
document.write(rand75());
}
// This code is contributed by rag2127
</script>
Producción
10110100111011011110111100101111110111100001111111
Tiempo Complejidad: O(1)
Espacio Auxiliar: O(1)
Tenga en cuenta que las soluciones anteriores producirán resultados diferentes cada vez que las ejecutemos.
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Artículo escrito por GeeksforGeeks-1 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA