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Generate 0 and 1 with 25% and 75% probability

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  • Difficulty Level : Medium
  • Last Updated : 01 Jul, 2022
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Given a function rand50() that returns 0 or 1 with equal probability, write a function that returns 1 with 75% probability and 0 with 25% probability using rand50() only. Minimize the number of calls to the rand50() method. Also, the use of any other library function and floating-point arithmetic are not allowed.

The idea is to use Bitwise OR. A bitwise OR takes two bits and returns 0 if both bits are 0, while otherwise, the result is 1. So it has 75% probability that it will return 1.

Below is the implementation of the above idea :

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>

Output

11101010110101011010000101011110100010111110101111

Time Complexity: O(1)
Auxiliary Space: O(1)

On similar lines, we can also use Bitwise AND. Since it returns 0 with 75% probability, we have to invert the result.

// Random Function to that returns 1 with 75% 
// probability and 0 with 25% probability using
// Bitwise AND
bool rand75() 
{
    return !(rand50() & rand50());
}

Below is the implementation of the above idea :

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

Output

11111111000111101111110011111110011110111111010111

We can replace Bitwise OR and Bitwise AND operators with OR and AND operators as well – 

// 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()
}

We can also achieve the result using the left shift operator and 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>

Output

10110100111011011110111100101111110111100001111111

Time Complexity: O(1)
Auxiliary Space: O(1)

Please note above solutions will produce different results every time we run them.
This article is contributed by Aditya Goel. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
 


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