Generate 0 and 1 with 25% and 75% probability

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.
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