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 :
// 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 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
# 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# 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
// 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
?>
<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 :
#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;
}
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());
}
}
}
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# 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 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 -
// 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 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
# 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# 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
// 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
?>
<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.