# Implement rand3() using rand2()

• Difficulty Level : Medium
• Last Updated : 09 Jun, 2022

Given a function rand2() that returns 0 or 1 with equal probability, implement rand3() using rand2() that returns 0, 1 or 2 with equal probability. Minimize the number of calls to rand2() method. Also, use of any other library function and floating point arithmetic are not allowed.

The idea is to use expression 2 * rand2() + rand2(). It returns 0, 1, 2, 3 with equal probability. To make it return 0, 1, 2 with equal probability, we eliminate the undesired event 3.
Below is the implementation of above idea –

## C++

 `// C++ Program to print 0, 1 or 2 with equal``// probability``#include ``using` `namespace` `std;` `// Random Function to that returns 0 or 1 with``// equal probability``int` `rand2()``{``    ``// 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 0, 1 or 2 with``// equal probability 1 with 75%``int` `rand3()``{``    ``// returns 0, 1, 2 or 3 with 25% probability``    ``int` `r = 2 * rand2() + rand2();``    ` `    ``if` `(r < 3)``        ``return` `r;``    ` `    ``return` `rand3();``}` `// Driver code to test above functions``int` `main()``{``    ``// Initialize random number generator``    ``srand``(``time``(NULL));`` ` `    ``for``(``int` `i = 0; i < 100; i++)``        ``cout << rand3();`` ` `    ``return` `0;``}`

## Java

 `// Java Program to print 0, 1 or 2 with equal ``// probability``import` `java.util.Random;``class` `GFG``{` `  ``// Random Function to that returns 0 or 1 with``  ``// equal probability``  ``static` `int` `rand2()``  ``{` `    ``// 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.``    ``Random rand = ``new` `Random(); ``    ``return` `(rand.nextInt() & ``1``);``  ``}` `  ``// Random Function to that returns 0, 1 or 2 with ``  ``// equal probability 1 with 75%``  ``static` `int` `rand3()``  ``{` `    ``// returns 0, 1, 2 or 3 with 25% probability``    ``int` `r = ``2` `* rand2() + rand2();` `    ``if` `(r < ``3``)``      ``return` `r;``    ``return` `rand3();``  ``}` `  ``// Driver code``  ``public` `static` `void` `main(String[] args) {``    ``for``(``int` `i = ``0``; i < ``100``; i++)``      ``System.out.print(rand3());``  ``}``}``// This code is contributed by divyesh072019.`

## Python3

 `# Python3 Program to print 0, 1 or 2 with equal``# Probability` `import` `random``# Random Function to that returns 0 or 1 with``# equal probability` `def` `rand2():` `    ``# randint(0,100) function will generate odd or even``    ``# number [1,100] with equal probability. If rand()``    ``# generates odd number, the function will``    ``# return 1 else it will return 0``    ``tmp``=``random.randint(``1``,``100``)``    ``return` `tmp``%``2``    ` `# Random Function to that returns 0, 1 or 2 with``# equal probability 1 with 75%``def` `rand3():``    ` `    ``# returns 0, 1, 2 or 3 with 25% probability``    ``r ``=` `2` `*` `rand2() ``+` `rand2()``    ``if` `r<``3``:``        ``return` `r``    ``return` `rand3()``    ` `# Driver code to test above functions``if` `__name__``=``=``'__main__'``:``    ``for` `i ``in` `range``(``100``):``        ``print``(rand3(),end``=``"")``        ` `#This code is contributed by sahilshelangia`

## C#

 `// C# Program to print 0, 1 or 2 with equal ``// probability``using` `System;``class` `GFG``{` `  ``// Random Function to that returns 0 or 1 with``  ``// equal probability``  ``static` `int` `rand2()``  ``{` `    ``// 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.``    ``Random rand = ``new` `Random();``    ``return` `(rand.Next() & 1);``  ``}` `  ``// Random Function to that returns 0, 1 or 2 with ``  ``// equal probability 1 with 75%``  ``static` `int` `rand3()``  ``{` `    ``// returns 0, 1, 2 or 3 with 25% probability``    ``int` `r = 2 * rand2() + rand2();` `    ``if` `(r < 3)``      ``return` `r;``    ``return` `rand3();``  ``}` `  ``// Driver code``  ``static` `void` `Main()``  ``{``    ``for``(``int` `i = 0; i < 100; i++)``      ``Console.Write(rand3());``  ``}``}` `// This code is contributed by divyeshrabadiya07.`

## PHP

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## Javascript

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Output :

`2111011101112002111002020210112022022022211100100121202021102100010200121121210122011022111020`

Another Solution –
If x = rand2() and y = rand2(), x + y will return 0 and 2 with 25% probability and 1 with 50% probability. To make probability of 1 equal to that of 0 and 2 i.e. 25%, we eliminate one undesired event that’s resulting in x + y = 1 i.e. either (x = 1, y = 0) or (x = 0, y = 1).

```int rand3()
{
int x, y;

do {
x = rand2();
y = rand2();
} while (x == 0 && y == 1);

return x + y;
}```

Please note above solutions will produce different results every time we run them.
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