# Implement rand3() using rand2()

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.

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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; ` `} `

## 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 `

## PHP

 ` `

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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