Implement rand12() using rand6() in one line

Given a function rand6() that returns random numbers from 1 to 6 with equal probability, implement one-liner function rand12() using rand6() that returns random numbers from 1 to 12 with equal probability. Solution should minimize the number of calls to rand6() method. Use of any other library function and floating point arithmetic are not allowed.

The idea is to use expression

rand6() + (rand6() % 2) * 6

. It returns random numbers from 1 to 12 with equal probability. The expression is equivalent to –

// if rand6() is even
if (rand6() % 2)
    return 6 + rand6();
else // if rand6() is odd
    return rand6();

We can also use any one of below expressions that works in a similar way –

• rand6() + !(rand6() % 2) * 6 or
• rand6() + (rand6() & 1) * 6 or
• rand6() + !(rand6() & 1) * 6

Below is C++ implementation of above idea –

CPP

// C++ Program to print random numbers from 1 to 12
// with equal probability using a function that returns
// random numbers from 1 to 6 with equal probability
#include <iostream>
using namespace std;

// Function that returns random numbers from 1 to 6
// with equal probability
int rand6()
{
    // rand() will generate random numbers between 0 and
    // RAND_MAX with equal probability
    // rand() % 6 returns number from 0 to 5 equal probability
    // (rand() % 6) + 1 returns number from 1 to 6 with
    // equal probability
    return (rand() % 6) + 1;
}

// The function uses rand6() to return random numbers
// from 1 to 12 with equal probability
int rand12()
{
    return rand6() + (rand6() % 2) * 6;
}

// Driver code to test above functions
int main()
{
    // Initialize random number generator
    srand(time(NULL));
    int N = 12;

    int freq[N + 1] = { 0 };

    // call rand12() multiple times and store its results
    for (int i = 0; i < N * 100000; i++)
        freq[rand12()]++;

    // print frequency of numbers 1-12
    for (int i = 1; i <= N; i++)
        cout << freq[i] << " ";

    return 0;
}

Java

import java.util.Random;

public class RandomNumbers {
    public static int rand6() {
        Random random = new Random();
        //nextInt(6) generates a random number from 0 to 5
        return random.nextInt(6) + 1;
    }

    public static int rand12() {
        return rand6() + (rand6() % 2) * 6;
    }

    public static void main(String[] args) {
        int N = 12;
        int[] freq = new int[N + 1];

        // Initialize random number generator
        Random random = new Random();

        // Call rand12() multiple times and store its results
        for (int i = 0; i < N * 100000; i++) {
            freq[rand12()]++;
        }

        // Print the frequency of numbers 1-12
        for (int i = 1; i <= N; i++) {
            System.out.print(freq[i] + " ");
        }
    }
}

C#

using System;

class Program
{
    // Create a single instance of Random for better performance
    static Random rand = new Random();

    // Function that returns random numbers from 1 to 6 with equal probability
    static int Rand6()
    {
        return rand.Next(1, 7);
    }

    // The function uses Rand6() to return random numbers from 1 to 12 with equal probability
    static int Rand12()
    {
        return Rand6() + (Rand6() % 2) * 6;
    }

    // Driver code to test above functions
    static void Main()
    {
        int N = 12;
        int iterations = 100000;

        int[] freq = new int[N + 1];

        // call Rand12() multiple times and store its results
        for (int i = 0; i < iterations; i++)
            freq[Rand12()]++;

        // print frequency of numbers 1-12
        for (int i = 1; i <= N; i++)
            Console.Write(freq[i] + " ");

        Console.ReadLine(); // Added to keep the console window open until a key is pressed
    }
}

Javascript

function rand6() {
  // Generates a random number from 1 to 6
  return Math.floor(Math.random() * 6) + 1;
}

function rand12() {
  return rand6() + (rand6() % 2) * 6;
}

const N = 12;
const freq = new Array(N + 1).fill(0);

// Call rand12() multiple times and store its results
for (let i = 0; i < N * 100000; i++) {
  freq[rand12()]++;
}

// Print the frequency of numbers 1-12
for (let i = 1; i <= N; i++) {
  console.log(freq[i]);
}

Output:

100237 100202 99678 99867 100253 99929 100287 100449 99827 99298 100019 99954 

Another Solution –

int rand12()
{
    return (rand6() * 2) - (rand6() & 1);
}

rand6() * 2

will return even numbers 2, 4, 6, 8, 10 and 12 with equal probability and

rand6() & 1

will return 0 or 1 based on rand6() is even or odd respectively. So, the expression

(rand6() * 2) – (rand6() & 1)

will return random numbers from 1 to 12 with equal probability.

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

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