Random walk with equal probability

Question

This method randomly increments or decrements (with equal probability) until either -3 or 3 are reached. I'd like to maintain printing the value of pos on each iteration, and printing the largest positive number max reached at the end of the loop. How can I improve this method using the Random() function? I know this sounds pretty ambiguous, but I'd like to know if I can make rand.nextInt(2) == 0 an easier condition to understand? Any suggestions/improvements are welcome!

public static void randomWalk() {
    Random rand = new Random();
    int pos = 0;
    int max = 0;
    System.out.println("position = " + pos);
    while (pos > -3 && pos < 3) {
        if (rand.nextInt(2) == 0) {
            pos++;
            if (pos > 0) {
                max = pos;
            }
        } else {
            pos--;
        }
        System.out.println("position = " + (int) pos);
            
    }
    System.out.println("max position = " + max);
}

Answer 1

There's a minor bug there:

        if (pos > 0) {
            max = pos;
        }

should test pos > max instead.

---

Use

max = Math.max(max, pos)

to make it shorter.

---

I'd like to know if I can make rand.nextInt(2) == 0 an easier condition to understand?

Use rand.nextBoolean(). For a probability of exactly 50%, it's perfect.

For other probabilities, you can use

 rand.nextDouble() < probability

---

Another possibility is simply

pos += 2 * rand.nextInt(2) - 1;
max = Math.max(max, pos);

or

pos += rand.nextBoolean() ? 1 : -1;
max = Math.max(max, pos);

or

private static final int[] DELTAS = {+1, -1};

pos += DELTAS[rand.nextInt(DELTAS.length)];
max = Math.max(max, pos);

without any conditionals. You may consider it tricky, but it isn't. Obviously, my last solution shouldn't be used for such a simple case.

Concerning the computation of max it may be slightly less efficient since it gets executed even if the value decreases. But this doesn't matter unless you need to optimize heavily (your print is many orders of magnitude slower than this).

Answer 2

Expression

pos > -3 && pos < 3

Can be

Math.abs(pos) < 3

Random choice

Java Random had method for sampling boolean values nextBoolean

Bug

This line

if (pos > 0) {

do not give you

the largest positive number max reached at the end of the loop

Improvement

You don't need to make loop at all. You need random generator that will provide 2 values at each iteration:

• max positive number
• 3 or -3

This can be done using random in following way

long sample = Math.abs(rand.nextLong());
int pos, max;
if (sample % 2 == 0) {
    pos = 3;
    max = 3;
} else {
    pos = -3;
    max = int(sample % 3);
}