How to generate a random permutation in Java?

Question

What is the best way to generate a random permutation of n numbers?

For example, say I have a set of numbers 1, 2 and 3 (n = 3)

Set of all possible permutations: {123, 132, 213, 231, 312, 321}

Now, how do I generate:

• one of the elements of the above sets (randomly chosen)
• a whole permutation set as shown above

In other words, if I have an array of n elements, how do I shuffle them randomly? Please assist. Thanks.

Solution

java.util.Collections.shuffle(List);

javadoc link for Collections.shuffle

List<Integer> list = new ArrayList<Integer>();
list.add(1);
list.add(2);
list.add(3);
java.util.Collections.shuffle(list);

It's worth noting that there are lots of algorithms you can use. Here is how it is implemented in the Sun JDK:

public static void shuffle(List<?> list, Random rnd) {
    int size = list.size();
    if (size < SHUFFLE_THRESHOLD || list instanceof RandomAccess) {
        for (int i=size; i>1; i--)
            swap(list, i-1, rnd.nextInt(i));
    } else {
        Object arr[] = list.toArray();

        // Shuffle array
        for (int i=size; i>1; i--)
            swap(arr, i-1, rnd.nextInt(i));

        // Dump array back into list
        ListIterator it = list.listIterator();
        for (int i=0; i<arr.length; i++) {
            it.next();
            it.set(arr[i]);
        }
    }
}

Comments

[Shankar Raju]

Thanks so much. But the api says it works in linear time. Is it possible for us to achieve this in less than O(n) complexity?

[BlueRaja - Danny Pflughoeft]

@Shankar: Yes

[corsiKa]

@Danny that's possible, but impractical.

[Shankar Raju]

My bad! I changed it. But, I wanted the permutations to get generated randomly.

[corsiKa]

@metdos can you elaborate? I believe it's the knuth shuffle, and he kind of wrote the book on algorithms. Literally.

[metdos]

Yes, you are right. I guess my problem is with the random generator. I created a list with length of 3, and I shuffled it 100000 times, and the results weren't satisfactory(is not close to uniform as much as I expect)