Generating all permutations of a given string

Question

What is an elegant way to find all the permutations of a string. E.g. permutation for ba, would be ba and ab, but what about longer st

Answer 1

Recursion is not necessary, even you can calculate any permutation directly, this solution uses generics to permute any array.

Here is a good information about this algorihtm.

For C# developers here is more useful implementation.

public static void main(String[] args) {
    String word = "12345";

    Character[] array = ArrayUtils.toObject(word.toCharArray());
    long[] factorials = Permutation.getFactorials(array.length + 1);

    for (long i = 0; i < factorials[array.length]; i++) {
        Character[] permutation = Permutation.getPermutation(i, array, factorials);
        printPermutation(permutation);
    }
}

private static void printPermutation(Character[] permutation) {
    for (int i = 0; i < permutation.length; i++) {
        System.out.print(permutation[i]);
    }
    System.out.println();
}

This algorithm has O(N) time and space complexity to calculate each permutation.

public class Permutation {
    public static  T[] getPermutation(long permutationNumber, T[] array, long[] factorials) {
        int[] sequence = generateSequence(permutationNumber, array.length - 1, factorials);
        T[] permutation = generatePermutation(array, sequence);

        return permutation;
    }

    public static  T[] generatePermutation(T[] array, int[] sequence) {
        T[] clone = array.clone();

        for (int i = 0; i < clone.length - 1; i++) {
            swap(clone, i, i + sequence[i]);
        }

        return clone;
    }

    private static int[] generateSequence(long permutationNumber, int size, long[] factorials) {
        int[] sequence = new int[size];

        for (int j = 0; j < sequence.length; j++) {
            long factorial = factorials[sequence.length - j];
            sequence[j] = (int) (permutationNumber / factorial);
            permutationNumber = (int) (permutationNumber % factorial);
        }

        return sequence;
    }

    private static  void swap(T[] array, int i, int j) {
        T t = array[i];
        array[i] = array[j];
        array[j] = t;
    }

    public static long[] getFactorials(int length) {
        long[] factorials = new long[length];
        long factor = 1;

        for (int i = 0; i < length; i++) {
            factor *= i <= 1 ? 1 : i;
            factorials[i] = factor;
        }

        return factorials;
    }
}