Is it possible to rearrange an array in place in O(N)?

Question

If I have a size N array of objects, and I have an array of unique numbers in the range 1...N, is there any algorithm to rearrange the object array in-place in the or

Answer 1

I think this should do:

static  void arrange(T[] data, int[] p) {
    boolean[] done = new boolean[p.length];        
    for (int i = 0; i < p.length; i++) {
        if (!done[i]) {
            T t = data[i];
            for (int j = i;;) {
                done[j] = true;

                if (p[j] != i) {
                    data[j] = data[p[j]];
                    j = p[j];
                } else {
                    data[j] = t;
                    break;
                }
            }                
        }
    }
}

Note: This is Java. If you do this in a language without garbage collection, be sure to delete done.

If you care about space, you can use a BitSet for done. I assume you can afford an additional bit per element because you seem willing to work with a permutation array, which is several times that size.

This algorithm copies instances of T n + k times, where k is the number of cycles in the permutation. You can reduce this to the optimal number of copies by skipping those i where p[i] = i.