You can definitely do this in O(n log n). But the best approach depends on what is more important: quick, clean code or not allocating extra memory.
If you don't care about using extra memory, you can allocate a separate array, where each element is a pair:
public class Pair implements Comparable {
...
}
Then you would sort the array of pairs using Arrays.sort(Object[]).
If you don't want to allocate quite so much space, you can use an auxiliary array that contains the indexes in Integer form:
final String[] array1 = ...;
final String[] array2 = ...;
assert array1.length == array2.length;
Comparator<Integer> c = new Comparator<Integer> {
int compare(Integer a, Integer b) {
return array1[a].compareTo(array1[b]);
}
};
Integer[] aux = new Integer[array1.length];
for (int i = 0; i < aux.length; ++i) { aux[i] = i; }
Arrays.sort(aux, c);
String[] result = new String[array1.length];
for (int i = 0; i < aux.length; ++i) {
result[i] = array2[aux[i]];
}
If you are trying to do the entire thing in-place and not allocate additional memory, then you will need to implement one of the n-log-n sort algorithms yourself...