| Generically sorts arbitrary shaped data (for example multiple arrays, 1,2 or 3-d matrices, and so on) using a
quicksort or mergesort. This class addresses two problems, namely
- Sorting multiple arrays in sync
- Sorting by multiple sorting criteria (primary, secondary, tertiary,
...)
Sorting multiple arrays in sync
Assume we have three arrays X, Y and Z. We want to sort all three arrays by
X (or some arbitrary comparison function). For example, we have
X=[3, 2, 1], Y=[3.0, 2.0, 1.0], Z=[6.0, 7.0, 8.0]. The output should
be
X=[1, 2, 3], Y=[1.0, 2.0, 3.0], Z=[8.0, 7.0, 6.0].
How can we achive this? Here are several alternatives. We could ...
- make a list of Point3D objects, sort the list as desired using a comparison
function, then copy the results back into X, Y and Z. The classic object-oriented
way.
- make an index list [0,1,2,...,N-1], sort the index list using a comparison function,
then reorder the elements of X,Y,Z as defined by the index list. Reordering
cannot be done in-place, so we need to copy X to some temporary array, then
copy in the right order back from the temporary into X. Same for Y and Z.
- use a generic quicksort or mergesort which, whenever two elements in X are swapped,
also swaps the corresponding elements in Y and Z.
Alternatives 1 and 2 involve quite a lot of copying and allocate significant amounts
of temporary memory. Alternative 3 involves more swapping, more polymorphic message dispatches, no copying and does not need any temporary memory.
This class implements alternative 3. It operates on arbitrary shaped data.
In fact, it has no idea what kind of data it is sorting. Comparisons and swapping
are delegated to user provided objects which know their data and can do the
job.
Lets call the generic data g (it may be one array, three linked lists
or whatever). This class takes a user comparison function operating on two indexes
(a,b), namely an
Sortable . The comparison function determines
whether g[a] is equal, less or greater than g[b]. The sort,
depending on its implementation, can decide to swap the data at index a
with the data at index b. It calls a user provided
Sortable object that knows how to swap the data of these indexes.
The following snippet shows how to solve the problem.
final int[] x;
final double[] y;
final double[] z;
x = new int[] {3, 2, 1 };
y = new double[] {3.0, 2.0, 1.0};
z = new double[] {6.0, 7.0, 8.0};
// this one knows how to swap two indexes (a,b)
Swapper swapper = new Swapper() {
public void swap(int a, int b) {
int t1; double t2, t3;
t1 = x[a]; x[a] = x[b]; x[b] = t1;
t2 = y[a]; y[a] = y[b]; y[b] = t2;
t3 = z[a]; z[a] = z[b]; z[b] = t3;
}
};
// simple comparison: compare by X and ignore Y,Z
IntComparator comp = new IntComparator() {
public int compare(int a, int b) {
return x[a]==x[b] ? 0 : (x[a]<x[b] ? -1 : 1);
}
};
System.out.println("before:");
System.out.println("X="+Arrays.toString(x));
System.out.println("Y="+Arrays.toString(y));
System.out.println("Z="+Arrays.toString(z));
GenericSorting.quickSort(0, X.length, comp, swapper);
// GenericSorting.mergeSort(0, X.length, comp, swapper);
System.out.println("after:");
System.out.println("X="+Arrays.toString(x));
System.out.println("Y="+Arrays.toString(y));
System.out.println("Z="+Arrays.toString(z));
|
Sorting by multiple sorting criterias (primary, secondary, tertiary, ...)
Assume again we have three arrays X, Y and Z. Now we want to sort all three
arrays, primarily by Y, secondarily by Z (if Y elements are equal). For example,
we have
X=[6, 7, 8, 9], Y=[3.0, 2.0, 1.0, 3.0], Z=[5.0, 4.0, 4.0, 1.0]. The
output should be
X=[8, 7, 9, 6], Y=[1.0, 2.0, 3.0, 3.0], Z=[4.0, 4.0, 1.0, 5.0].
Here is how to solve the problem. All code in the above example stays the same,
except that we modify the comparison function as follows
//compare by Y, if that doesn't help, reside to Z
IntComparator comp = new IntComparator() {
public int compare(int a, int b) {
if (y[a]==y[b]) return z[a]==z[b] ? 0 : (z[a]<z[b] ? -1 : 1);
return y[a]<y[b] ? -1 : 1;
}
};
|
Notes
Sorts involving floating point data and not involving comparators, like, for
example provided in the JDK
java.util.Arrays and in the Colt
(cern.colt.Sorting) handle floating point numbers in special ways to guarantee
that NaN's are swapped to the end and -0.0 comes before 0.0. Methods delegating
to comparators cannot do this. They rely on the comparator. Thus, if such boundary
cases are an issue for the application at hand, comparators explicitly need
to implement -0.0 and NaN aware comparisons. Remember: -0.0 < 0.0 == false,
(-0.0 == 0.0) == true, as well as 5.0 < Double.NaN == false,
5.0 > Double.NaN == false. Same for float.
Implementation
The quicksort is a derivative of the JDK 1.2 V1.26 algorithms (which are, in
turn, based on Bentley's and McIlroy's fine work).
The mergesort is a derivative of the JAL algorithms, with optimisations taken from the JDK algorithms.
Both quick and merge sort are "in-place", i.e. do not allocate temporary memory (helper arrays).
Mergesort is stable (by definition), while quicksort is not.
A stable sort is, for example, helpful, if matrices are sorted successively
by multiple columns. It preserves the relative position of equal elements.
author:
wolfgang.hoschek@cern.ch
version:
1.0, 03-Jul-99 |
