Class GenericSorter
- 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.
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 |
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 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 invalid input: '<' 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.
- Version:
- 1.0, 03-Jul-99
- Author:
- wolfgang.hoschek@cern.ch
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Constructor Summary
ConstructorsModifierConstructorDescriptionprotected
Makes this class non instantiable, but still let's others inherit from it. -
Method Summary
Modifier and TypeMethodDescriptionstatic void
Sorts the specified range of elements according to the order induced by the specified comparator.static void
Sorts the specified range of elements according to the order induced by the specified comparator.
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Constructor Details
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GenericSorter
protected GenericSorter()Makes this class non instantiable, but still let's others inherit from it.
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Method Details
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quickSort
Sorts the specified range of elements according to the order induced by the specified comparator. All elements in the range must be mutually comparable by the specified comparator (that is, c.compare(a, b) must not throw an exception for any indexes a and b in the range).The sorting algorithm is a tuned quicksort, adapted from Jon L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function", Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November 1993). For details, see http://citeseer.ist.psu.edu/bentley93engineering.html. This algorithm offers n*log(n) performance on many data sets that cause other quicksorts to degrade to quadratic performance.
- Parameters:
fromIndex
- the index of the first element (inclusive) to be sorted.toIndex
- the index of the last element (exclusive) to be sorted.c
- the comparator to determine the order of the generic data; an object that knows how to swap the elements at any two indexes (a,b).
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mergeSort
Sorts the specified range of elements according to the order induced by the specified comparator. All elements in the range must be mutually comparable by the specified comparator (that is, c.compare(a, b) must not throw an exception for any indexes a and b in the range).This sort is guaranteed to be stable: equal elements will not be reordered as a result of the sort.
The sorting algorithm is a modified mergesort (in which the merge is omitted if the highest element in the low sublist is less than the lowest element in the high sublist). This algorithm offers guaranteed n*log(n) performance, and can approach linear performance on nearly sorted lists.
- Parameters:
fromIndex
- the index of the first element (inclusive) to be sorted.toIndex
- the index of the last element (exclusive) to be sorted.c
- the comparator to determine the order of the generic data; an object that knows how to swap the elements at any two indexes (a,b).
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