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java.lang.Object cern.colt.GenericSorting
Generically sorts arbitrary shaped data (for example multiple arrays, 1,2 or 3d matrices, and so on) using a quicksort or mergesort. This class addresses two problems, namely
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 ...
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 IntComparator
. 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 Swapper
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 
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; } }; 
Sorts involving floating point data and not involving comparators, like, for
example provided in the JDK Arrays
and in the 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.
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 "inplace", 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.
Arrays
,
Sorting
,
Sorting
Method Summary  
static void 
mergeSort(int fromIndex,
int toIndex,
IntComparator c,
Swapper swapper)
Sorts the specified range of elements according to the order induced by the specified comparator. 
static void 
quickSort(int fromIndex,
int toIndex,
IntComparator c,
Swapper swapper)
Sorts the specified range of elements according to the order induced by the specified comparator. 
Methods inherited from class java.lang.Object 
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
Method Detail 
public static void mergeSort(int fromIndex, int toIndex, IntComparator c, Swapper swapper)
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.
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.swapper
 an object that knows how to swap the elements at any two indexes (a,b).IntComparator
,
Swapper
public static void quickSort(int fromIndex, int toIndex, IntComparator c, Swapper swapper)
The sorting algorithm is a tuned quicksort, adapted from Jon L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function", SoftwarePractice and Experience, Vol. 23(11) P. 12491265 (November 1993). This algorithm offers n*log(n) performance on many data sets that cause other quicksorts to degrade to quadratic performance.
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.swapper
 an object that knows how to swap the elements at any two indexes (a,b).IntComparator
,
Swapper

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