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## cern.colt
Class GenericSorting

    java.lang.Object
      cern.colt.GenericSorting

public class GenericSorting
extends Object

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 ...

1. 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.
2. 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.
3. 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 `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

    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 `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`.

#### 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
See Also:
  `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

### mergeSort

    public 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. 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.
    `swapper` - an object that knows how to swap the elements at any two indexes (a,b).
  See Also:
    `IntComparator`, `Swapper`

### quickSort

    public 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. 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). 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.
    `swapper` - an object that knows how to swap the elements at any two indexes (a,b).
  See Also:
    `IntComparator`, `Swapper`

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