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  • 07/16/99 05:58 PM
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    Elementary Sorting Techniques

    General and Gameplay Programming

                           Elementary Sorting Algorithms
    There is a suprisingly diverse collection of algorithms that have been
    developed to solve the apparently simple problem of "Sorting".
    The general sorting problem is simple enough to describe: Given an
    initially unordered array of N records, with one field distinguished as the
    key, rearrange the records so they are sorted into increasing (or
    decreasing) order, according to each record's key.
    Sorting algorithms are used in all kinds of applications and are necessary,
    for instance, if we plan to use efficient searching algorithms like Binary
    Search or Interpolation Search, since these require their data to be
    Sorting algorithms are often subdivided into "elementary" algorithms that
    are simple to implement compared to more complex algorithms that, while
    more efficient, are also more difficult to understand, implement, and
    It is not always true that the more complex algorithms are the preferred
    ones. Elementary algorithms are generally more appropriate in the following
       * less than 100 values to be sorted
       * the values will be sorted just once
       * special cases such as:
            o the input data are "almost sorted"
            o there are many equal keys
    In general, elementary sorting methods require O(N2) steps for N random key
    values. The more complex methods can often sort the same data in just O(N
    log N) steps. Although it is rather difficult to prove, it can be shown
    that roughly N log N comparisons are required, in the general case.
    Internal vs. External Sorting
    Normally, when considering a sorting problem, we will assume that the
    number of records to be sorted is small enough that we can fit the entire
    data set in the computer's memory (RAM) all at once. When this is true, we
    can make use of an internal sorting algorithm, which assumes that any key
    or record can be accessed or moved at any time. That is, we have "random
    access" to the data.
    Sometimes, when sorting an extremely large data set such as Canada's Census
    Data, there are simply too many records for them to all fit in memory at
    once. In this case, we have to resort to external sorting algorithms that
    don't assume we have random access to the data. Instead, these algorithms
    assume the data is stored on magnetic tapes or disks and only portions of
    the data will fit in memory. These algorithms use "sequential access" to
    the data and proceed by reading in, processing, and writing out blocks of
    records at a time. These partially sorted blocks need to be combined or
    merged in some manner to eventually sort the entire list.
    When a sorting algorithm is applied to a set of records, some of which
    share the same key, there are several different orderings that are all
    correctly sorted. If the ordering of records with identical keys is always
    the same as in the original input, then we say that the sorting algorithm
    used is "stable".
    This property can be useful. For instance, consider sorting a list of
    student records alphabetically by name, and then sorting the list again,
    but this time by letter grade in a particular course. If the sorting
    algorithm is stable, then all the students who got "A" will be listed
    Stability is a difficult property to achieve if we also want our sorting
    algorithm to be efficient.
    Indirect Sorting
    One final issue to keep in mind when implementing a sorting algorithm is
    the size of the records themselves. Many sorting algorithms move and
    interchange records in memory several times before they are moved into
    their final sorted position. For large records, this can add up to lots of
    execution time spent simply copying data.
    A popular solution to this problem is called "indirect sorting". The idea
    is to sort the indices of the records, rather than the records themselves.

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