Comparison of Sorting Algorithms

The following table summarizes the basic strategies used in various sorting
algorithms, and lists the algorithms that use these strategies.

     Comparison-Based Sorting Methods
          Transposition (exchange adjacent values)
               Bubble Sort **
          Priority Queue (select largest value)
               Selection Sort **
               Heap Sort
          Insert and Keep Sorted
               Insertion Sort **
               Tree Sort
          Diminishing Increment
               Shell Sort
          Divide & Conquer
               Merge Sort
     Address-Calculation Sorting Methods
          Radix Sort

Algorithms marked with ** have been discussed in class. Implementations of
some of these algorithms are available on the Pascal Page.

The diagrams below may help you develop an intuitive sense of how the
algorithms work. The vertical axis is the position within the array and the
horizontal axis is time. Values within the array are represented by small
squares with differing brightness. The goal of the algorithm is to sort the
values from darkest to lightest. In each diagram, the input array is
represented by a vertical column on the left, with an random assortment of
brightess values. (Click on an image to see a larger version.)

  [bubble sort]     [selection sort]     [insertion sort]     [quicksort]
      bubble            selection            insertion         quicksort

Bubble Sort exchanges adjacent values so lighter ones "bubble up" towards
the top, and darker ones "sink down" towards the bottom. Selection Sort
minimizes exchanges by scanning the unsorted portion to find the largest
remaining value on each iteration. Insertion Sort is familiar to anyone who
plays cards. It works by taking the next value from the unsorted portion
and inserting it into the already sorted portion of the array. Of these
three, Insertion Sort is the most efficient, on average, but Selection Sort
is preferred when the records are large. Bubble Sort is never preferred.
(Quicksort will be discussed later in this course.)

The following table summarizes what we have learned about the relative
efficiency of various sorting algorithms.

     Bubble Sort (version discussed in class)
          best case:
               about N comparisons, 0 exchanges,
               (input already sorted)
          worst case:
               about N^2 comparisons, N^2 exchanges,
               (input sorted in reverse order)
          average case:
               quite close to worst case (difficult to analyze)
               Very inefficient and should never be used. Uses an
               excessive and unnecessary number of exchanges.

     Bubble Sort (version in textbook)
          best case:
               about N^2/2 comparisons, 0 exchanges,
               (input already sorted)
          worst, average cases:
               about N^2/2 comparisons, N^2/2 exchanges

     Selection Sort
          all cases:
               about N^2/2 comparisons, N exchanges
               minimizes the number of exchanges;
               execution time quite insensitive to original ordering
               of input data.

     Insertion Sort
          best case:
               about N comparisons, 0 moves,
               (input already sorted)
          worst case:
               about N^2/2 comparisons, N^2/2 moves,
               (input sorted in reverse order)
          average case:
               about N^2/4 comparisons, N^2/4 moves
               very efficient when input is "almost sorted";
               moving a record is about half the work of exchanging
               two records, so average case is equivalent to roughly
               N^2/8 exchanges.


Discuss this article in the forums

Date this article was posted to 7/16/1999
(Note that this date does not necessarily correspond to the date the article was written)

See Also:
Sorting Algorithms

© 1999-2011 All rights reserved. Terms of Use Privacy Policy
Comments? Questions? Feedback? Click here!