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)
- Priority Queue (select largest value)
- Insert and Keep Sorted
- Diminishing Increment
- Divide & Conquer
Address-Calculation Sorting Methods
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 from 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)
notes: Very inefficient and should never be used. Uses an excessive and unnecessary number of exchanges.
Bubble Sort (Version from 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
notes: 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
notes: 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.
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