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Sorting Algorithms Animations

The following animations illustrate how effectively data sets from different starting points can be sorted using different algorithms.

How to use: Press "Play all", or choose the    button for the individual row/column to animate.

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Play AllInsertionSelectionBubbleShellMergeHeapQuickQuick3
Random
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Nearly Sorted
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Reversed
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Few Unique
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Play AllRandomNearly SortedReversedFew Unique
Insertion
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Selection
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Bubble
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Shell
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Merge
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Heap
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Quick
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Quick3
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Key:

  • Black values are sorted.
  • Gray values are unsorted.
  • A red triangle marks the algorithm position.
  • Dark gray values denote the current interval (shell, merge, quick).
  • A pair of red triangles marks the left and right pointers (quick).

Discussion:

These pages show 8 different sorting algorithms on 4 different initial conditions. These visualizations are intended to:

  • Show how each algorithm operates.
  • Show that there is no best sorting algorithm.
  • Show the advantages and disadvantages of each algorithm.
  • Show that worse-case asymptotic behavior is not always the deciding factor in choosing an algorithm.
  • Show that the initial condition (input order and key distribution) affects performance as much as the algorithm choice.

The ideal sorting algorithm would have the following properties:

  • Stable: Equal keys aren’t reordered.
  • Operates in place, requiring O(1) extra space.
  • Worst-case O(n·lg(n)) key comparisons.
  • Worst-case O(n) swaps.
  • Adaptive: Speeds up to O(n) when data is nearly sorted or when there are few unique keys.

There is no algorithm that has all of these properties, and so the choice of sorting algorithm depends on the application.

Sorting is a vast topic; this site explores the topic of in-memory generic algorithms for arrays. External sorting, radix sorting, string sorting, and linked list sorting—all wonderful and interesting topics—are deliberately omitted to limit the scope of discussion.

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References

Algorithms in Java, Parts 1-4, 3rd edition by Robert Sedgewick. Addison Wesley, 2003.

Quicksort is Optimal by Robert Sedgewick and Jon Bentley, Knuthfest, Stanford University, January, 2002.

Dual Pivot Quicksort: Code by Discussion.

Bubble-sort with Hungarian (“Csángó”) folk dance YouTube video, created at Sapientia University, Tirgu Mures (Marosvásárhely), Romania.

Select-sort with Gypsy folk dance YouTube video, created at Sapientia University, Tirgu Mures (Marosvásárhely), Romania.

Sorting Out Sorting, Ronald M. Baecker with the assistance of David Sherman, 30 minute color sound film, Dynamic Graphics Project, University of Toronto, 1981. Excerpted and reprinted in SIGGRAPH Video Review 7, 1983. Distributed by Morgan Kaufmann, Publishers. Excerpt.