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Fast and stable sort algorithm that uses O(1) memory. Public domain.
Java C C++
branch: master
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Chapter 1. Tools.md Fixing broken links
Chapter 2. Merging.md Code cleanup and fixed typos
Chapter 3. In-Place.md Tag the first value of each A block
Chapter 4. Faster!.md Adding the cached version of Rotate back again...
LICENSE Initial commit
README.md
WikiSort.c That's what I get for copying and pasting
WikiSort.cpp
WikiSort.java Slight changes

README.md

WikiSort

Update (04/28/14): Check out the GrailSort project on GitHub for a similar algorithm based on a paper by Huang and Langston. It's actually faster than WikiSort for the Random and RandomFew tests when you remove the 512-item cache! It goes to show that this is still an open area of research that could use your expertise.


WikiSort is an implementation of "block merge sort", or "block sort" for short, which is a stable merge sort based on the work described in "Ratio based stable in-place merging", by Pok-Son Kim and Arne Kutzner [PDF].

WikiSort is generally as fast as a standard merge sort while using O(1) memory, and is even faster when the input is partially ordered or as the arrays get larger. It can also be modified to use any additional memory optionally provided to it, which can further improve its speed.

C, C++, and Java versions are currently available, and you have permission from me and the authors of the paper (Dr. Kim and Dr. Kutzner) to do whatever you want with this code.


If you want to learn how it works, check out the documentation:
  • Chapter 1: Tools
  • Chapter 2: Merging
  • Chapter 3: In-Place
  • Chapter 4: Faster!

Or you can check out the Wikipedia page that is now up and running! Technically block sort is still a merge sort despite requiring the use of some other sorting algorithm like insertion sort to function properly, but it was too detailed to justify putting in the existing in-place merge sort page.


WikiSort vs. std::stable_sort()
(clang++ version 3.2, sorting 0 to 1.5 million items)

Using a 512-item fixed-size cache for O(1) memory:

Test             Fast comparisons   Slow comparisons   150,000,000 items    0-32 items
Random               6% faster        95% as fast         35% faster        45% faster
RandomFew            5% faster        16% faster          20% faster        45% faster
MostlyDescending    97% as fast       13% faster          99% as fast       53% faster
MostlyAscending    149% faster       117% faster         286% faster        47% faster
Ascending         1280% faster       518% faster        1101% faster       242% faster
Descending          23% faster       121% faster          12% faster       164% faster
Equal             1202% faster       418% faster        1031% faster       227% faster
Jittered           526% faster       298% faster         733% faster        70% faster
MostlyEqual         15% faster        57% faster          10% faster        42% faster
Append             153% faster        90% faster         348% faster       112% faster

Using a dynamically allocated half-size cache:

Test             Fast comparisons   Slow comparisons
Random              11% faster         3% faster
RandomFew           10% faster         5% faster
MostlyDescending    19% faster        26% faster
MostlyAscending     98% faster        79% faster
Ascending          861% faster       463% faster
Descending          39% faster       142% faster
Equal              837% faster       460% faster
Jittered           326% faster       243% faster
MostlyEqual         15% faster         2% faster
Append             159% faster        94% faster
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