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Instead of popping only the maximum element from the heap during each iteration, we now pop the two largest elements at once. Although this introduces an additional comparison to determine the second largest element, it enables a reduction in the height of the tree by one during the heapify operations starting from root's left/right child. This reduction in tree height by one leads to a decrease of one comparison and one swap. This optimization results in saving approximately 0.5 * n swaps without increasing the number of comparisons. Additionally, the heap size during heapify is now one less than the original size, offering a chance for further reduction in comparisons and swaps. The following experimental data is based on the array generated using get_random_u32(). | N | swaps (old) | swaps (new) | comparisons (old) | comparisons (new) | |-------|-------------|-------------|-------------------|-------------------| | 1000 | 9054 | 8569 | 10328 | 10320 | | 2000 | 20137 | 19182 | 22634 | 22587 | | 3000 | 32062 | 30623 | 35833 | 35752 | | 4000 | 44274 | 42282 | 49332 | 49306 | | 5000 | 57195 | 54676 | 63300 | 63294 | | 6000 | 70205 | 67202 | 77599 | 77557 | | 7000 | 83276 | 79831 | 92113 | 92032 | | 8000 | 96630 | 92678 | 106635 | 106617 | | 9000 | 110349 | 105883 | 121505 | 121404 | | 10000 | 124165 | 119202 | 136628 | 136617 | Link: https://lkml.kernel.org/r/20240113031352.2395118-3-visitorckw@gmail.com Signed-off-by: Kuan-Wei Chiu <visitorckw@gmail.com> Cc: Ching-Chun (Jim) Huang <jserv@ccns.ncku.edu.tw> Cc: George Spelvin <lkml@sdf.org> Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Linux kernel
============
There are several guides for kernel developers and users. These guides can
be rendered in a number of formats, like HTML and PDF. Please read
Documentation/admin-guide/README.rst first.
In order to build the documentation, use ``make htmldocs`` or
``make pdfdocs``. The formatted documentation can also be read online at:
https://www.kernel.org/doc/html/latest/
There are various text files in the Documentation/ subdirectory,
several of them using the Restructured Text markup notation.
Please read the Documentation/process/changes.rst file, as it contains the
requirements for building and running the kernel, and information about
the problems which may result by upgrading your kernel.