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Commit 0e02ca29 authored by Kuan-Wei Chiu's avatar Kuan-Wei Chiu Committed by Andrew Morton
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lib/sort: optimize heapsort with double-pop variation

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: default avatarKuan-Wei Chiu <visitorckw@gmail.com>
Cc: Ching-Chun (Jim) Huang <jserv@ccns.ncku.edu.tw>
Cc: George Spelvin <lkml@sdf.org>
Signed-off-by: default avatarAndrew Morton <akpm@linux-foundation.org>
parent db946a42
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