Author: Dann Corbit
Date: 11:48:54 10/25/99
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On October 25, 1999 at 12:26:37, Michel Langeveld wrote: >On October 25, 1999 at 10:17:53, Dann Corbit wrote: >>On October 23, 1999 at 10:36:40, Robert Hyatt wrote: >> >>>On October 22, 1999 at 10:03:29, Dann Corbit wrote: >>> >>>>Change to binary insertion and you will see a much bigger benefit. >>> >>>I tried both (from Knuth Sorting and Searching). Binary is very bad for >>>lists that have 1-5 entries max. from testing on my machine. Simple >>>insertion is no faster than the bubble sort I used, but it also turns out >>>to be no slower either, after testing Crafty over 300 different positions. >>> >>>I think I'll leave insertion in, to prevent such discussions in the >>>future, however. :) >>I have found a new modification to insertion sort (binary or linear) that will >>make a large improvement in speed. It has to do with the data movements to >>perform the actual insertion. By delaying the insertion, I can do all data >>movements as a single permutation and never move any element more than once. It >>won't work for big lists though, since the code size is O(n!). With just ten >>items there are a million leaves in the tree. However, for very small sublists >>I think it will do very well. > >Best way to prove your statement is code it, and prove it's faster! >Good news by the way. Got the idea from a web page. Here is an example for n=3. Number of comparisons is O(n*log(n)). For the left branch (1,2,3) do not move anything. For (1,3,2) permute the 3 & 2. For (3,1,2) and (2,3,1) we must move all of them, since none is in the right place, and for (3,2,1) we permute 1 & 3. It is very simple, really. I have a code generator to write the output, but I think I can simplify it a lot and use the inline keyword (it's C99). The colon in the diagram means compare. We don't actually compare twice (e.g. if I test for 1 < 2 I do not have another test for 2<1 {because that only finds equal which is unlikely and therefore a mostly wasted comparison} 1:2 / \ < / > \ / \ 2:3 1:3 / \ / \ < / > \ < / > \ / \ / \ 1,2,3 1:3 2,1,3 2:3 / \ / \ < / > \ < / > \ / \ / \ 1,3,2 3,1,2 2,3,1 3,2,1
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