| Line 18: | Line 18: | ||
It's a log2(N) algorithm where we recursively compare and swap elements 2 by 2 in a very specific manner. | It's a log2(N) algorithm where we recursively compare and swap elements 2 by 2 in a very specific manner. | ||
| − | For 8 values, we first perform 4 compare&swaps like this: | + | For 8 values, we first perform 4 compare&swaps like this (pass 1): |
[[File:BitonicBuild0.png]] | [[File:BitonicBuild0.png]] | ||
| − | Then we perform 4 compares&swaps like this: | + | Then we perform 4 compares&swaps like this (pass 2): |
[[File:BitonicBuild1.png]] | [[File:BitonicBuild1.png]] | ||
| − | Finally we perform 4 compares&swaps like this: | + | Finally we perform 4 compares&swaps like this (pass 3): |
[[File:BitonicBuild2.png]] | [[File:BitonicBuild2.png]] | ||
| Line 35: | Line 35: | ||
Well it's another log2(N) algorithm as in part 1. You'll need to swap numbers log2(N) times. | Well it's another log2(N) algorithm as in part 1. You'll need to swap numbers log2(N) times. | ||
| − | For 8 values, we first perform 4 compares&swaps like this: | + | For 8 values, we first perform 4 compares&swaps like this (pass 1): |
[[File:BitonicCompare0.png]] | [[File:BitonicCompare0.png]] | ||
| − | Then we perform 4 compares&swaps like this: | + | Then we perform 4 compares&swaps like this (pass 2): |
[[File:BitonicCompare1.png]] | [[File:BitonicCompare1.png]] | ||
| − | Finally we perform 4 compares&swaps like this: | + | Finally we perform 4 compares&swaps like this (pass 3): |
[[File:BitonicCompare2.png]] | [[File:BitonicCompare2.png]] | ||
| Line 52: | Line 52: | ||
==Example== | ==Example== | ||
| + | |||
| + | Here x0, x1, ..., xn}+ describes a set of values in ascending order and {x0, x1, ..., xn}- describes a set of values in descending order. While { {...}+, {...}- }B describes a bitonic sequence. | ||
| + | |||
| + | |||
| + | Initial random sequence: 35, 16, 31, 4, 4, 16, 17, 12 | ||
| + | |||
| + | After part 1 pass 1: {{16, 35}+, {31, 4}-}B, {{4, 16}+, {17, 12}-}B ← We already have 2 size 4 bitonic sequences | ||
| + | |||
| + | After part 1 pass 2: 16, 4, 31, 35, 17, 16, 4, 12 ← It's becoming somewhat random again while we're sorting the 2 size 4 bitonic sequences into a single size 8 sequence | ||
| + | |||
| + | After part 1 pass 3: {{4, 16, 31, 35}+, {17, 16, 12, 4}-}B ← And we're done! | ||
Revision as of 16:17, 11 September 2015
I wanted to write a short explanation about bitonic sort because it's simple as hell but no one does a good job at explaining it correctly.
You can find the video explanation here https://www.youtube.com/watch?v=GEQ8y26blEY but it's a bit tedious so to sum up the algorithm, here's what you need to know:
- A bitonic sequence is a sequence of numbers that can be ordered as first ascending then descending (or the opposite)
- For example: (1, 2, 3, 4) followed by (4,3,2,1) is bitonic.
- The bitonic sort algorithm works in 2 parts:
- (1) First, you need to transform any random sequence of numbers into a bitonic sequence
- (2) Second, you can then sort the bitonic sequence in ascending order
And that is all there is to it! Now let's see how to execute the 2 parts of the algorithm.
Contents
Quick Algorithm
Part 1: Transforming any sequence of numbers into a bitonic sequence
It's a log2(N) algorithm where we recursively compare and swap elements 2 by 2 in a very specific manner.
For 8 values, we first perform 4 compare&swaps like this (pass 1):
Then we perform 4 compares&swaps like this (pass 2):
Finally we perform 4 compares&swaps like this (pass 3):
Part 2: Sorting the bitonic sequence
Well it's another log2(N) algorithm as in part 1. You'll need to swap numbers log2(N) times.
For 8 values, we first perform 4 compares&swaps like this (pass 1):
Then we perform 4 compares&swaps like this (pass 2):
Finally we perform 4 compares&swaps like this (pass 3):
The way I see it
Example
Here x0, x1, ..., xn}+ describes a set of values in ascending order and {x0, x1, ..., xn}- describes a set of values in descending order. While { {...}+, {...}- }B describes a bitonic sequence.
Initial random sequence: 35, 16, 31, 4, 4, 16, 17, 12
After part 1 pass 1: {{16, 35}+, {31, 4}-}B, {{4, 16}+, {17, 12}-}B ← We already have 2 size 4 bitonic sequences
After part 1 pass 2: 16, 4, 31, 35, 17, 16, 4, 12 ← It's becoming somewhat random again while we're sorting the 2 size 4 bitonic sequences into a single size 8 sequence
After part 1 pass 3: {{4, 16, 31, 35}+, {17, 16, 12, 4}-}B ← And we're done!