* The implementation of the following problem:
Place N queens on an NxN chess board so that none of them attack
each other (the classic n-queens problem). Additionally, please
make sure that no three queens are in a straight line at ANY angle,
so queens on A1, C2 and E3, despite not attacking each other, form
a straight line at some angle.
* Run it with after build:
#+begin_example shell
// n = 15
$java -jar nqueen-1.0-SNAPSHOT.jar 15
#+end_example
* Performance optimization
test under N=15 (Solution size=18752).
| # | | time | git branch |
| | | (seconds) | |
|---+----------------------+-----------+-------------------------|
| 1 | initial version | 13.55 | recursive |
|---+----------------------+-----------+-------------------------|
| 2 | multi-thread | 7.07 | recursive_multi_threads |
| | | | |
| | | | |
| | | | |
| | | | |
|---+----------------------+-----------+-------------------------|
| 3 | multi-thread with | 5.73 | main |
| | validation method | | |
| | optimized | | |
|---+----------------------+-----------+-------------------------|
| 4 | iterative version | 9.72 | iterate_1st |
| | (abandoned) | | |
| | | | |
|---+----------------------+-----------+-------------------------|
| 5 | further optimization | N/A | N/A |
| | (TODO) | | |
| | | | |
| | | | |
| | | | |
|---+----------------------+-----------+-------------------------|
note for each version:
1. N/A
2. 4 threads does not provide 4 times better performance here due to
my test host is 2 cores CPU with hyper-threading. Since this task
is computational intensive, we will not benifit from
hyper-threading here.
3. replace O(n^2) any angle validation algorithm with O(n) replace
O(n) vertical validation algorithm with O(1)
4. iterative version is *abandoned* due to its the BFS behavior
introduced some limitation. Refer more details at the
interate_2nd branch.
5. from the profiling result. The any angle validation is still a
hot spot. Profiling in more details level will guide me to
optimize it to a better version, i.e. profiling tool like perf
can give more details profiling result on assembly generated by
OpenJDK's C2 compiler.
** profiling
I did some basic CPU profiling. Here are the result for above
version. (The iterate_2nd branch has more profiling result. But it
is not very relevant now as I abandon the iterative path.)
file: profile_recursive_single_thread.html is the profiling result for
version #1. file: profile_recursive_multi_thread.html is the profiling
result for version #3.
#+begin_example shell
// https://github.com/jvm-profiling-tools/async-profiler
$java -XX:+UnlockDiagnosticVMOptions -XX:+DebugNonSafepoints -agentpath:$ASYNC_PROF_PATH/libasyncProfiler.dylib=start,event=cpu,file=profile.html,flamegraph -jar nqueen-1.0-SNAPSHOT.jar 15
#+end_example
* Example output
** N=8
N=8. There are 8 solutions.
Runtime (seconds): 0.026625877 by 4 threads
The first 8 Solutions are: [[4, 6, 0, 3, 1, 7, 5, 2], [5, 1, 6, 0, 3, 7, 4, 2], [5, 2, 0, 6, 4, 7, 1, 3], [5, 3, 0, 4, 7, 1, 6, 2], [2, 4, 7, 3, 0, 6, 1, 5], [2, 5, 7, 1, 3, 0, 6, 4], [2, 6, 1, 7, 4, 0, 3, 5], [3, 1, 7, 4, 6, 0, 2, 5]]
Solution(#1): [5, 1, 6, 0, 3, 7, 4, 2]
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** N=18
This biggest number tried is N = 18.
N=18. There are 1001972 solutions.
Runtime (seconds): 954.997365061 by 4 threads
The first 10 Solutions are: [[0, 2, 5, 9, 6, 12, 16, 11, 13, 17, 3, 8, 4, 1, 10, 14, 7, 15], [0, 2, 5, 9, 14, 3, 8, 16, 13, 6, 17, 15, 7, 12, 10, 1, 4, 11], [0, 2, 5, 10, 12, 9, 4, 16, 14, 3, 7, 13, 17, 6, 1, 11, 15, 8], [0, 2, 5, 10, 12, 9, 4, 16, 14, 3, 7, 13, 17, 8, 6, 11, 15, 1], [0, 2, 5, 10, 13, 11, 8, 3, 1, 17, 14, 16, 6, 12, 9, 7, 4, 15], [0, 2, 5, 12, 6, 11, 14, 1, 13, 8, 17, 3, 16, 9, 4, 10, 7, 15], [0, 2, 5, 12, 9, 17, 8, 13, 1, 16, 14, 7, 4, 10, 3, 6, 15, 11], [0, 2, 5, 12, 15, 7, 3, 13, 6, 14, 17, 10, 16, 4, 8, 11, 9, 1], [0, 2, 5, 12, 15, 13, 16, 1, 6, 4, 14, 10, 8, 3, 11, 17, 7, 9], [0, 2, 5, 12, 15, 17, 3, 9, 6, 16, 14, 10, 1, 7, 4, 8, 11, 13]]
Solution(#1): [0, 2, 5, 9, 14, 3, 8, 16, 13, 6, 17, 15, 7, 12, 10, 1, 4, 11]
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