Perl QOTW #2010-02-22 - Freecell Scans with Short Solutions

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Today I'm borrowing the collective wisdom of the Perl Quiz-of-the-Whatever
forum for an algorithmic task I need to accomplish for my own project.
The project in question is Freecell Solver ( http://fc-solve.berlios.de/ ),
which is an automated solver for http://en.wikipedia.org/wiki/FreeCell and 
several other types of card solitaire. 

fc-solve starts from the initial layout of the solitaire game and recurses
into more and more positions, which are counted by the solver's iterations,
until it reaches the final, solved state where all cards were moved to the
foundations.

After a certain number of iterations (which are roughly indicative of 
how long it took it to run), it yields a solution of a certain length ,which 
is desired to be as short as possible. Note that it may also report that it
is unable to solve the board (after going over all the derived positions) or 
that it could not find a solution within the quota of iterations that have
been allocated for it. 

Now, fc-solve has many different atomic scans, that when run alone, each
yields different solutions with different iteration counts and lengths.

In this Subversion directory, I have collected the iterations counts and the
solutions lengths of a sample of boards - the first 32,000 games in Microsoft
Windows FreeCell:

http://svn.berlios.de/svnroot/repos/fc-solve/trunk/fc-solve/presets/soft-
threads/meta-moves/auto-gen/

(short URL - http://xrl.us/bgwj3o ; there's also an https:// equivalent, which
may work better, but it's a self-signed certificate).

After installing the dependencies - PDL (= the Perl Data Language) , 
Class::XSAccessor and Exception::Class (and maybe some others) you can query 
it by using the script query.pl like that:

<<<
shlomi[fcs]:$presets$ scan_id="1"
shlomi[fcs]:$presets$ board_idx="120"
shlomi[fcs]:$presets$ perl query.pl -l "$scan_id" "$board_idx"
123
128
>>>

(First line is the iterations count; second line is the solution's length).

You probably would like to inspect the query.pl source code and
see how you can access the data directly using PDL, and possibly use PDL
to convert it to a different format.

Now, what I'd like to do is create a meta-scan that runs several of these
individual scans one after the other, each with a certain quota of iterations, 
and will select the shortest solution of all those that were able to solve
the board. 

Let's look at a numeric example (based on the actual statistics):

----------------------------------------------------------------
Deal No. | Scans Statistics                                    |
         | 1 Iters | 1 Len | 2 Iters | 2 Len | 3 Iters | 3 Len |
----------------------------------------------------------------
 1       |  123    | 127   |  1711   | 120   | 1285    | 161   |
 2       |   98    | 145   |    96   | 138   |   98    | 107   |
 3       |  125    | 115   |   104   | 109   |   93    | 110   |
 4       |  117    | 123   |   236   | 129   |  447    | 153   |
 5       |  110    | 143   |   101   | 136   |  691    | 175   |
 6       |  403    | 176   |   262   | 122   |  125    | 130   |
 7       | 1260    | 134   |   307   | 125   | 1823    | 165   |
 8       |   70    |  98   |    70   |  98   |  122    | 125   |
 9       |   -1    |  -1   | 47169   | 135   | 1097    | 136   |
10       |  189    | 135   |   115   | 125   | 3043    | 202   |
----------------------------------------------------------------

Now if I allocate 400 iterations to each of the three scans here (and
none to any other) then for deal #1, scan #1 will yield a solution of
127 steps, while scan #2 will not yield any solution at all (since it requires
1,711 iterations) and neither will scan #3 giving us a solution of 127 moves.

For deal #2 all scans will finish well before the iterations limit, and the
shortest solution chosen will be scan #3 with its 107 steps solution. 

Etc.

Let's suppose I have a total of $tot iterations to split among all the 
scans in scans.txt in the distribution, into @q[0 .. $last_scan] quotas.

My question is: given $tot, what should @q be so it will, on average,
yield the shortest solutions for the 32,000 sample board?

Hope you enjoy this quiz.

Regards,

	Shlomi Fish

--

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Shlomi Fish       http://www.shlomifish.org/
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