Sunday, September 2, 2012

Two Freecell Solvability Report for the First 400,000 Deals

With some help from some people on the fc-solve-discuss list and off the list (namely Amadiro from the University of Oslo and someone else that I met on IRC , I ran my solvers on the first 400,000 Windows Freecell deals with only two available freecells to see how many of them can be solved.

Here is the report:

Start Index End Index Solved Impossible Intractable
1 32,000 25,381 6,619 0
32,001 50,000 14,302 3,698 0
50,001 100,000 39,775 10,225 0
100,001 400,000 238,415 61,584 1 (No. 384243)
Total 317,873 82,126 1

So about 79.47% of the deals can be solved and the rest are impossible. The only intractable deal that none of my solvers could yield a verdict for is No. 384,243, and it spans a very large number of states:

  • The dbm_fc_solver got into Reached 12,821,000,000 ; States-in-collection: 13,620,999,440 before it failed to produce more results due to a limitation of the hardware where it was deployed on.

  • The depth_dbm_fc_solver yielded this:

    Reached 13,763,700,000 ; States-in-collection: 16,226,294,490 ; Time: 1345126456.520408 Queue Stats: inserted=16,226,294,490 items_in_queue=2,462,594,490 extracted=13,763,700,000

    with a curr_depth of 38. However, that solver may have some yet undiscovered bugs.

So what's next? I’d like to investigate some ways to scale to a larger number of states, perhaps by creating a distributed solver. A google search for distributed breadth first search yields some results:

I hope you enjoy the statistics for the time being.

3 comments:

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