From @mitvma.mit.edu,@WVNVM.WVNET.EDU:BRYAN@WVNVM.WVNET.EDU Mon Dec 6 21:32:55 1993 Return-Path: <@mitvma.mit.edu,@WVNVM.WVNET.EDU:BRYAN@WVNVM.WVNET.EDU> Received: from mitvma.mit.edu by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA10000; Mon, 6 Dec 93 21:32:55 EST Message-Id: <9312070232.AA10000@life.ai.mit.edu> Received: from MITVMA.MIT.EDU by mitvma.mit.edu (IBM VM SMTP V2R2) with BSMTP id 3272; Mon, 06 Dec 93 21:32:56 EST Received: from WVNVM.WVNET.EDU (NJE origin MAILER@WVNVM) by MITVMA.MIT.EDU (LMail V1.1d/1.7f) with BSMTP id 0517; Mon, 6 Dec 1993 21:32:56 -0500 Received: from WVNVM.WVNET.EDU (NJE origin BRYAN@WVNVM) by WVNVM.WVNET.EDU (LMail V1.1d/1.7f) with BSMTP id 6339; Mon, 6 Dec 1993 21:30:26 -0500 X-Acknowledge-To: Date: Mon, 6 Dec 1993 21:30:25 EST From: "Jerry Bryan" To: Subject: Re: Unique antipode of edges only In-Reply-To: Message of 12/06/93 at 10:45:00 from mark.longridge@canrem.com On 12/06/93 at 10:45:00 mark.longridge@canrem.com said: >-> I was somewhat startled to see the unique antipode of the 3x3x3 edges >-> in the quarter-turn metric. Do you know what pattern that is? >-> >-> Dan >It's got to be all edges flipped in place. I had to stare at my picture for a couple of minutes to be sure, but yes it is. How did you know? >I would like to see the process generating the position! This is doable, but it is a little harder said than done. My "data base" is just a simple flat file with the states and the level associated with each state. In the case of the 2x2x2, the file is about 625K, and I have programs to search it readily. If you use the file in "Solver mode", my "Solver program" just generates all successors of the current node, finds each successor in the data base (it is a simple binary search, the file is sorted), chooses one at level N-1 (there is always at least one), and makes that the new current node. It stops when N=0. I have a "Solver program" for the "corners plus centers of the 3x3x3" as well, but again the data base is small. It is actually the original 625K file for the 2x2x2 case, plus three additional 625K files. This simple file structure was chosen to keep the file small. There are no pointers, trees, or processes stored in the data base. The "edges of the 3x3x3 without centers" is a little tougher. Early in the project, I generated a data base for the first few levels (six or seven, I think), and I have a "Solver program" that will work up to that level. However, the full "edges of the 3x3x3 without centers" is a 4.2 gigabyte file on tape, so it is hard to process. Also, the size of the equivalence classes is not in the data base, only the level. I have to calculate the size of each equivalence class, and it is an expensive calculation. I made a pass at the file and calculated the number of equivalence classes (took 125 hours on a mainframe), but I only saved a summary. I did not save the number of equivalence classes for each state. I found the antipodal by looking for level 15, since I knew there was only one occurrence, and since the level was in the data base. I did save the summaries by tape, so I should only have to look on two tapes to find the other two equivalence classes which have 24 elements. = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) (304) 293-5192 Associate Director, WVNET (304) 293-5540 fax 837 Chestnut Ridge Road BRYAN@WVNVM Morgantown, WV 26505 BRYAN@WVNVM.WVNET.EDU If you don't have time to do it right today, what makes you think you are going to have time to do it over again tomorrow?