From BRYAN@wvnvm.wvnet.edu Sun Dec 18 10:23:35 1994 Return-Path: Received: from WVNVM.WVNET.EDU by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA01444; Sun, 18 Dec 94 10:23:35 EST Message-Id: <9412181523.AA01444@life.ai.mit.edu> Received: from WVNVM.WVNET.EDU by WVNVM.WVNET.EDU (IBM VM SMTP V2R2) with BSMTP id 8075; Sun, 18 Dec 94 10:23:33 EST Received: from WVNVM.WVNET.EDU (NJE origin BRYAN@WVNVM) by WVNVM.WVNET.EDU (LMail V1.2a/1.8a) with BSMTP id 2308; Sun, 18 Dec 1994 10:23:33 -0500 X-Acknowledge-To: Date: Sun, 18 Dec 1994 10:23:32 EST From: "Jerry Bryan" To: "Cube Lovers List" Subject: Re: How Big is Big? In-Reply-To: Message of 12/17/94 at 22:46:08 from txr@alumni.caltech.edu On 12/17/94 at 22:46:08 txr@alumni.caltech.edu said: >In mlist.cube-lovers you write: >>For each cube position, we only need to store the depth, assuming >>we have some way to index to the proper cell in a data structure >>containing the depth for each cube position. As long as the depth >>does not exceed 31, then 5 bits will suffice for each cell. >I think depth modulo 3 is enough, since depth of adjacent positions >will differ by at most one -- just move in the direction of depth >getting less. So we could get by with 2 bits per cell. >regards, >Tim Rentsch You are certainly correct. And as Dan Hoey pointed out to me via private E-mail once upon a time, for Q turns you can get it down to only one bit by storing (depth modulo 4)/2 because you can infer the state of the low order bit from the parity of cube position. (Parity of the cube position equals the parity of the depth for Q turns, but not for Q+H turns.) But I tend to think that certain kinds of interesting analyses of a data base for the entire God's Algorithm would be greatly assisted by storing the entire depth. = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 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