Disjoint Pattern Database Heuristics
Disjoint Pattern Database Heuristics
Disjoint Pattern Database Heuristics
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33planeofthecubecanberotatedindependently,andthetaskisto cameaworld-widesensation.Morethan100millionRubik'sCubeshave beensold,makingitthebest-knowncombinatorialpuzzleofalltime.Each rearrangetheindividualpiecessothateachsideshowsonlyonecolor(see Figure3).<br />
states.Thereare20movablesubcubes,orcubies,whichcanbedividedinto The333Rubik'sCubecontainsabout4:32521019dierentreachable Figure3:333Rubik'sCube<br />
faceseach.Thereare88;179;840dierentpositionsandorientationsofthe cornercubies,andthenumberofmovesneededtosolvejustthecorner cubiesrangesfromzerotoeleven.Atfourbitsperentry,apatterndatabase eightcornercubies,withthreefaceseach,andtwelveedgecubies,withtwo<br />
ofthetwelveedgecubiesgenerate42;577;920dierentpossibilities,anda forthecornercubiescanbestoredinabout42megabytesofmemory.Six correspondingpatterndatabaseoccupiesabout20megabytesofmemory. Theremainingsixedgecubiesgenerateanotherdatabaseofthesamesize. cubiestocomputeanindexintothecorner-cubiepatterndatabase,whose valuetellsusthenumberofmovesneededtosolvejustthecornercubies.We alsouseeachofthetwosetsofsixedgecubiestocomputeindicesintothe GivenastateofanIDA*search,weusethecongurationofthecorner<br />
correspondingedge-cubiedatabases,yieldingthenumberofmovesneeded tosolveeachsetofsixedgecubies.Giventhesethreedierentheuristic values,thebestwaytocombinethem,withoutoverestimatingactualsolution 7
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