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Hello

I have recently started to become really interested in optimal 3x3x3 solvers. Specially Korf´s and Kociemba algorithm. How fast are those on a normal computer ? pruning tables from depth 0 to 11 work pretty well, but it would still take a decent time to solve a cube which needs 18 or 19 moves, right ? And Kociemba division into 2 phases just doesnt work well all the time. (just imagine optimal solution to some particular scramble, where the last move is F....meaning that there would be no phase 2 in Kociemba algorithm, simply because during the optimal solution the cube would never be in the group which is the result of phase1).

With Korf´s algorithm, in the prunning tables we store the lower bound to solve some particular corner configuration (or edge, whatever..), wouldn´t it be faster to store the exact number of moves in which you can solve the corners ? (one table entry could for example have values 6,8,10 ... instead of 6 as a lower bound). I think this could eliminate some decent number of nodes in a search tree. Yes pruning tables would be larger, but not by a huge factor.

Also, has anyone ever tried to analyse and categorize cube scrambles by minimum number of moves required to solve them ? Lets take primitive example, if there are more than 4 misplaced corners on the cube, you can say certainly that it requires minimum of 2 moves to solve.......so i was thinking of something like this, but with much larger depths than 2.I know that it would be much more difficult than this. Both edge and corner positions and orientations must be watched. Perhaps if the edge is on the right place, but wrongly oriented it makes it hard to solve (superflip, eh..). I think you can get really creative here and think of many ways to do this.

(btw i programmed both Korf and Kociemba, but didnt make the complete tables because it takes me a long time to do that, although i will do it sometimes in the future. If i can download the tables somewhere, please let me know )

Thank you so much for your answers, dear cubers

I have recently started to become really interested in optimal 3x3x3 solvers. Specially Korf´s and Kociemba algorithm. How fast are those on a normal computer ? pruning tables from depth 0 to 11 work pretty well, but it would still take a decent time to solve a cube which needs 18 or 19 moves, right ? And Kociemba division into 2 phases just doesnt work well all the time. (just imagine optimal solution to some particular scramble, where the last move is F....meaning that there would be no phase 2 in Kociemba algorithm, simply because during the optimal solution the cube would never be in the group which is the result of phase1).

With Korf´s algorithm, in the prunning tables we store the lower bound to solve some particular corner configuration (or edge, whatever..), wouldn´t it be faster to store the exact number of moves in which you can solve the corners ? (one table entry could for example have values 6,8,10 ... instead of 6 as a lower bound). I think this could eliminate some decent number of nodes in a search tree. Yes pruning tables would be larger, but not by a huge factor.

Also, has anyone ever tried to analyse and categorize cube scrambles by minimum number of moves required to solve them ? Lets take primitive example, if there are more than 4 misplaced corners on the cube, you can say certainly that it requires minimum of 2 moves to solve.......so i was thinking of something like this, but with much larger depths than 2.I know that it would be much more difficult than this. Both edge and corner positions and orientations must be watched. Perhaps if the edge is on the right place, but wrongly oriented it makes it hard to solve (superflip, eh..). I think you can get really creative here and think of many ways to do this.

(btw i programmed both Korf and Kociemba, but didnt make the complete tables because it takes me a long time to do that, although i will do it sometimes in the future. If i can download the tables somewhere, please let me know )

Thank you so much for your answers, dear cubers