This is an extension of problem 42842. In this case, the puzzle is three-dimensional and is of size 3x3x3. Of the 27 positions in the puzzle, 26 are occupied by cubes numbered 1 thru 26, while the remaining position is empty. You can slide an adjacent cube into the empty position, similarly to sliding an adjacent tile into the empty position in the 15 puzzle.
In this case, for simplicity, the puzzle is represented by a vectorized form of the puzzle, such that the 3D form of the puzzle can be obtained by reshape(p,[3 3 3]). Therefore, a solved cube shall look like this:
p = [1;2;3;4;5;6;7;8;9;10;11;12;13;14;15;16;17;18;19;20;21;22;23;24;25;26;0]
Given the initial state vector, p, return a vector, m, comprising a sequence of integers, representing the linear indices of the cubes you wish to slide, in turn, into the empty position, in order to solve the puzzle.
As before, the solution does not have to be efficient. It must simply result in a correctly solved puzzle. Illegal moves, such as trying to slide a tile that is not adjacent to the open slot, will be ignored.
Example:
p = [0;2;3;1;5;6;4;7;9;10;11;12;13;17;14;16;8;18;19;20;21;22;23;15;25;26;24]
m = [4 7 8 17 14 15 24 27]
there is a bug in the evaluation function, I believe "abs(a1 + b1 + c1 - a0 - b0 - c0) == 1" should be changed to "abs(a1-a0) + abs(b1-b0) + abs(c1-c0) == 1". In any way, this was a very cool problem, unless I am misremembering this would be the very first one that forced me to implement some version of A* in Cody :)
Alfonso, it is an honor and a pleasure to have read your comment. I'm glad you enjoyed the problem. Thank you for spotting the bug. I will update accordingly.
Alfonso, I've fixed the bug. As a result, I've actually located a tiny typo, one single character in my own solution that was, in fact, the difference between a correct and an incorrect solution based on your correction. Fixed that too, of course. Thanks again!
It takes 9 seconds to solve the four inputs on my laptop, but the system rejected my code with the error of long run time. What's the acceptable time for the four inputs?
This one kept my busy, and I think my solution is a bit of a tour de force. It is recipe based, rather than optimal, but there are just too many corner cases to program around. I should have made better use of invariant sets, I guess.
Difficult problem
Good problem. Tip: use the L1-norm or manhattan distance using the 3 indexes as a cost function.
Cheater!
Can someone remove this cheating solution?
wow, I love everything about this solution, the equivalence with a 3x9 board, the BubbleSort strategy, even the 190-size :)
Thank you.
This problem was so difficult for me to solve, would you mind explaining what search algorithm did you implement? Thanks.
It is a best-first search using a heuristic based on the sum of manhattan distances to target for each of the 26 tiles; solution 1310071 is slightly commented in case that helps
@daniel and by the way congrats on finishing all cody5-hard problems, that is quite an accomplishment! (I had it easier, having created a couple of problems in that same group, so mine does not count :)
I tried a similiar search but it did not end on time, and I don't know why.
PD: You're being too modest! I've been pulling all nighters all the week to finish them all, I'm sure it didn't take you all that time to solve them all.
PD2: I've made a problem (44390) in honour to all the suffering and latter satisfaction these 5th anniversay problems brought to me, you should check it out :)
I have tried something similar to this "best-first search" algorithm (if I understand the term correctly), but as I get closer to the final solution, I keep running into situations where all of the available moves move a tile out of its correct position, so my heuristic judges all of them equally, and the algorithm just starts making pseudo-random moves. Are you looking at all possibilities of some small number of moves, and picking one set of moves to move on from?
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