原帖由 Cielo 于 2008-12-5 19:48 发表
有算最少步数的软件了：cube explorer
但那程序到底怎么编出来的我也不知道……
| The Two-Phase-Algorithm |
| The following description is intended to give you a basic idea of how the algorithm works. The 6 different faces of the Cube are called U(p), D(own), R(ight), L(eft), F(ront) and B(ack). While U denotes an Up Face quarter turn of 90 degrees clockwise, U2 denotes a 180 degrees turn and U' denotes a quarter turn of 90 degrees counter-clockwise. A sequence like U D R' D2 of Cube moves is called a maneuver. If you turn the faces of a solved cube and do not use the moves R, R', L, L', F, F', B and B' you will only generate a subset of all possible cubes. This subset is denoted by G1 = <U,D,R2,L2,F2,B2>. In this subset, the orientations of the corners and edges cannot be changed. That is, the orientation of an edge or corner at a certain location is always the same. And the four edges in the UD-slice (between the U-face and D-face) stay isolated in that slice. |
| In phase 1, the algorithm looks for maneuvers which will transform a scrambled cube to G1. That is, the orientations of corners and edges have to be constrained and the edges of the UD-slice have to be transferred into that slice. In this abstract space, a move just transforms a triple (x,y,z) into another triple (x',y',z'). All cubes of G1 have the same triple (x0,y0,z0) and this is the goal state of phase 1. To find this goal state the program uses a search algorithm which, in terms of the current research, is called iterative deepening A* with a lowerbound heuristic function (IDA*). In the case of the Cube, this means that it iterates through all maneuvers of increasing length. The heuristic function h1(x,y,z) estimates for each cube state (x,y,z) the number of moves that are necessary to reach the goal state. It is essential that the function never overestimates this number. In Cube Explorer 2, it gives the exact number of moves which are necessary to reach the goal state in Phase 1. The heuristic allows pruning while generating the maneuvers, which is essential if you do not want to wait a very, very long time before the goal state is reached. The heuristic function h1 is a memory based lookup table and allows pruning up to 12 moves in advance. |
| In phase 2 the algorithm restores the cube in the subgroup G1, using only moves of this subgroup. It restores the permutation of the 8 corners, the permutation of the 8 edges of the U-face and D-face and the permutation of the 4 UD-slice edges. The heuristic function h2(a,b,c) only estimates the number of moves that are necessary to reach the goal state, because there are too many different elements in G1. |
| The algorithm does not stop when a first solution is found but continues to search for shorter solutions by carrying out phase 2 from suboptimal solutions of phase 1. For example, if the first solution has 10 moves in phase 1 followed by 12 moves in phase 2, the second solution could have 11 moves in phase 1 and only 5 moves in phase 2. The length of the phase 1 maneuvers increase and the length of the phase 2 maneuvers decrease. If the phase 2 length reaches zero, the solution is optimal and the algorithm stops. |
| In the current implementation the Two-Phase-Algorithm does not look for some solutions that are optimal overall, those that must cross into and back out of phase 2. This increases the speed considerably. Use the Optimal Solver, if you want to prove some maneuver to be optimal. |
The following pages are an attempt to give some insight of the mathematical ideas and algorithms developed and used in Cube Explorer.
There are several problems I had to struggle with. First, English is not my native language and some of my explanations may be difficult to understand or incomprehensible at all. Second, I studied mathematics a long time ago and my terminology will surely be incorrect in some parts. Third, I only could sketch the main ideas of all that, what was necessary to write Cube Explorer.
But I hope that nevertheless it is a help for those who are interested in understanding the Two-Phase Algorithm or want to implement the algorithm in their own program.
还有cube explore 的免费下载，还有别的一个算法还是什么的c源程序。这里我不提供链接了，想找的去他网站自己看吧。
我正在学习中，看来是比较难，我不是学计算机的，编程有点困难……
原帖由 Cielo 于 2008-12-5 19:48 发表
有算最少步数的软件了：cube explorer
但那程序到底怎么编出来的我也不知道……
原帖由 conwood 于 2008-12-5 21:03 发表
在单片机里做最好还是用cfop。
感觉更容易一些
原帖由 shifujun 于 2008-12-5 22:01 发表
好几秒一步是够笨的了……晕
教它玩二阶吧！
原帖由 light13 于 2008-12-6 15:27 发表
C语言要编的话有点困难……
毕竟要做出来的是图形界面，C有点心有余而力不足
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