README
REPRESENTING THE CUBE STATE
Each cubie is represented by one of the facelets. The relevant facelets are numbered as
follows:
There are 24 positions for edge facelets and 24 positions for corner facelets. The positions
are labelled below:
The positions of the 12 edges are stored in the array edges and the positions of the 8 corners are stored in the array corners.
The position of the U facelet of the UF edge cubie is stored in edges[0], the position of the U facelet of the UR cubie in edges[1], and so forth. Similarly, the position of the U facelet of the UFR corner cubie is in corners[0], the position of the U facelet of the URB cubie in corners[1], and so forth.
A solved cube has an edges array of {0, 1, 2, 3, 8, 9, 10, 11, 20, 21, 22, 23} and corners array of {0, 1, 2, 3, 20, 21, 22, 23}. After the move R+, the resulting arrays are {0, 13, 2, 3, 1, 17, 10, 11, 20, 8, 22, 23} and {9, 17, 2, 3, 4, 12, 22, 23}, respectively.
SOLVING METHOD
This program solves the cube using a method that humans never use. However, it is well suited for computers because it is highly repetitive. (It is easy to code too!) One cubie is solved at a time, restricting the unsolved ones to fewer and fewer positions, until the entire cube is solved. The method goes like this:
for i = 1 to 4 {
solve the DF edge
rotate cube
}
for i = 1 to 4 {
solve the DRF corner
rotate cube
}
for i = 1 to 4 {
solve the FR edge
rotate cube
}
for i = 1 to 4
solve the URF corner
rotate cube
}
for i = 1 to 4
solve the UF edge
rotate cube
}
where rotate is a cube rotation in the direction of a U turn. The cube usually takes
around 105 moves to solve using this method.
CODING ALGORITHMS
To reduce the program size, the algorithms are encoded. In prior versions, each move was given a number and an array of numbers represented an algorithm. In this version, an algorithm is converted into a long integer.
First, the moves are assigned the following values:
X+ X2 X-
----------------
F 1 2 3
R 4 5 6
B 7 8 9
L 10 11 12
U 13 14 15
D 16 17 18
For the algorithm R+ U+ R-, I turn it into an integer as follows:
4*190 + 13*191 + 6*192 + 0*193 + 0*194 + 0*195 + 0*196 = 2417
A zero indicates the end of the algorithm. Longer algorithms are broken into chunks of 7 moves.