In this exercise we will encode in ASP a
simple planning puzzle called Unblock. The puzzle
consists of a set of tiles of different dimensions on a
square grid of n × n cells (normally, 6 × 6). Tiles can be horizontal
blocks of 1 × k cells or vertical blocks of k × 1 cells
(in all cases k > 1).
Each block can only be moved in its longitudinal axis,
always inside the grid and without pushing the other
blocks. The goal consists in moving a particular block
(the goal block in red) to a given grid position
(the exit position).
To understand the game rules, you can try playing at the
webpages below (a smartphone version, Unblock Me Free, is
also available for Android and iPhone);
We will build a program that performs the following
Read an Unblock puzzle from a text
file with the following format. The file will begin
with n text lines of n characters.
Each character can be a dot '.' to represent that the
cell is empty, or a letter 'a' to 'z' meaning that a
block with that name is on that cell. The last line
contains an expression X=M meaning that
the goal block is X and its target position is
some integer value M=0 .. n-2. M
represents a column index if the block is horizontal,
or a row index if the block is vertical. As an
example, the first level in the picture above would be
represented as the text file:
Note that the goal block in this
case is b and its target position is column
4. The program that reads these input files and
generates the corresponding ASP facts can be written
in any standard language (C, java, python, perl,...)
but without using non-standard libraries (i.e.
exclusively using the standard language installation).
Encode the puzzle as an ASP
incremental planning problem.
- Call the solver clingo and obtain a solution in the
form move(B,D,T) where B is a block, D
an increment (1 or -1) and T a time instant. For
instance move(e,-1,1) move(a,1,2) would mean
that we move block e one cell to the left at
instant 1, and then we move block a one cell
downwards at instant 2.
- Most Unblock games will count a shift of N cells in
the same direction as a single movement. For simplicity,
we will assume that each movement exclusively implies one
cell shift, that is, we can increment the column
(for horizontal blocks) or the row (for vertical ones)
in +1 or -1 positions.
- These are some problem instances and their solutions
Assessment & delivery
The maximum grade for this exercise (1a)
is 1 point = 10% of the course. The deadline for
delivery is Friday, April 29h,
2016 using the lab work mailbox or buzón de prácticas.