POLYOMINO_MONOHEDRAL
Seek Solutions of Polyomino Monohedral Tiling
POLYOMINO_MONOHEDRAL,
a MATLAB library which
is given matrices defining a region R and a polyomino P; it sets up
the corresponding linear system, and solves for
binary solutions x that represent possible tilings of the region R by
the polyomino P.
A region R is a subset of an MRxNR grid of squares.
A polyomino P is a subset of an MPxNP grid of squares.
Both objects are represented by binary matrices, with the property that
there are no initial or final zero rows or columns.
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the GNU LGPL license.
Languages:
polyomino_monohedral is available in
a MATLAB version.
Related Data and Programs:
polyomino_monohedral_test
Source Code:
-
i4mat_is_binary.m,
is TRUE if an I4MAT contains only 0 and 1 entries.
-
ksub_next4.m,
returns, one at a time, all the K-subsets of a set.
-
polyomino_condense.m,
cleans up a matrix that represents a polyomino by setting all nonzero
entries to 1, and removing initial and final rows and columns of zeros.
-
polyomino_embed_list.m,
for each possible embedding, lists the translation necessary to
to apply to the polyomino.
-
polyomino_embed_number.m,
reports the number of ways a polyomino can be embedded in a region.
-
polyomino_equal.m,
is true if two polyominoes are equal.
-
polyomino_index.m,
computes an index for each nonzero polyomino entry.
-
polyomino_lp_write.m,
writes an LP file describing a particular problem.
-
polyomino_monohedral.m,
sets up and solves a polyomino monohedral tiling problem.
-
polyomino_monohedral_matrix.m,
determines the matrix and right hand side for a polyomino monohedral
problem.
-
polyomino_monohedral_tiling_print.m,
prints a tiling of a region R by a polyomino P, based on a solution
computed by polyomino_monohedral.
-
polyomino_monohedral_variants.m,
carries out reflections and rotations of a polyomino to
determine which transformations yield distinct variants.
-
polyomino_print.m,
prints a polyomino.
-
polyomino_transform.m,
carries out reflections and rotations of a polyomino.
-
r8mat_rref.m,
returns the reduced row echelon form of an R8MAT.
-
r8mat_rref_solve_binary_nz.m,
seeks binary solutions (if any) of a row reduced echelon form
linear system in which exactly NZ entries are nonzero.
-
r8mat_u_solve.m,
solves an upper triangular linear system.
-
r8vec_identity_row.m,
returns a row of the identity matrix as an R8VEC.
-
r8vec_is_binary.m,
is true if all entries of an R8VEC are 0 or 1.
-
timestamp.m,
prints the YMDHMS date as a timestamp.
Last revised on 27 February 2019.