pariomino
pariomino,
an Octave code which
considers pariominoes, which are polyominoes with a checkerboard parity.
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the MIT license
Languages:
pariomino is available in
a MATLAB version and
an Octave version and
a Python version.
Related Data and Programs:
boundary_word,
an Octave code which
works with a polyomino that is described by a sequence of symbols
that indicate how to trace out its boundary.
pariomino_test
polyiamonds,
an Octave code which
works with polyiamonds, simple shapes constructed by edgewise
connections of congruent equilateral triangles.
polyomino_parity,
an Octave code which
uses parity considerations to determine whether a given set of
polyominoes can tile a specified region.
polyominoes,
an Octave code which
defines, solves, and plots a variety of polyomino tiling problems,
which are solved by a direct algebraic approach involving the
reduced row echelon form (RREF) of a specific matrix, instead of the
more typical brute-force or backtracking methods.
Reference:
-
Marcus Garvie, John Burkardt,
A new mathematical model for tiling finite regions of the plane
with polyominoes,
Contributions to Discrete Mathematics,
Volume 15, Number 2, July 2020.
-
Solomon Golomb,
Polyominoes: Puzzles, Patterns, Problems, and Packings,
Princeton University Press, 1996,
ISBN: 9780691024448
Source code:
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colour_poly.m,
creates a matrix for a pariomino using -1, 0, and +1 values.
-
cplex_solution_single_read.m,
extracts solution data from a structure obtained from a
CPLEX data that contained a single solution.
-
cplex_solution_multiple_read.m,
extracts solution data from a structure obtained from a
CPLEX data that contained multiple solutions.
-
cplex_solution_read.m,
reads an XML file, converts the data to a structure,
and extracts the data representing solutions.
-
file_line_count.m,
returns the number of lines in a file.
-
filename_inc.m
numerically "increments" a file name.
-
gurobi_solution_read.m,
reads a file created by GUROBI, representing a solution of a
polyomino tiling problem, and extracts the solutions as a
simple vector.
-
i4mat_is_ternary.m,
is TRUE if an I4MAT contains only -1, 0 and 1 entries.
-
i4mat_print.m,
prints an I4MAT;
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i4mat_print_some.m,
prints some of an I4MAT;
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i4vec2_print.m,
prints a pair of integer vectors.
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ksub_next4.m,
returns, one at a time, all the K-subsets of a set.
-
pariomino_area.m,
returns the area of a pariomino, simply the number of 1's
in the representation.
-
pariomino_condense.m,
cleans up a matrix that represents a pariomino by setting all nonzero
entries to 1, and removing initial and final rows and columns of zeros.
-
pariomino_embed_list.m,
for each possible embedding, lists the translation necessary to
to apply to the pariomino.
-
pariomino_embed_number.m,
reports the number of ways a pariomino can be embedded in a region.
-
pariomino_equal.m,
is true if two pariominoes are equal.
-
pariomino_index.m,
computes an index for each nonzero pariomino entry.
-
pariomino_lp_write.m,
writes an LP file describing a particular problem.
-
pariomino_matrix.m,
determines the matrix and right hand side for a pariomino problem.
-
pariomino_matrix_reid.m,
returns the matrix associated with the Reid tiling problem.
-
pariomino_parity.m,
computes the parity of a pariomino.
-
pariomino_print.m,
prints a pariomino.
-
pariomino_reverse.m,
reverses the parity of the cells of a pariomino.
-
pariomino_tiling_plot.m,
is given matrices defining a region R and a set of pariominoes P,
and a solution vector X, which represents
a tiling of R by the pariominoes in P, and plots a representation
of that tiling.
-
pariomino_tiling_print.m,
is given matrices defining a region R and a set of pariominoes P,
and a solution vector X, which represents
a tiling of R by the pariominoes in P, and prints out a representation
of that tiling.
-
pariomino_tiling_solver.m,
sets up and solves a pariomino tiling problem.
-
pariomino_transform.m,
carries out reflections and rotations of a pariomino.
-
pariomino_variants.m,
carries out reflections and rotations of a set of pariominoes to
determine which transformations yield distinct variants.
-
pariominoes_print.m,
prints pariominoes packed in an array.
-
plot_checker_tile.m,
plots a pariomino in gray and black.
-
polyomino_charge.m,
creates a pariomino from a polyomino, by assigning a parity
to each cell.
-
polyomino_print.m,
prints a polyomino.
-
r8mat_rref.m,
returns the reduced row echelon form of an R8MAT.
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r8mat_rref_solve_binary.m,
seeks binary solutions of an RREF system.
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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_binary_next.m,
generates the next binary vector.
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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.
-
r8vec_print.m,
prints an R8VEC.
-
s_len_trim.m
returns the length of a string to the last nonblank;
-
s_word_extract_first.m
extracts the first word from a string;
-
scip_index_read.m,
reads a file created by SCIP, representing solutions to a
polyomino tiling problem, and extracts information about the
permutation of the variables.
-
scip_solution_read.m,
reads a file created by SCIP, representing solutions to a
polyomino tiling problem, and extracts the solutions as a
simple vector.
-
timestamp.m,
prints the YMDHMS date as a timestamp.
-
xml2struct.m,
reads an XML file and converts the data to a structure.
Last revised on 04 August 2020.