def get_exact_covers(cols, rows, num_cols=None):
"""
Use Algorithm X to get all solutions to the exact cover problem
https://en.wikipedia.org/wiki/Knuth%27s_Algorithm_X
Args:
cols (list[int]): A list of integers representing the columns to be covered
rows (list[list[int]]): A list of lists of integers representing the rows
num_cols (int): The total number of columns
Returns:
list: All exact covers
"""
if num_cols is None:
num_cols = max(cols) + 1
ec = DLX([(c, 0 if c in cols else 1) for c in range(num_cols)])
ec.appendRows([[c] for c in cols])
ec.appendRows(rows)
exact_covers = []
for s in ec.solve():
cover = []
for i in s:
cover.append(ec.getRowList(i))
exact_covers.append(cover)
return exact_covers
def __init__(self, squares):
"""Squares is a nested list representing an initial sudoku board. A 0
represents an empty square, while a nonzero digit represents a square
filled with that value."""
self.dlxrows = squares
self.sparseMatrix = SparseMatrix(self.dlxrows)
self.dlx = DLX(self.sparseMatrix)
def main():
if (len(sys.argv) != 2):
print("usage: python3 solveitup.py <problem description>")
return
numvars, clauses = getproblem(sys.argv[1])
grid = buildgrid(numvars, clauses)
dlx = DLX(SparseMatrix(grid))
results = dlx.search()
printresults(results)
X="#BB99DD", Y="#CC88CC", Z="#DD99BB")
# Grid for Scott's pentomino problem: 8x8 with a 2x2 hole in the middle
GRID = Grid((8, 8), holes=[(3, 3), (3, 4), (4, 3), (4, 4)])
# Generate all pentominoes that can be placed on the grid
POLYMINOES = generate_all(PENTOMINOES, GRID)
# convert to list of lists
POLYMINOES = [polymino.aslist for polymino in POLYMINOES]
# calculate labels for DLX
LABELS = list(set([element for polymino in POLYMINOES for element in polymino]))
LABELS = sorted(LABELS, key=sortkey)
COVER = DLX(LABELS, POLYMINOES)
SOLUTIONS = []
for i, SOLUTION in enumerate(COVER.generate_solutions()):
print(i)
SOLUTIONS.append(Grid.from_DLX(SOLUTION))
DISTINCT_SOLUTIONS = unique_grids(SOLUTIONS)
solutions_svg(DISTINCT_SOLUTIONS, filename='scott_distinct_solutions1.svg',
columns=13, colour=COLOURS.get)
# removing X pentominoes
POLYMINOES = [pol for pol in POLYMINOES if not (pol[0] == 'X' and pol[1] not in [(5, 3), (5, 2), (4, 2)])]
COVER = DLX(LABELS, POLYMINOES)