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satisfiability/examples/nurikabe.py
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#! /usr/bin/env python | |
from sat import * | |
""" | |
many many flood fills! | |
a limited flood for each number | |
one big flood for stream | |
optimization: exact floods don't cover the whole board | |
""" | |
puzzle = """\ | |
2........2 | |
......2... | |
.2..7..... | |
.......... | |
......3.3. | |
..2....3.. | |
2..4...... | |
.......... | |
.1....2.4.""" | |
def clean(puz): | |
puz = [list(line) for line in puz.split('\n')] | |
table = {} | |
for y,line in enumerate(puz): | |
for x,n in enumerate(line): | |
if n == '.': | |
continue | |
table[(x,y)] = int(n) | |
return table | |
table = clean(puzzle) | |
y_dim = len(puzzle.split('\n')) | |
x_dim = len(puzzle.split('\n')[0].strip()) | |
z_dim = int(x_dim * y_dim / 2) | |
xs = range(x_dim) | |
ys = range(y_dim) | |
cnf = CNF('/tmp/nurikabe.cnf') | |
f = cnf.auto_term | |
# hit all the base numbers early for clean ordering | |
base_layer = [f('base', x, y) for x,y in product(xs, ys)] | |
cnf.comment('numbers are clear') | |
for x,y in table: | |
cnf.write_one(-f('base', x, y)) | |
cnf.comment('no pools') | |
for x,y in product(xs[:-1], ys[:-1]): | |
cells = [f('base',x,y), f('base',x+1,y), f('base',x,y+1), f('base',x+1,y+1)] | |
cnf.write([neg(cells)]) | |
adj = cartesian_table(xs, ys) | |
cnf.comment('walls') | |
wall_labels = [] | |
wall_summaries = set() | |
for x,y in table: | |
label = 'wall %i %i' % (x,y) | |
wall_labels.append(label) | |
size = table[(x,y)] | |
cnf.comment(label) | |
mapping = floodfill(cnf, label, adj, size, exact=True, seed=(x,y)) | |
wall_summaries.update(mapping.values()) | |
cnf.comment('link ' + label) | |
for x2,y2 in mapping: | |
cnf.write(if_then(f(*mapping[(x2,y2)]), -f('base', x2, y2))) | |
cnf.comment("walls can't touch") | |
# little tricky to explain | |
# forbid summary + !summary neighbor + !base neighbor | |
for x,y in table: | |
label = 'wall %i %i' % (x,y) | |
cnf.comment('dont touch ' + label) | |
for x2,y2 in product(xs,ys): | |
for x3,y3 in neighbors(x2,y2,xs,ys): | |
cell1 = f(label, 'summary', (x2,y2)) | |
cell2 = f(label, 'summary', (x3,y3)) | |
cell3 = f('base', x3, y3) | |
cnf.write_one(-cell1, cell2, cell3) | |
cnf.comment("stream") | |
# use a seed for faster fill | |
seed = None | |
for x,y in table: | |
if table[(x,y)] == 1: | |
seed = neighbors(x,y,xs,ys)[0] | |
break | |
mapping = floodfill(cnf, 'stream', adj, z_dim, seed=seed) | |
cnf.comment("stream summary") | |
for x,y in mapping: | |
cnf.write(if_then(f(*mapping[(x,y)]), f('base', x, y))) | |
cnf.comment('no overlap between regions') | |
for x,y in product(xs,ys): | |
cells = [f(label, 'summary', (x,y)) for label in wall_labels + ['stream']] | |
cnf.write(window(cells, 1, 1)) | |
print('terms:', cnf.maxterm) | |
print('clauses:', cnf.clauses) | |
print() | |
cnf.verify() | |
# pretty print | |
for solution in cnf.solutions(interesting = base_layer): | |
for y in ys: | |
line = '' | |
for x in xs: | |
if (x,y) in table: | |
line += str(table[(x,y)]) | |
line += ' ' | |
elif f('base', x, y) in solution: | |
line += 'X ' | |
else: | |
line += '. ' | |
print(line) | |
print('\n') | |