# Copyright 2010 Hakan Kjellerstrand hakank@bonetmail.com
#
# Licensed under the Apache License, Version 2.0 (the 'License');
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an 'AS IS' BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""
Nonogram (Painting by numbers) in Google CP Solver.
http://en.wikipedia.org/wiki/Nonogram
'''
Nonograms or Paint by Numbers are picture logic puzzles in which cells in a
grid have to be colored or left blank according to numbers given at the
side of the grid to reveal a hidden picture. In this puzzle type, the
numbers measure how many unbroken lines of filled-in squares there are
in any given row or column. For example, a clue of '4 8 3' would mean
there are sets of four, eight, and three filled squares, in that order,
with at least one blank square between successive groups.
'''
See problem 12 at http://www.csplib.org/.
http://www.puzzlemuseum.com/nonogram.htm
Haskell solution:
http://twan.home.fmf.nl/blog/haskell/Nonograms.details
Brunetti, Sara & Daurat, Alain (2003)
'An algorithm reconstructing convex lattice sets'
http://geodisi.u-strasbg.fr/~daurat/papiers/tomoqconv.pdf
The Comet model (http://www.hakank.org/comet/nonogram_regular.co)
was a major influence when writing this Google CP solver model.
I have also blogged about the development of a Nonogram solver in Comet
using the regular constraint.
* 'Comet: Nonogram improved: solving problem P200 from 1:30 minutes
to about 1 second'
http://www.hakank.org/constraint_programming_blog/2009/03/comet_nonogram_improved_solvin_1.html
* 'Comet: regular constraint, a much faster Nonogram with the regular
constraint,
some OPL models, and more'
http://www.hakank.org/constraint_programming_blog/2009/02/comet_regular_constraint_a_muc_1.html
Compare with the other models:
* Gecode/R: http://www.hakank.org/gecode_r/nonogram.rb (using 'regexps')
* MiniZinc: http://www.hakank.org/minizinc/nonogram_regular.mzn
* MiniZinc: http://www.hakank.org/minizinc/nonogram_create_automaton.mzn
* MiniZinc: http://www.hakank.org/minizinc/nonogram_create_automaton2.mzn
Note: nonogram_create_automaton2.mzn is the preferred model
This model was created by Hakan Kjellerstrand (hakank@bonetmail.com)
Also see my other Google CP Solver models:
http://www.hakank.org/google_or_tools/
"""
import sys
from ortools.constraint_solver import pywrapcp
#
# Global constraint regular
#
# This is a translation of MiniZinc's regular constraint (defined in
# lib/zinc/globals.mzn), via the Comet code refered above.
# All comments are from the MiniZinc code.
# '''
# The sequence of values in array 'x' (which must all be in the range 1..S)
# is accepted by the DFA of 'Q' states with input 1..S and transition
# function 'd' (which maps (1..Q, 1..S) -> 0..Q)) and initial state 'q0'
# (which must be in 1..Q) and accepting states 'F' (which all must be in
# 1..Q). We reserve state 0 to be an always failing state.
# '''
#
# x : IntVar array
# Q : number of states
# S : input_max
# d : transition matrix
# q0: initial state
# F : accepting states
def regular(x, Q, S, d, q0, F):
solver = x[0].solver()
assert Q > 0, 'regular: "Q" must be greater than zero'
assert S > 0, 'regular: "S" must be greater than zero'
# d2 is the same as d, except we add one extra transition for
# each possible input; each extra transition is from state zero
# to state zero. This allows us to continue even if we hit a
# non-accepted input.
d2 = []
for i in range(Q + 1):
for j in range(S):
if i == 0:
d2.append((0, j, 0))
else:
d2.append((i, j, d[i - 1][j]))
# If x has index set m..n, then a[m-1] holds the initial state
# (q0), and a[i+1] holds the state we're in after processing
# x[i]. If a[n] is in F, then we succeed (ie. accept the
# string).
x_range = range(0, len(x))
m = 0
n = len(x)
a = [solver.IntVar(0, Q + 1, 'a[%i]' % i) for i in range(m, n + 1)]
# Check that the final state is in F
solver.Add(solver.MemberCt(a[-1], F))
# First state is q0
solver.Add(a[m] == q0)
for i in x_range:
solver.Add(x[i] >= 1)
solver.Add(x[i] <= S)
# Determine a[i+1]: a[i+1] == d2[a[i], x[i]]
solver.Add(solver.AllowedAssignments((a[i], x[i] - 1, a[i + 1]), d2))
#
# Make a transition (automaton) matrix from a
# single pattern, e.g. [3,2,1]
#
def make_transition_matrix(pattern):
p_len = len(pattern)
num_states = p_len + sum(pattern)
# this is for handling 0-clues. It generates
# just the state 1,2
if num_states == 0:
num_states = 1
t_matrix = []
for i in range(num_states):
row = []
for j in range(2):
row.append(0)
t_matrix.append(row)
# convert pattern to a 0/1 pattern for easy handling of
# the states
tmp = [0 for i in range(num_states)]
c = 0
tmp[c] = 0
for i in range(p_len):
for j in range(pattern[i]):
c += 1
tmp[c] = 1
if c < num_states - 1:
c += 1
tmp[c] = 0
t_matrix[num_states - 1][0] = num_states
t_matrix[num_states - 1][1] = 0
for i in range(num_states):
if tmp[i] == 0:
t_matrix[i][0] = i + 1
t_matrix[i][1] = i + 2
else:
if i < num_states - 1:
if tmp[i + 1] == 1:
t_matrix[i][0] = 0
t_matrix[i][1] = i + 2
else:
t_matrix[i][0] = i + 2
t_matrix[i][1] = 0
# print 'The states:'
# for i in range(num_states):
# for j in range(2):
# print t_matrix[i][j],
# print
# print
return t_matrix
#
# check each rule by creating an automaton
# and regular
#
def check_rule(rules, y):
solver = y[0].solver()
r_len = sum([1 for i in range(len(rules)) if rules[i] > 0])
rules_tmp = []
for i in range(len(rules)):
if rules[i] > 0:
rules_tmp.append(rules[i])
transition_fn = make_transition_matrix(rules_tmp)
n_states = len(transition_fn)
input_max = 2
# Note: we cannot use 0 since it's the failing state
initial_state = 1
accepting_states = [n_states] # This is the last state
regular(y, n_states, input_max, transition_fn,
initial_state, accepting_states)
def main(rows, row_rule_len, row_rules,
cols, col_rule_len, col_rules):
# Create the solver.
solver = pywrapcp.Solver('Regular test')
#
# data
#
#
# variables
#
board = {}
for i in range(rows):
for j in range(cols):
board[i, j] = solver.IntVar(1, 2, 'board[%i, %i]' % (i, j))
board_flat = [board[i, j] for i in range(rows) for j in range(cols)]
# Flattened board for labeling.
# This labeling was inspired by a suggestion from
# Pascal Van Hentenryck about my Comet nonogram model.
board_label = []
if rows * row_rule_len < cols * col_rule_len:
for i in range(rows):
for j in range(cols):
board_label.append(board[i, j])
else:
for j in range(cols):
for i in range(rows):
board_label.append(board[i, j])
#
# constraints
#
for i in range(rows):
check_rule([row_rules[i][j] for j in range(row_rule_len)],
[board[i, j] for j in range(cols)])
for j in range(cols):
check_rule([col_rules[j][k] for k in range(col_rule_len)],
[board[i, j] for i in range(rows)])
#
# solution and search
#
db = solver.Phase(board_label,
solver.CHOOSE_FIRST_UNBOUND,
solver.ASSIGN_MIN_VALUE)
solver.NewSearch(db)
num_solutions = 0
while solver.NextSolution():
print
num_solutions += 1
for i in range(rows):
row = [board[i, j].Value() - 1 for j in range(cols)]
row_pres = []
for j in row:
if j == 1:
row_pres.append('#')
else:
row_pres.append(' ')
print ' ', ''.join(row_pres)
print
print ' ', '-' * cols
if num_solutions >= 2:
print '2 solutions is enough...'
break
solver.EndSearch()
print
print 'num_solutions:', num_solutions
print 'failures:', solver.Failures()
print 'branches:', solver.Branches()
print 'WallTime:', solver.WallTime(), 'ms'
#
# Default problem
#
# From http://twan.home.fmf.nl/blog/haskell/Nonograms.details
# The lambda picture
#
rows = 12
row_rule_len = 3
row_rules = [
[0, 0, 2],
[0, 1, 2],
[0, 1, 1],
[0, 0, 2],
[0, 0, 1],
[0, 0, 3],
[0, 0, 3],
[0, 2, 2],
[0, 2, 1],
[2, 2, 1],
[0, 2, 3],
[0, 2, 2]
]
cols = 10
col_rule_len = 2
col_rules = [
[2, 1],
[1, 3],
[2, 4],
[3, 4],
[0, 4],
[0, 3],
[0, 3],
[0, 3],
[0, 2],
[0, 2]
]
if __name__ == '__main__':
if len(sys.argv) > 1:
file = sys.argv[1]
execfile(file)
main(rows, row_rule_len, row_rules, cols, col_rule_len, col_rules)