# 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.
"""Strimko problem in Google CP Solver.
From
360: A New Twist on Latin Squares
http://threesixty360.wordpress.com/2009/08/04/a-new-twist-on-latin-squares/
'''
The idea is simple: each row and column of an nxn grid must contain
the number 1, 2, ... n exactly once (that is, the grid must form a
Latin square), and each "stream" (connected path in the grid) must
also contain the numbers 1, 2, ..., n exactly once.
'''
For more information, see:
* http://www.strimko.com/
* http://www.strimko.com/rules.htm
* http://www.strimko.com/about.htm
* http://www.puzzlersparadise.com/Strimko.htm
I have blogged about this (using MiniZinc model) in
'Strimko - Latin squares puzzle with "streams"'
http://www.hakank.org/constraint_programming_blog/2009/08/strimko_latin_squares_puzzle_w_1.html
Compare with the following models:
* MiniZinc: http://hakank.org/minizinc/strimko2.mzn
* ECLiPSe: http://hakank.org/eclipse/strimko2.ecl
* SICStus: http://hakank.org/sicstus/strimko2.pl
* Gecode: http://hakank.org/gecode/strimko2.cpp
This model was created by Hakan Kjellerstrand (hakank@bonetmail.com)
See my other Google CP Solver models: http://www.hakank.org/google_or_tools/
"""
import sys
from ortools.constraint_solver import pywrapcp
def main(streams='', placed=''):
# Create the solver.
solver = pywrapcp.Solver('Strimko')
#
# default problem
#
if streams == '':
streams = [
[1, 1, 2, 2, 2, 2, 2],
[1, 1, 2, 3, 3, 3, 2],
[1, 4, 1, 3, 3, 5, 5],
[4, 4, 3, 1, 3, 5, 5],
[4, 6, 6, 6, 7, 7, 5],
[6, 4, 6, 4, 5, 5, 7],
[6, 6, 4, 7, 7, 7, 7]]
# Note: This is 1-based
placed = [
[2, 1, 1],
[2, 3, 7],
[2, 5, 6],
[2, 7, 4],
[3, 2, 7],
[3, 6, 1],
[4, 1, 4],
[4, 7, 5],
[5, 2, 2],
[5, 6, 6]]
n = len(streams)
num_placed = len(placed)
print 'n:', n
#
# variables
#
x = {}
for i in range(n):
for j in range(n):
x[i, j] = solver.IntVar(1, n, 'x[%i,%i]' % (i, j))
x_flat = [x[i, j] for i in range(n) for j in range(n)]
#
# constraints
#
# all rows and columns must be unique, i.e. a Latin Square
for i in range(n):
row = [x[i, j] for j in range(n)]
solver.Add(solver.AllDifferent(row))
col = [x[j, i] for j in range(n)]
solver.Add(solver.AllDifferent(col))
#
# streams
#
for s in range(1, n + 1):
tmp = [x[i, j] for i in range(n) for j in range(n) if streams[i][j] == s]
solver.Add(solver.AllDifferent(tmp))
#
# placed
#
for i in range(num_placed):
# note: also adjust to 0-based
solver.Add(x[placed[i][0] - 1, placed[i][1] - 1] == placed[i][2])
#
# search and solution
#
db = solver.Phase(x_flat,
solver.INT_VAR_DEFAULT,
solver.INT_VALUE_DEFAULT)
solver.NewSearch(db)
num_solutions = 0
while solver.NextSolution():
for i in range(n):
for j in range(n):
print x[i, j].Value(),
print
print
num_solutions += 1
solver.EndSearch()
print
print 'num_solutions:', num_solutions
print 'failures:', solver.Failures()
print 'branches:', solver.Branches()
print 'WallTime:', solver.WallTime(), 'ms'
if __name__ == '__main__':
if len(sys.argv) > 1:
problem_file = sys.argv[1]
execfile(problem_file)
main(streams, placed)
else:
main()