159 lines
4.1 KiB
Python
159 lines
4.1 KiB
Python
# Copyright 2010 Hakan Kjellerstrand hakank@bonetmail.com
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#
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# Licensed under the Apache License, Version 2.0 (the 'License');
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an 'AS IS' BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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"""Strimko problem in Google CP Solver.
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From
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360: A New Twist on Latin Squares
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http://threesixty360.wordpress.com/2009/08/04/a-new-twist-on-latin-squares/
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'''
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The idea is simple: each row and column of an nxn grid must contain
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the number 1, 2, ... n exactly once (that is, the grid must form a
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Latin square), and each "stream" (connected path in the grid) must
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also contain the numbers 1, 2, ..., n exactly once.
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'''
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For more information, see:
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* http://www.strimko.com/
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* http://www.strimko.com/rules.htm
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* http://www.strimko.com/about.htm
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* http://www.puzzlersparadise.com/Strimko.htm
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I have blogged about this (using MiniZinc model) in
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'Strimko - Latin squares puzzle with "streams"'
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http://www.hakank.org/constraint_programming_blog/2009/08/strimko_latin_squares_puzzle_w_1.html
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Compare with the following models:
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* MiniZinc: http://hakank.org/minizinc/strimko2.mzn
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* ECLiPSe: http://hakank.org/eclipse/strimko2.ecl
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* SICStus: http://hakank.org/sicstus/strimko2.pl
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* Gecode: http://hakank.org/gecode/strimko2.cpp
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This model was created by Hakan Kjellerstrand (hakank@bonetmail.com)
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See my other Google CP Solver models: http://www.hakank.org/google_or_tools/
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"""
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import sys
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from constraint_solver import pywrapcp
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def main(streams="", placed=""):
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# Create the solver.
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solver = pywrapcp.Solver('Strimko')
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#
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# default problem
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#
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if streams == "":
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streams = [
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[1,1,2,2,2,2,2],
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[1,1,2,3,3,3,2],
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[1,4,1,3,3,5,5],
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[4,4,3,1,3,5,5],
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[4,6,6,6,7,7,5],
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[6,4,6,4,5,5,7],
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[6,6,4,7,7,7,7]]
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# Note: This is 1-based
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placed = [
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[2,1,1],
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[2,3,7],
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[2,5,6],
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[2,7,4],
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[3,2,7],
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[3,6,1],
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[4,1,4],
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[4,7,5],
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[5,2,2],
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[5,6,6]]
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n = len(streams)
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num_placed = len(placed)
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print "n:", n
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#
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# variables
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#
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x = {}
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for i in range(n):
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for j in range(n):
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x[i,j] = solver.IntVar(1, n, 'x[%i,%i]' % (i,j))
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x_flat = [x[i,j] for i in range(n) for j in range(n)]
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#
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# constraints
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#
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# all rows and columns must be unique, i.e. a Latin Square
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for i in range(n):
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row = [x[i,j] for j in range(n)]
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solver.Add(solver.AllDifferent(row))
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col = [x[j,i] for j in range(n)]
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solver.Add(solver.AllDifferent(col))
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#
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# streams
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#
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for s in range(1, n+1):
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tmp = [x[i,j] for i in range(n) for j in range(n) if streams[i][j] == s]
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solver.Add(solver.AllDifferent(tmp))
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#
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# placed
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#
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for i in range(num_placed):
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# note: also adjust to 0-based
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solver.Add(x[placed[i][0]-1, placed[i][1]-1] == placed[i][2])
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#
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# search and solution
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#
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db = solver.Phase(x_flat,
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solver.INT_VAR_DEFAULT,
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solver.INT_VALUE_DEFAULT)
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solver.NewSearch(db)
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num_solutions = 0
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while solver.NextSolution():
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for i in range(n):
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for j in range(n):
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print x[i,j].Value(),
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print
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print
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num_solutions += 1
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solver.EndSearch()
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print
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print 'num_solutions:', num_solutions
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print 'failures:', solver.Failures()
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print 'branches:', solver.Branches()
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print 'WallTime:', solver.WallTime(), 'ms'
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if __name__ == '__main__':
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if len(sys.argv) > 1:
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problem_file = sys.argv[1]
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execfile(problem_file)
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main(streams, placed)
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else:
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main()
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