# 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 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()