# 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.

"""

  Quasigroup completion Google CP Solver.


  See Carla P. Gomes and David Shmoys:
  "Completing Quasigroups or Latin Squares: Structured Graph Coloring Problem"

  See also
  Ivars Peterson "Completing Latin Squares"
  http://www.maa.org/mathland/mathtrek_5_8_00.html
  '''
    Using only the numbers 1, 2, 3, and 4, arrange four sets of these numbers into
    a four-by-four array so that no column or row contains the same two numbers.
    The result is known as a Latin square.
    ...
    The so-called quasigroup completion problem concerns a table that is correctly
    but only partially filled in. The question is whether the remaining blanks in
    the table can be filled in to obtain a complete Latin square (or a proper
    quasigroup multiplication table).
    '''

    Compare with the following models:
    * Choco: http://www.hakank.org/choco/QuasigroupCompletion.java
    * Comet: http://www.hakank.org/comet/quasigroup_completion.co
    * ECLiPSE: http://www.hakank.org/eclipse/quasigroup_completion.ecl
    * Gecode: http://www.hakank.org/gecode/quasigroup_completion.cpp
    * Gecode/R: http://www.hakank.org/gecode_r/quasigroup_completion.rb
    * JaCoP: http://www.hakank.org/JaCoP/QuasigroupCompletion.java
    * MiniZinc: http://www.hakank.org/minizinc/quasigroup_completion.mzn
    * Tailor/Essence': http://www.hakank.org/tailor/quasigroup_completion.eprime
    * SICStus: http://hakank.org/sicstus/quasigroup_completion.pl
    * Zinc: http://hakank.org/minizinc/quasigroup_completion.zinc

  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

default_n = 5
X = 0
# default problem
# (This is the same as quasigroup1.txt)
default_puzzle = [
    [1, X, X, X, 4],
    [X, 5, X, X, X],
    [4, X, X, 2, X],
    [X, 4, X, X, X],
    [X, X, 5, X, 1]
    ]

def main(puzzle="", n=0):

    # Create the solver.
    solver = pywrapcp.Solver('Quasigroup completion')

    #
    # data
    #

    if puzzle == "":
        puzzle = default_puzzle
        n = default_n

    print "Problem:"
    print_game(puzzle, n,n)


    # declare variables
    x = {}
    for i in range(n):
        for j in range(n):
            x[(i,j)] = solver.IntVar(1,n, 'x %i %i' % (i, j))

    xflat = [x[(i,j)] for i in range(n) for j in range(n)]

    #
    # constraints
    #

    #
    # set the clues
    #
    for i in range(n):
        for j in range(n):
            if puzzle[i][j] > X:
                solver.Add(x[i,j] == puzzle[i][j])



    #
    # rows and columns must be different
    #
    for i in range(n):
        solver.Add(solver.AllDifferent([x[i,j] for j in range(n)]))
        solver.Add(solver.AllDifferent([x[j,i] for j in range(n)]))

    #
    # solution and search
    #
    solution = solver.Assignment()
    solution.Add(xflat)

    # This version prints out the solution directly, and
    # don't collect them as solver.FirstSolutionCollector(solution) do
    # (db: DecisionBuilder)
    db = solver.Phase(xflat,
                 solver.INT_VAR_SIMPLE,
                 solver.ASSIGN_MIN_VALUE)

    solver.NewSearch(db)
    num_solutions = 0
    while solver.NextSolution():
        num_solutions += 1
        print "Solution %i" % num_solutions
        xval = [x[(i,j)].Value() for i in range(n) for j in range(n)]
        for i in range(n):
            for j in range(n):
                print xval[i*n+j],
            print
        print
    solver.EndSearch()

    if num_solutions == 0:
        print "No solutions found"

    # # Note: AllSolution may take very much RAM, hence I choose to
    # # show just the first solution.
    # # collector = solver.AllSolutionCollector(solution)
    # collector = solver.FirstSolutionCollector(solution)
    # solver.Solve(solver.Phase([x[(i,j)] for i in range(n) for j in range(n)],
    #                           solver.CHOOSE_FIRST_UNBOUND,
    #                           solver.ASSIGN_MIN_VALUE),
    #                           [collector])
    #
    # num_solutions = collector.SolutionCount()
    # print "\nnum_solutions: ", num_solutions
    # if num_solutions > 0:
    #     print "\nJust showing the first solution..."
    #     for s in range(num_solutions):
    #         xval = [collector.Value(s, x[(i,j)]) for i in range(n) for j in range(n)]
    #         for i in range(n):
    #             for j in range(n):
    #                 print xval[i*n+j],
    #             print
    #         print

    print
    print "num_solutions:", num_solutions
    print "failures:", solver.Failures()
    print "branches:", solver.Branches()
    print "WallTime:", solver.WallTime()



#
# Read a problem instance from a file
#
def read_problem(file):
    f = open(file, 'r')
    n = int(f.readline())
    game = []
    for i in range(n):
        x = f.readline()
        row_x = (x.rstrip()).split(" ")
        row = [0]*n
        for j in range(n):
            if row_x[j] == ".":
                tmp = 0
            else:
                tmp = int(row_x[j])
            row[j] = tmp
        game.append(row)
    return [game, n]


def print_board(x, rows, cols):
    for i in range(rows):
        for j in range(cols):
            print "% 2s" % x[i,j],
        print ''

def print_game(game, rows, cols):
    for i in range(rows):
        for j in range(cols):
            print "% 2s" % game[i][j],
        print ''



if __name__ == '__main__':

    if len(sys.argv) > 1:
        file = sys.argv[1]
        print "Problem instance from", file
        [game, n] = read_problem(file)
        main(game, n)
    else:
        main()