# Copyright 2010 Hakan Kjellerstrand hakank@gmail.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.

"""

  Place number puzzle Google CP Solver.

  http://ai.uwaterloo.ca/~vanbeek/Courses/Slides/introduction.pdf
  '''
  Place numbers 1 through 8 on nodes
  - each number appears exactly once
  - no connected nodes have consecutive numbers
       2 - 5
     / | X | \
   1 - 3 - 6 - 8
     \ | X | /
       4 - 7
  ""

  Compare with the following models:
  * MiniZinc: http://www.hakank.org/minizinc/place_number.mzn
  * Comet: http://www.hakank.org/comet/place_number_puzzle.co
  * ECLiPSe: http://www.hakank.org/eclipse/place_number_puzzle.ecl
  * SICStus Prolog: http://www.hakank.org/sicstus/place_number_puzzle.pl
  * Gecode: http://www.hakank.org/gecode/place_number_puzzle.cpp

  This model was created by Hakan Kjellerstrand (hakank@gmail.com)
  Also see my other Google CP Solver models:
  http://www.hakank.org/google_or_tools/

"""
from __future__ import print_function
import sys
from ortools.constraint_solver import pywrapcp


def main():

  # Create the solver.
  solver = pywrapcp.Solver("Place number")

  # data
  m = 32
  n = 8
  # Note: this is 1-based for compatibility (and lazyness)
  graph = [
      [1, 2],
      [1, 3],
      [1, 4],
      [2, 1],
      [2, 3],
      [2, 5],
      [2, 6],
      [3, 2],
      [3, 4],
      [3, 6],
      [3, 7],
      [4, 1],
      [4, 3],
      [4, 6],
      [4, 7],
      [5, 2],
      [5, 3],
      [5, 6],
      [5, 8],
      [6, 2],
      [6, 3],
      [6, 4],
      [6, 5],
      [6, 7],
      [6, 8],
      [7, 3],
      [7, 4],
      [7, 6],
      [7, 8],
      [8, 5],
      [8, 6],
      [8, 7]
  ]

  # declare variables
  x = [solver.IntVar(1, n, "x%i" % i) for i in range(n)]

  #
  # constraints
  #
  solver.Add(solver.AllDifferent(x))
  for i in range(m):
    # Note: make 0-based
    solver.Add(abs(
        x[graph[i][0] - 1] - x[graph[i][1] - 1]) > 1)

  # symmetry breaking
  solver.Add(x[0] < x[n - 1])

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

  collector = solver.AllSolutionCollector(solution)

  solver.Solve(solver.Phase(x,
                            solver.CHOOSE_FIRST_UNBOUND,
                            solver.ASSIGN_MIN_VALUE),
               [collector])

  num_solutions = collector.SolutionCount()
  for s in range(num_solutions):
    print("x:", [collector.Value(s, x[i]) for i in range(len(x))])

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

if __name__ == "__main__":
  main()