# 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.

"""

  Simple coloring problem using MIP in Google CP Solver.

  Inspired by the GLPK:s model color.mod
  '''
  COLOR, Graph Coloring Problem

  Written in GNU MathProg by Andrew Makhorin <mao@mai2.rcnet.ru>

  Given an undirected loopless graph G = (V, E), where V is a set of
  nodes, E <= V x V is a set of arcs, the Graph Coloring Problem is to
  find a mapping (coloring) F: V -> C, where C = {1, 2, ... } is a set
  of colors whose cardinality is as small as possible, such that
  F(i) != F(j) for every arc (i,j) in E, that is adjacent nodes must
  be assigned different colors.
  '''

  Compare with the MiniZinc model:
    http://www.hakank.org/minizinc/coloring_ip.mzn

  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 linear_solver import pywraplp


def main(sol = 'GLPK'):
  
  # Create the solver.

  print 'Solver: ', sol

  if sol == 'GLPK':
    # using GLPK
    solver = pywraplp.Solver('CoinsGridGLPK',
                             pywraplp.Solver.GLPK_MIXED_INTEGER_PROGRAMMING)
  else:
    # Using CBC
        solver = pywraplp.Solver('CoinsGridCLP',
                               pywraplp.Solver.CBC_MIXED_INTEGER_PROGRAMMING)

  #
  # data
  #

  # max number of colors
  # [we know that 4 suffices for normal maps]
  nc = 5

  # number of nodes
  n = 11
  # set of nodes
  V = range(n)
  
  num_edges = 20

  #
  # Neighbours
  #
  # This data correspond to the instance myciel3.col from:
  # http://mat.gsia.cmu.edu/COLOR/instances.html 
  #
  # Note: 1-based (adjusted below)
  E =  [[1, 2],
        [1, 4],
        [1, 7],
        [1, 9],
        [2, 3],
        [2, 6],
        [2, 8],
        [3, 5],
        [3, 7],
        [3, 10],
        [4, 5],
        [4, 6],
        [4, 10],
        [5, 8],
        [5, 9],
        [6, 11],
        [7, 11],
        [8, 11],
        [9, 11],
        [10, 11]]

  
  #
  # declare variables
  #
  
  # x[i,c] = 1 means that node i is assigned color c 
  x = {}
  for v in V:
    for j in range(nc):
      x[v,j] = solver.IntVar(0, 1, 'v[%i,%i]' % (v, j))

      
  # u[c] = 1 means that color c is used, i.e. assigned to some node 
  u = [solver.IntVar(0, 1, 'u[%i]' % i) for i in range(nc)]

  # number of colors used, to minimize
  obj = solver.Sum(u)


  #
  # constraints
  #

  # each node must be assigned exactly one color 
  for i in V:
       solver.Add(solver.Sum([x[i,c] for c in range(nc)]) == 1)

  # adjacent nodes cannot be assigned the same color
  # (and adjust to 0-based)
  for i in range(num_edges):
      for c in range(nc):
        solver.Add(x[E[i][0]-1,c] + x[E[i][1]-1,c] <= u[c])



  # objective
  objective = solver.Minimize(obj)

  #
  # solution
  #
  solver.Solve()

  print
  print "number of colors:", int(solver.objective_value())
  print "colors used:", [int(u[i].solution_value()) for i in range(nc)] 
  print

  for v in V:
    print 'v%i' % v, ' color ',
    for c in range(nc):
      if int(x[v,c].solution_value()) == 1:
        print c

  print
  print "wall_time:", solver.wall_time()
  if sol == 'CBC':
    print 'iterations:', solver.iterations()
  


if __name__ == '__main__':

  sol = 'GLPK'
  if len(sys.argv) > 1:
    sol = sys.argv[1]
    if sol != 'GLPK' and sol != 'CBC':
      print 'Solver must be either GLPK or CBC'
      sys.exit(1)
  
  main(sol)