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# 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.
"""

  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@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.linear_solver import pywraplp



# 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 = list(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].SolutionValue()) for i in range(nc)])
print()

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

print()
print('WallTime:', solver.WallTime())
if sol == 'CBC':
  print('iterations:', solver.Iterations())