# 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.
"""
Lectures problem in Google CP Solver.
Biggs: Discrete Mathematics (2nd ed), page 187.
'''
Suppose we wish to schedule six one-hour lectures, v1, v2, v3, v4, v5, v6.
Among the the potential audience there are people who wish to hear both
- v1 and v2
- v1 and v4
- v3 and v5
- v2 and v6
- v4 and v5
- v5 and v6
- v1 and v6
How many hours are necessary in order that the lectures can be given
without clashes?
'''
Compare with the following models:
* MiniZinc: http://www.hakank.org/minizinc/lectures.mzn
* SICstus: http://hakank.org/sicstus/lectures.pl
* ECLiPSe: http://hakank.org/eclipse/lectures.ecl
* Gecode: http://hakank.org/gecode/lectures.cpp
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
def main():
# Create the solver.
solver = pywrapcp.Solver('Lectures')
#
# data
#
#
# The schedule requirements:
# lecture a cannot be held at the same time as b
# Note: 1-based
g = [
[1, 2],
[1, 4],
[3, 5],
[2, 6],
[4, 5],
[5, 6],
[1, 6]
]
# number of nodes
n = 6
# number of edges
edges = len(g)
#
# declare variables
#
v = [solver.IntVar(0, n - 1, 'v[%i]' % i) for i in range(n)]
# maximum color, to minimize
# Note: since Python is 0-based, the
# number of colors is +1
max_c = solver.IntVar(0, n - 1, 'max_c')
#
# constraints
#
solver.Add(max_c == solver.Max(v))
# ensure that there are no clashes
# also, adjust to 0-base
for i in range(edges):
solver.Add(v[g[i][0] - 1] != v[g[i][1] - 1])
# symmetry breaking:
# - v0 has the color 0,
# - v1 has either color 0 or 1
solver.Add(v[0] == 0)
solver.Add(v[1] <= 1)
# objective
objective = solver.Minimize(max_c, 1)
#
# solution and search
#
db = solver.Phase(v,
solver.CHOOSE_MIN_SIZE_LOWEST_MIN,
solver.ASSIGN_CENTER_VALUE)
solver.NewSearch(db, [objective])
num_solutions = 0
while solver.NextSolution():
num_solutions += 1
print 'max_c:', max_c.Value() + 1, 'colors'
print 'v:', [v[i].Value() for i in range(n)]
print
print 'num_solutions:', num_solutions
print 'failures:', solver.Failures()
print 'branches:', solver.Branches()
print 'WallTime:', solver.WallTime(), 'ms'
if __name__ == '__main__':
main()