examples/notebook/contrib/lectures.ipynb
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.
First, you must install ortools package in this colab.
%pip install ortools
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 potential audience there are people who wish to hear both
How many hours are necessary in order that the lectures can be given without clashes? '''
Compare with the following models:
This model was created by Hakan Kjellerstrand ([email protected]) 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')
main()