126 lines
3.5 KiB
Python
126 lines
3.5 KiB
Python
# Copyright 2010 Hakan Kjellerstrand hakank@bonetmail.com
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#
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# Licensed under the Apache License, Version 2.0 (the 'License');
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an 'AS IS' BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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"""
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Set covering in Google CP Solver.
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Example from Steven Skiena, The Stony Brook Algorithm Repository
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http://www.cs.sunysb.edu/~algorith/files/set-cover.shtml
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'''
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Input Description: A set of subsets S_1, ..., S_m of the
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universal set U = {1,...,n}.
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Problem: What is the smallest subset of subsets T subset S such
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that \cup_{t_i in T} t_i = U?
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'''
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Data is from the pictures INPUT/OUTPUT.
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Compare with the following models:
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* MiniZinc: http://www.hakank.org/minizinc/set_covering_skiena.mzn
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* Comet: http://www.hakank.org/comet/set_covering_skiena.co
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* ECLiPSe: http://www.hakank.org/eclipse/set_covering_skiena.ecl
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* SICStus Prolog: http://www.hakank.org/sicstus/set_covering_skiena.pl
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* Gecode: http://hakank.org/gecode/set_covering_skiena.cpp
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This model was created by Hakan Kjellerstrand (hakank@bonetmail.com)
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Also see my other Google CP Solver models: http://www.hakank.org/google_or_tools/
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"""
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from constraint_solver import pywrapcp
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def main():
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# Create the solver.
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solver = pywrapcp.Solver('Set covering Skiena')
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#
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# data
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#
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num_sets = 7
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num_elements = 12
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belongs = [
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# 1 2 3 4 5 6 7 8 9 0 1 2 elements
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[1,1,0,0,0,0,0,0,0,0,0,0], # Set 1
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[0,1,0,0,0,0,0,1,0,0,0,0], # 2
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[0,0,0,0,1,1,0,0,0,0,0,0], # 3
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[0,0,0,0,0,1,1,0,0,1,1,0], # 4
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[0,0,0,0,0,0,0,0,1,1,0,0], # 5
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[1,1,1,0,1,0,0,0,1,1,1,0], # 6
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[0,0,1,1,0,0,1,1,0,0,1,1] # 7
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]
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#
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# variables
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#
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x = [solver.IntVar(0, 1, 'x[%i]' % i) for i in range(num_sets)]
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# number of choosen sets
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z = solver.IntVar(0, num_sets*2, 'z')
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# total number of elements in the choosen sets
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tot_elements = solver.IntVar(0, num_sets*num_elements)
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#
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# constraints
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#
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solver.Add(z == solver.Sum(x))
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# all sets must be used
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for j in range(num_elements):
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s = solver.Sum([belongs[i][j]*x[i] for i in range(num_sets)])
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solver.Add(s >= 1)
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# number of used elements
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solver.Add(tot_elements ==
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solver.Sum([x[i]*belongs[i][j]
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for i in range(num_sets)
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for j in range(num_elements)]))
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# objective
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objective = solver.Minimize(z, 1)
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#
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# search and result
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#
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db = solver.Phase(x,
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solver.INT_VAR_DEFAULT,
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solver.INT_VALUE_DEFAULT
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)
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solver.NewSearch(db, [objective])
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num_solutions = 0
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while solver.NextSolution():
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num_solutions += 1
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print "z:", z.Value()
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print "tot_elements:", tot_elements.Value()
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print 'x:', [x[i].Value() for i in range(num_sets)]
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solver.EndSearch()
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print
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print 'num_solutions:', num_solutions
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print 'failures:', solver.Failures()
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print 'branches:', solver.Branches()
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print 'WallTime:', solver.WallTime(), 'ms'
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if __name__ == '__main__':
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main()
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