105 lines
2.8 KiB
Python
105 lines
2.8 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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Coin application in Google CP Solver.
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From 'Constraint Logic Programming using ECLiPSe'
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pages 99f and 234 ff.
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The solution in ECLiPSe is at page 236.
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'''
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What is the minimum number of coins that allows one to pay _exactly_
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any amount smaller than one Euro? Recall that there are six different
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euro cents, of denomination 1, 2, 5, 10, 20, 50
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'''
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Compare with the following models:
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* MiniZinc: http://hakank.org/minizinc/coins3.mzn
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* Comet : http://www.hakank.org/comet/coins3.co
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* Gecode : http://hakank.org/gecode/coins3.cpp
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* SICStus : http://hakank.org/sicstus/coins3.pl
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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:
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http://www.hakank.org/google_or_tools/
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"""
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import sys
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import string
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from ortools.constraint_solver import pywrapcp
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def main():
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# Create the solver.
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solver = pywrapcp.Solver("Coins")
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#
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# data
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#
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n = 6 # number of different coins
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variables = [1, 2, 5, 10, 25, 50]
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# declare variables
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x = [solver.IntVar(0, 99, "x%i" % i) for i in range(n)]
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num_coins = solver.IntVar(0, 99, "num_coins")
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#
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# constraints
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#
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# number of used coins, to be minimized
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solver.Add(num_coins == solver.Sum(x))
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# Check that all changes from 1 to 99 can be made.
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for j in range(1, 100):
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tmp = [solver.IntVar(0, 99, "b%i" % i) for i in range(n)]
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solver.Add(solver.ScalProd(tmp, variables) == j)
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[solver.Add(tmp[i] <= x[i]) for i in range(n)]
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# objective
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objective = solver.Minimize(num_coins, 1)
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#
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# solution and search
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#
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solution = solver.Assignment()
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solution.Add(x)
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solution.Add(num_coins)
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solution.AddObjective(num_coins)
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db = solver.Phase(x,
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solver.CHOOSE_MIN_SIZE_LOWEST_MAX,
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solver.ASSIGN_MIN_VALUE)
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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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print "x: ", [x[i].Value() for i in range(n)]
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print "num_coins:", num_coins.Value()
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print
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num_solutions += 1
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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()
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if __name__ == "__main__":
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main()
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