130 lines
3.2 KiB
Python
130 lines
3.2 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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Crypto problem in Google CP Solver.
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Martin Gardner (February 1967):
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'''
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The integers 1,3,8, and 120 form a set with a remarkable property: the
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product of any two integers is one less than a perfect square. Find
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a fifth number that can be added to the set without destroying
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this property.
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'''
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Solution: The number is 0.
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There are however other sets of five numbers with this property.
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Here are the one in the range of 0.10000:
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[0, 1, 3, 8, 120]
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[0, 1, 3, 120, 1680]
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[0, 1, 8, 15, 528]
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[0, 1, 8, 120, 4095]
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[0, 1, 15, 24, 1520]
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[0, 1, 24, 35, 3480]
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[0, 1, 35, 48, 6888]
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[0, 2, 4, 12, 420]
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[0, 2, 12, 24, 2380]
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[0, 2, 24, 40, 7812]
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[0, 3, 5, 16, 1008]
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[0, 3, 8, 21, 2080]
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[0, 3, 16, 33, 6440]
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[0, 4, 6, 20, 1980]
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[0, 4, 12, 30, 5852]
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[0, 5, 7, 24, 3432]
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[0, 6, 8, 28, 5460]
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[0, 7, 9, 32, 8160]
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Compare with the following models:
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* MiniZinc: http://www.hakank.org/minizinc/crypta.mzn
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* Comet : http://www.hakank.org/comet/crypta.co
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* ECLiPSe : http://www.hakank.org/eclipse/crypta.ecl
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* SICStus : http://hakank.org/sicstus/crypta.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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from __future__ import print_function
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from ortools.constraint_solver import pywrapcp
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def decreasing(solver, x):
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for i in range(len(x) - 1):
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solver.Add(x[i] <= x[i + 1])
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def main():
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# Create the solver.
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solver = pywrapcp.Solver("Curious set of integers")
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#
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# data
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#
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n = 5
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max_val = 10000
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#
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# variables
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#
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x = [solver.IntVar(0, max_val, "x[%i]" % i) for i in range(n)]
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#
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# constraints
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#
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solver.Add(solver.AllDifferent(x))
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decreasing(solver, x)
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for i in range(n):
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for j in range(n):
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if i != j:
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p = solver.IntVar(0, max_val, "p[%i,%i]" % (i, j))
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solver.Add(p * p - 1 == (x[i] * x[j]))
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# This is the original problem:
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# Which is the fifth number?
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v = [1, 3, 8, 120]
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b = [solver.IsMemberVar(x[i], v) for i in range(n)]
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solver.Add(solver.Sum(b) == 4)
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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.CHOOSE_MIN_SIZE_LOWEST_MIN,
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solver.ASSIGN_MIN_VALUE)
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solver.NewSearch(db)
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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("x:", [int(x[i].Value()) for i in range(n)])
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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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