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