8927b03942
Some of these imports are not used. The rest of them only import string to use the string.atoi function. But string.atoi(s) on a string input is identical to just int(s). See the docs: "deprecated since 2.0".
170 lines
4.5 KiB
Python
170 lines
4.5 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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Pandigital numbers in Google CP Solver.
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From Albert H. Beiler 'Recreations in the Theory of Numbers',
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quoted from http://www.worldofnumbers.com/ninedig1.htm
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'''
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Chapter VIII : Digits - and the magic of 9
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The following curious table shows how to arrange the 9 digits so that
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the product of 2 groups is equal to a number represented by the
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remaining digits.
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12 x 483 = 5796
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42 x 138 = 5796
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18 x 297 = 5346
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27 x 198 = 5346
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39 x 186 = 7254
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48 x 159 = 7632
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28 x 157 = 4396
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4 x 1738 = 6952
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4 x 1963 = 7852
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'''
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See also MathWorld http://mathworld.wolfram.com/PandigitalNumber.html
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'''
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A number is said to be pandigital if it contains each of the digits
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from 0 to 9 (and whose leading digit must be nonzero). However,
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'zeroless' pandigital quantities contain the digits 1 through 9.
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Sometimes exclusivity is also required so that each digit is
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restricted to appear exactly once.
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'''
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* Wikipedia http://en.wikipedia.org/wiki/Pandigital_number
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Compare with the the following models:
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* MiniZinc: http://www.hakank.org/minizinc/pandigital_numbers.mzn
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* Comet : http://www.hakank.org/comet/pandigital_numbers.co
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* ECLiPSe : http://www.hakank.org/eclipse/pandigital_numbers.ecl
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* Gecode/R: http://www.hakank.org/gecoder/pandigital_numbers.rb
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* ECLiPSe : http://hakank.org/eclipse/pandigital_numbers.ecl
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* SICStus : http://hakank.org/sicstus/pandigital_numbers.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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from ortools.constraint_solver import pywrapcp
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#
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# converts a number (s) <-> an array of integers (t) in the specific base.
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#
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def toNum(solver, t, s, base):
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tlen = len(t)
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solver.Add(
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s == solver.Sum([(base ** (tlen - i - 1)) * t[i] for i in range(tlen)]))
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def main(base=10, start=1, len1=1, len2=4):
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# Create the solver.
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solver = pywrapcp.Solver("Pandigital numbers")
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#
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# data
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#
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max_d = base - 1
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x_len = max_d + 1 - start
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max_num = base ** 4 - 1
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#
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# declare variables
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#
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num1 = solver.IntVar(0, max_num, "num1")
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num2 = solver.IntVar(0, max_num, "num2")
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res = solver.IntVar(0, max_num, "res")
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x = [solver.IntVar(start, max_d, "x[%i]" % i) for i in range(x_len)]
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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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toNum(solver, [x[i] for i in range(len1)], num1, base)
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toNum(solver, [x[i] for i in range(len1, len1 + len2)], num2, base)
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toNum(solver, [x[i] for i in range(len1 + len2, x_len)], res, base)
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solver.Add(num1 * num2 == res)
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# no number must start with 0
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solver.Add(x[0] > 0)
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solver.Add(x[len1] > 0)
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solver.Add(x[len1 + len2] > 0)
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# symmetry breaking
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solver.Add(num1 < num2)
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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(num1)
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solution.Add(num2)
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solution.Add(res)
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db = solver.Phase(x,
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solver.INT_VAR_SIMPLE,
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solver.INT_VALUE_DEFAULT)
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solver.NewSearch(db)
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num_solutions = 0
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solutions = []
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while solver.NextSolution():
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print_solution([x[i].Value() for i in range(x_len)], len1, len2, x_len)
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num_solutions += 1
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solver.EndSearch()
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if 0 and num_solutions > 0:
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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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print
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def print_solution(x, len1, len2, x_len):
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print "".join([str(x[i]) for i in range(len1)]), "*",
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print "".join([str(x[i]) for i in range(len1, len1 + len2)]), "=",
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print "".join([str(x[i]) for i in range(len1 + len2, x_len)])
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base = 10
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start = 1
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if __name__ == "__main__":
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if len(sys.argv) > 1:
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base = int(sys.argv[1])
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if len(sys.argv) > 2:
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start = int(sys.argv[2])
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x_len = base - 1 + 1 - start
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for len1 in range(1 + (x_len)):
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for len2 in range(1 + (x_len)):
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if x_len > len1 + len2:
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main(base, start, len1, len2)
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