205 lines
5.0 KiB
Python
205 lines
5.0 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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KenKen puzzle in Google CP Solver.
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http://en.wikipedia.org/wiki/KenKen
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'''
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KenKen or KEN-KEN is a style of arithmetic and logical puzzle sharing
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several characteristics with sudoku. The name comes from Japanese and
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is translated as 'square wisdom' or 'cleverness squared'.
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...
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The objective is to fill the grid in with the digits 1 through 6 such that:
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* Each row contains exactly one of each digit
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* Each column contains exactly one of each digit
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* Each bold-outlined group of cells is a cage containing digits which
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achieve the specified result using the specified mathematical operation:
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addition (+),
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subtraction (-),
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multiplication (x),
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and division (/).
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(Unlike in Killer sudoku, digits may repeat within a group.)
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...
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More complex KenKen problems are formed using the principles described
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above but omitting the symbols +, -, x and /, thus leaving them as
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yet another unknown to be determined.
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'''
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The solution is:
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5 6 3 4 1 2
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6 1 4 5 2 3
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4 5 2 3 6 1
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3 4 1 2 5 6
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2 3 6 1 4 5
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1 2 5 6 3 4
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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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import sys
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from constraint_solver import pywrapcp
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#
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# Ensure that the sum of the segments
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# in cc == res
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#
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def calc(cc, x, res):
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solver = x.values()[0].solver()
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if len(cc) == 2:
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# for two operands there may be
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# a lot of variants
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c00, c01 = cc[0]
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c10, c11 = cc[1]
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a = x[c00-1, c01-1]
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b = x[c10-1, c11-1]
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r1 = solver.IsEqualCstVar(a + b, res)
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r2 = solver.IsEqualCstVar(a * b, res)
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r3 = solver.IsEqualVar(a * res, b)
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r4 = solver.IsEqualVar(b * res, a)
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r5 = solver.IsEqualCstVar(a - b, res)
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r6 = solver.IsEqualCstVar(b - a, res)
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solver.Add(r1+r2+r3+r4+r5+r6 >= 1)
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else:
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# res is either sum or product of the segment
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xx = [x[i[0]-1,i[1]-1] for i in cc]
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# Sum
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# # SumEquality don't work:
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# this_sum = solver.SumEquality(xx, res)
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this_sum = solver.IsEqualCstVar(solver.Sum(xx), res)
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# Product
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# # Prod (or MakeProd) don't work:
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# this_prod = solver.IsEqualCstVar(solver.Prod(xx), res)
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this_prod = solver.IsEqualCstVar(reduce(lambda a, b: a*b, xx), res)
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solver.Add(this_sum + this_prod >= 1)
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def main():
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# Create the solver.
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solver = pywrapcp.Solver('KenKen')
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#
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# data
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#
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# size of matrix
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n = 6
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# For a better view of the problem, see
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# http://en.wikipedia.org/wiki/File:KenKenProblem.svg
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# hints
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# [sum, [segments]]
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# Note: 1-based
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problem = [
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[ 11, [[1,1], [2,1]]],
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[ 2, [[1,2], [1,3]]],
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[ 20, [[1,4], [2,4]]],
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[ 6, [[1,5], [1,6], [2,6], [3,6]]],
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[ 3, [[2,2], [2,3]]],
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[ 3, [[2,5], [3,5]]],
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[240, [[3,1], [3,2], [4,1], [4,2]]],
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[ 6, [[3,3], [3,4]]],
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[ 6, [[4,3], [5,3]]],
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[ 7, [[4,4], [5,4], [5,5]]],
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[ 30, [[4,5], [4,6]]],
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[ 6, [[5,1], [5,2]]],
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[ 9, [[5,6], [6,6]]],
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[ 8, [[6,1], [6,2], [6,3]]],
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[ 2, [[6,4], [6,5]]]]
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num_p = len(problem)
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#
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# variables
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#
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# the set
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x = {}
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for i in range(n):
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for j in range(n):
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x[i,j] = solver.IntVar(1, n, 'x[%i,%i]' % (i,j))
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x_flat = [x[i,j] for i in range(n) for j in range(n)]
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#
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# constraints
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#
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# all rows and columns must be unique
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for i in range(n):
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row = [x[i,j] for j in range(n)]
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solver.Add(solver.AllDifferent(row))
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col = [x[j,i] for j in range(n)]
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solver.Add(solver.AllDifferent(col))
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# calculate the segments
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for (res, segment) in problem:
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calc(segment, x, res)
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#
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# search and solution
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#
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db = solver.Phase(x_flat,
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solver.INT_VAR_DEFAULT,
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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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while solver.NextSolution():
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for i in range(n):
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for j in range(n):
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print x[i,j].Value(),
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print
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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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