119 lines
3.6 KiB
Python
119 lines
3.6 KiB
Python
# Copyright 2010 Hakan Kjellerstrand hakank@gmail.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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All interval problem in Google CP Solver.
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CSPLib problem number 7
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http://www.cs.st-andrews.ac.uk/~ianm/CSPLib/prob/prob007/index.html
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'''
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Given the twelve standard pitch-classes (c, c , d, ...), represented by
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numbers 0,1,...,11, find a series in which each pitch-class occurs exactly
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once and in which the musical intervals between neighbouring notes cover
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the full set of intervals from the minor second (1 semitone) to the major
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seventh (11 semitones). That is, for each of the intervals, there is a
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pair of neigbhouring pitch-classes in the series, between which this
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interval appears. The problem of finding such a series can be easily
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formulated as an instance of a more general arithmetic problem on Z_n,
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the set of integer residues modulo n. Given n in N, find a vector
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s = (s_1, ..., s_n), such that (i) s is a permutation of
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Z_n = {0,1,...,n-1}; and (ii) the interval vector
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v = (|s_2-s_1|, |s_3-s_2|, ... |s_n-s_{n-1}|) is a permutation of
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Z_n-{0} = {1,2,...,n-1}. A vector v satisfying these conditions is
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called an all-interval series of size n; the problem of finding such
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a series is the all-interval series problem of size n. We may also be
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interested in finding all possible series of a given size.
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'''
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Compare with the following models:
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* MiniZinc: http://www.hakank.org/minizinc/all_interval.mzn
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* Comet : http://www.hakank.org/comet/all_interval.co
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* Gecode/R: http://www.hakank.org/gecode_r/all_interval.rb
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* ECLiPSe : http://www.hakank.org/eclipse/all_interval.ecl
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* SICStus : http://www.hakank.org/sicstus/all_interval.pl
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This model was created by Hakan Kjellerstrand (hakank@gmail.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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import sys
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from ortools.constraint_solver import pywrapcp
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def main(n=12):
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# Create the solver.
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solver = pywrapcp.Solver("All interval")
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#
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# data
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#
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print("n:", n)
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#
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# declare variables
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#
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x = [solver.IntVar(1, n, "x[%i]" % i) for i in range(n)]
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diffs = [solver.IntVar(1, n - 1, "diffs[%i]" % i) for i in range(n - 1)]
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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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solver.Add(solver.AllDifferent(diffs))
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for k in range(n - 1):
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solver.Add(diffs[k] == abs(x[k + 1] - x[k]))
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# symmetry breaking
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solver.Add(x[0] < x[n - 1])
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solver.Add(diffs[0] < diffs[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(diffs)
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db = solver.Phase(x,
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solver.CHOOSE_FIRST_UNBOUND,
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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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print("x:", [x[i].Value() for i in range(n)])
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print("diffs:", [diffs[i].Value() for i in range(n - 1)])
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num_solutions += 1
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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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n = 12
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if __name__ == "__main__":
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if len(sys.argv) > 1:
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n = int(sys.argv[1])
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main(n)
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