177 lines
4.8 KiB
Python
177 lines
4.8 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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Global constraint contiguity using regularin Google CP Solver.
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This is a decomposition of the global constraint
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global contiguity.
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From Global Constraint Catalogue
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http://www.emn.fr/x-info/sdemasse/gccat/Cglobal_contiguity.html
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'''
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Enforce all variables of the VARIABLES collection to be assigned to 0 or 1.
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In addition, all variables assigned to value 1 appear contiguously.
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Example:
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(<0, 1, 1, 0>)
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The global_contiguity constraint holds since the sequence 0 1 1 0 contains
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no more than one group of contiguous 1.
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'''
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Compare with the following model:
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* MiniZinc: http://www.hakank.org/minizinc/contiguity_regular.mzn
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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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from ortools.constraint_solver import pywrapcp
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#
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# Global constraint regular
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#
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# This is a translation of MiniZinc's regular constraint (defined in
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# lib/zinc/globals.mzn), via the Comet code refered above.
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# All comments are from the MiniZinc code.
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# '''
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# The sequence of values in array 'x' (which must all be in the range 1..S)
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# is accepted by the DFA of 'Q' states with input 1..S and transition
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# function 'd' (which maps (1..Q, 1..S) -> 0..Q)) and initial state 'q0'
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# (which must be in 1..Q) and accepting states 'F' (which all must be in
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# 1..Q). We reserve state 0 to be an always failing state.
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# '''
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#
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# x : IntVar array
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# Q : number of states
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# S : input_max
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# d : transition matrix
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# q0: initial state
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# F : accepting states
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def regular(x, Q, S, d, q0, F):
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solver = x[0].solver()
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assert Q > 0, 'regular: "Q" must be greater than zero'
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assert S > 0, 'regular: "S" must be greater than zero'
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# d2 is the same as d, except we add one extra transition for
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# each possible input; each extra transition is from state zero
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# to state zero. This allows us to continue even if we hit a
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# non-accepted input.
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# Comet: int d2[0..Q, 1..S]
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d2 = []
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for i in range(Q + 1):
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row = []
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for j in range(S):
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if i == 0:
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row.append(0)
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else:
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row.append(d[i - 1][j])
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d2.append(row)
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d2_flatten = [d2[i][j] for i in range(Q + 1) for j in range(S)]
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# If x has index set m..n, then a[m-1] holds the initial state
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# (q0), and a[i+1] holds the state we're in after processing
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# x[i]. If a[n] is in F, then we succeed (ie. accept the
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# string).
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x_range = list(range(0, len(x)))
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m = 0
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n = len(x)
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a = [solver.IntVar(0, Q + 1, 'a[%i]' % i) for i in range(m, n + 1)]
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# Check that the final state is in F
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solver.Add(solver.MemberCt(a[-1], F))
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# First state is q0
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solver.Add(a[m] == q0)
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for i in x_range:
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solver.Add(x[i] >= 1)
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solver.Add(x[i] <= S)
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# Determine a[i+1]: a[i+1] == d2[a[i], x[i]]
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solver.Add(
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a[i + 1] == solver.Element(d2_flatten, ((a[i]) * S) + (x[i] - 1)))
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def main():
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# Create the solver.
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solver = pywrapcp.Solver('Global contiguity using regular')
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#
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# data
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#
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# the DFA (for regular)
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n_states = 3
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input_max = 2
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initial_state = 1 # 0 is for the failing state
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# all states are accepting states
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accepting_states = [1, 2, 3]
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# The regular expression 0*1*0*
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transition_fn = [
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[1, 2], # state 1 (start): input 0 -> state 1, input 1 -> state 2 i.e. 0*
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[3, 2], # state 2: 1*
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[3, 0], # state 3: 0*
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]
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n = 7
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#
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# declare variables
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#
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# We use 1..2 and subtract 1 in the solution
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reg_input = [solver.IntVar(1, 2, '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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regular(reg_input, n_states, input_max, transition_fn, initial_state,
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accepting_states)
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#
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# solution and search
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#
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db = solver.Phase(reg_input, 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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num_solutions += 1
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# Note: here we subract 1 from the solution
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print('reg_input:', [int(reg_input[i].Value() - 1) 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('wall_time:', solver.WallTime(), 'ms')
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if __name__ == '__main__':
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main()
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