1850 lines
67 KiB
Python
1850 lines
67 KiB
Python
# Copyright 2010-2018 Google LLC
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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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"""Methods for building and solving CP-SAT models.
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The following two sections describe the main
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methods for building and solving CP-SAT models.
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* [`CpModel`](#cp_model.CpModel): Methods for creating
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models, including variables and constraints.
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* [`CPSolver`](#cp_model.CpSolver): Methods for solving
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a model and evaluating solutions.
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The following methods implement callbacks that the
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solver calls each time it finds a new solution.
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* [`CpSolverSolutionCallback`](#cp_model.CpSolverSolutionCallback):
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A general method for implementing callbacks.
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* [`ObjectiveSolutionPrinter`](#cp_model.ObjectiveSolutionPrinter):
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Print objective values and elapsed time for intermediate solutions.
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* [`VarArraySolutionPrinter`](#cp_model.VarArraySolutionPrinter):
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Print intermediate solutions (variable values, time).
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* [`VarArrayAndObjectiveSolutionPrinter`]
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(#cp_model.VarArrayAndObjectiveSolutionPrinter):
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Print both intermediate solutions and objective values.
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Additional methods for solving CP-SAT models:
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* [`Constraint`](#cp_model.Constraint): A few utility methods for modifying
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contraints created by `CpModel`.
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* [`LinearExpr`](#lineacp_model.LinearExpr): Methods for creating constraints
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and the objective from large arrays of coefficients.
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Other methods and functions listed are primarily used for developing OR-Tools,
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rather than for solving specific optimization problems.
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"""
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from __future__ import absolute_import
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from __future__ import division
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from __future__ import print_function
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import collections
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import numbers
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import time
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from six import iteritems
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from ortools.sat import cp_model_pb2
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from ortools.sat import sat_parameters_pb2
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from ortools.sat.python import cp_model_helper
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from ortools.sat import pywrapsat
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from ortools.util import sorted_interval_list
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Domain = sorted_interval_list.Domain
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# Documentation cleaning.
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# Remove the documentation of some functions.
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# See https://pdoc3.github.io/pdoc/doc/pdoc/#overriding-docstrings-with-
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__pdoc__ = {}
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__pdoc__['DisplayBounds'] = False
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__pdoc__['EvaluateLinearExpr'] = False
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__pdoc__['EvaluateBooleanExpression'] = False
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__pdoc__['ShortName'] = False
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# The classes below allow linear expressions to be expressed naturally with the
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# usual arithmetic operators +-*/ and with constant numbers, which makes the
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# python API very intuitive. See ../samples/*.py for examples.
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INT_MIN = -9223372036854775808 # hardcoded to be platform independent.
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INT_MAX = 9223372036854775807
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INT32_MAX = 2147483647
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INT32_MIN = -2147483648
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# CpSolver status (exported to avoid importing cp_model_cp2).
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UNKNOWN = cp_model_pb2.UNKNOWN
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MODEL_INVALID = cp_model_pb2.MODEL_INVALID
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FEASIBLE = cp_model_pb2.FEASIBLE
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INFEASIBLE = cp_model_pb2.INFEASIBLE
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OPTIMAL = cp_model_pb2.OPTIMAL
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# Variable selection strategy
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CHOOSE_FIRST = cp_model_pb2.DecisionStrategyProto.CHOOSE_FIRST
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CHOOSE_LOWEST_MIN = cp_model_pb2.DecisionStrategyProto.CHOOSE_LOWEST_MIN
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CHOOSE_HIGHEST_MAX = cp_model_pb2.DecisionStrategyProto.CHOOSE_HIGHEST_MAX
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CHOOSE_MIN_DOMAIN_SIZE = (
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cp_model_pb2.DecisionStrategyProto.CHOOSE_MIN_DOMAIN_SIZE)
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CHOOSE_MAX_DOMAIN_SIZE = (
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cp_model_pb2.DecisionStrategyProto.CHOOSE_MAX_DOMAIN_SIZE)
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# Domain reduction strategy
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SELECT_MIN_VALUE = cp_model_pb2.DecisionStrategyProto.SELECT_MIN_VALUE
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SELECT_MAX_VALUE = cp_model_pb2.DecisionStrategyProto.SELECT_MAX_VALUE
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SELECT_LOWER_HALF = cp_model_pb2.DecisionStrategyProto.SELECT_LOWER_HALF
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SELECT_UPPER_HALF = cp_model_pb2.DecisionStrategyProto.SELECT_UPPER_HALF
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# Search branching
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AUTOMATIC_SEARCH = sat_parameters_pb2.SatParameters.AUTOMATIC_SEARCH
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FIXED_SEARCH = sat_parameters_pb2.SatParameters.FIXED_SEARCH
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PORTFOLIO_SEARCH = sat_parameters_pb2.SatParameters.PORTFOLIO_SEARCH
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LP_SEARCH = sat_parameters_pb2.SatParameters.LP_SEARCH
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def DisplayBounds(bounds):
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"""Displays a flattened list of intervals."""
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out = ''
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for i in range(0, len(bounds), 2):
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if i != 0:
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out += ', '
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if bounds[i] == bounds[i + 1]:
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out += str(bounds[i])
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else:
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out += str(bounds[i]) + '..' + str(bounds[i + 1])
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return out
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def ShortName(model, i):
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"""Returns a short name of an integer variable, or its negation."""
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if i < 0:
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return 'Not(%s)' % ShortName(model, -i - 1)
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v = model.variables[i]
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if v.name:
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return v.name
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elif len(v.domain) == 2 and v.domain[0] == v.domain[1]:
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return str(v.domain[0])
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else:
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return '[%s]' % DisplayBounds(v.domain)
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class LinearExpr(object):
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"""Holds an integer linear expression.
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A linear expression is built from integer constants and variables.
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For example, x + 2 * (y - z + 1).
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Linear expressions are used in CP-SAT models in two ways:
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* To define constraints. For example
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model.Add(x + 2 * y <= 5)
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model.Add(sum(array_of_vars) == 5)
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* To define the objective function. For example
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model.Minimize(x + 2 * y + z)
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For large arrays, you can create constraints and the objective
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from lists of linear expressions or coefficients as follows:
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model.Minimize(cp_model.LinearExpr.Sum(expressions))
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model.Add(cp_model.LinearExpr.ScalProd(expressions, coefficients) >= 0)
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"""
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@classmethod
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def Sum(cls, expressions):
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"""Creates the expression sum(expressions)."""
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return _SumArray(expressions)
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@classmethod
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def ScalProd(cls, expressions, coefficients):
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"""Creates the expression sum(expressions[i] * coefficients[i])."""
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return _ScalProd(expressions, coefficients)
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@classmethod
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def Term(cls, expression, coefficient):
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"""Creates `expression * coefficient`."""
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return expression * coefficient
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def GetVarValueMap(self):
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"""Scans the expression, and return a list of (var_coef_map, constant)."""
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coeffs = collections.defaultdict(int)
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constant = 0
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to_process = [(self, 1)]
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while to_process: # Flatten to avoid recursion.
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expr, coef = to_process.pop()
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if isinstance(expr, _ProductCst):
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to_process.append(
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(expr.Expression(), coef * expr.Coefficient()))
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elif isinstance(expr, _SumArray):
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for e in expr.Expressions():
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to_process.append((e, coef))
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constant += expr.Constant() * coef
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elif isinstance(expr, _ScalProd):
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for e, c in zip(expr.Expressions(), expr.Coefficients()):
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to_process.append((e, coef * c))
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constant += expr.Constant() * coef
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elif isinstance(expr, IntVar):
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coeffs[expr] += coef
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elif isinstance(expr, _NotBooleanVariable):
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constant += coef
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coeffs[expr.Not()] -= coef
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else:
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raise TypeError('Unrecognized linear expression: ' + str(expr))
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return coeffs, constant
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def __hash__(self):
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return object.__hash__(self)
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def __abs__(self):
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raise NotImplementedError(
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'calling abs() on a linear expression is not supported, '
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'please use CpModel.AddAbsEquality')
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def __add__(self, expr):
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return _SumArray([self, expr])
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def __radd__(self, arg):
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return _SumArray([self, arg])
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def __sub__(self, expr):
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return _SumArray([self, -expr])
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def __rsub__(self, arg):
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return _SumArray([-self, arg])
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def __mul__(self, arg):
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if isinstance(arg, numbers.Integral):
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if arg == 1:
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return self
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elif arg == 0:
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return 0
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cp_model_helper.AssertIsInt64(arg)
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return _ProductCst(self, arg)
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else:
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raise TypeError('Not an integer linear expression: ' + str(arg))
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def __rmul__(self, arg):
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cp_model_helper.AssertIsInt64(arg)
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if arg == 1:
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return self
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return _ProductCst(self, arg)
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def __div__(self, _):
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raise NotImplementedError(
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'calling / on a linear expression is not supported, '
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'please use CpModel.AddDivisionEquality')
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def __truediv__(self, _):
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raise NotImplementedError(
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'calling // on a linear expression is not supported, '
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'please use CpModel.AddDivisionEquality')
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def __mod__(self, _):
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raise NotImplementedError(
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'calling %% on a linear expression is not supported, '
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'please use CpModel.AddModuloEquality')
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def __neg__(self):
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return _ProductCst(self, -1)
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def __eq__(self, arg):
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if arg is None:
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return False
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if isinstance(arg, numbers.Integral):
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cp_model_helper.AssertIsInt64(arg)
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return BoundedLinearExpression(self, [arg, arg])
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else:
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return BoundedLinearExpression(self - arg, [0, 0])
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def __ge__(self, arg):
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if isinstance(arg, numbers.Integral):
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cp_model_helper.AssertIsInt64(arg)
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return BoundedLinearExpression(self, [arg, INT_MAX])
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else:
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return BoundedLinearExpression(self - arg, [0, INT_MAX])
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def __le__(self, arg):
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if isinstance(arg, numbers.Integral):
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cp_model_helper.AssertIsInt64(arg)
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return BoundedLinearExpression(self, [INT_MIN, arg])
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else:
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return BoundedLinearExpression(self - arg, [INT_MIN, 0])
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def __lt__(self, arg):
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if isinstance(arg, numbers.Integral):
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cp_model_helper.AssertIsInt64(arg)
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if arg == INT_MIN:
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raise ArithmeticError('< INT_MIN is not supported')
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return BoundedLinearExpression(self, [INT_MIN, arg - 1])
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else:
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return BoundedLinearExpression(self - arg, [INT_MIN, -1])
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def __gt__(self, arg):
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if isinstance(arg, numbers.Integral):
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cp_model_helper.AssertIsInt64(arg)
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if arg == INT_MAX:
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raise ArithmeticError('> INT_MAX is not supported')
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return BoundedLinearExpression(self, [arg + 1, INT_MAX])
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else:
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return BoundedLinearExpression(self - arg, [1, INT_MAX])
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def __ne__(self, arg):
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if arg is None:
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return True
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if isinstance(arg, numbers.Integral):
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cp_model_helper.AssertIsInt64(arg)
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if arg == INT_MAX:
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return BoundedLinearExpression(self, [INT_MIN, INT_MAX - 1])
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elif arg == INT_MIN:
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return BoundedLinearExpression(self, [INT_MIN + 1, INT_MAX])
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else:
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return BoundedLinearExpression(
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self, [INT_MIN, arg - 1, arg + 1, INT_MAX])
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else:
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return BoundedLinearExpression(self - arg,
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[INT_MIN, -1, 1, INT_MAX])
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class _ProductCst(LinearExpr):
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"""Represents the product of a LinearExpr by a constant."""
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def __init__(self, expr, coef):
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cp_model_helper.AssertIsInt64(coef)
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if isinstance(expr, _ProductCst):
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self.__expr = expr.Expression()
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self.__coef = expr.Coefficient() * coef
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else:
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self.__expr = expr
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self.__coef = coef
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def __str__(self):
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if self.__coef == -1:
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return '-' + str(self.__expr)
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else:
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return '(' + str(self.__coef) + ' * ' + str(self.__expr) + ')'
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def __repr__(self):
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return 'ProductCst(' + repr(self.__expr) + ', ' + repr(
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self.__coef) + ')'
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def Coefficient(self):
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return self.__coef
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def Expression(self):
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return self.__expr
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class _SumArray(LinearExpr):
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"""Represents the sum of a list of LinearExpr and a constant."""
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def __init__(self, expressions):
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self.__expressions = []
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self.__constant = 0
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for x in expressions:
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if isinstance(x, numbers.Integral):
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cp_model_helper.AssertIsInt64(x)
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self.__constant += x
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elif isinstance(x, LinearExpr):
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self.__expressions.append(x)
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else:
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raise TypeError('Not an linear expression: ' + str(x))
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def __str__(self):
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if self.__constant == 0:
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return '({})'.format(' + '.join(map(str, self.__expressions)))
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else:
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return '({} + {})'.format(' + '.join(map(str, self.__expressions)),
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self.__constant)
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def __repr__(self):
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return 'SumArray({}, {})'.format(
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', '.join(map(repr, self.__expressions)), self.__constant)
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def Expressions(self):
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return self.__expressions
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def Constant(self):
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return self.__constant
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class _ScalProd(LinearExpr):
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"""Represents the scalar product of expressions with constants and a constant."""
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def __init__(self, expressions, coefficients):
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self.__expressions = []
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self.__coefficients = []
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self.__constant = 0
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if len(expressions) != len(coefficients):
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raise TypeError(
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'In the LinearExpr.ScalProd method, the expression array and the '
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' coefficient array must have the same length.')
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for e, c in zip(expressions, coefficients):
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cp_model_helper.AssertIsInt64(c)
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if c == 0:
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continue
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if isinstance(e, numbers.Integral):
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cp_model_helper.AssertIsInt64(e)
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self.__constant += e * c
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elif isinstance(e, LinearExpr):
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self.__expressions.append(e)
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self.__coefficients.append(c)
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else:
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raise TypeError('Not an linear expression: ' + str(e))
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def __str__(self):
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output = None
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for expr, coeff in zip(self.__expressions, self.__coefficients):
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if not output and coeff == 1:
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output = str(expr)
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elif not output and coeff == -1:
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output = '-' + str(expr)
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elif not output:
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output = '{} * {}'.format(coeff, str(expr))
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elif coeff == 1:
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output += ' + {}'.format(str(expr))
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elif coeff == -1:
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output += ' - {}'.format(str(expr))
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elif coeff > 1:
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output += ' + {} * {}'.format(coeff, str(expr))
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elif coeff < -1:
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output += ' - {} * {}'.format(-coeff, str(expr))
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if self.__constant > 0:
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output += ' + {}'.format(self.__constant)
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elif self.__constant < 0:
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output += ' - {}'.format(-self.__constant)
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return output
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def __repr__(self):
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return 'ScalProd([{}], [{}], {})'.format(
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', '.join(map(repr, self.__expressions)),
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', '.join(map(repr, self.__coefficients)), self.__constant)
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def Expressions(self):
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return self.__expressions
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def Coefficients(self):
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return self.__coefficients
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def Constant(self):
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return self.__constant
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class IntVar(LinearExpr):
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"""An integer variable.
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An IntVar is an object that can take on any integer value within defined
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ranges. Variables appear in constraint like:
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x + y >= 5
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AllDifferent([x, y, z])
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Solving a model is equivalent to finding, for each variable, a single value
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from the set of initial values (called the initial domain), such that the
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model is feasible, or optimal if you provided an objective function.
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"""
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def __init__(self, model, domain, name):
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"""See CpModel.NewIntVar below."""
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self.__model = model
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self.__index = len(model.variables)
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self.__var = model.variables.add()
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self.__var.domain.extend(domain.FlattenedIntervals())
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self.__var.name = name
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self.__negation = None
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def Index(self):
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"""Returns the index of the variable in the model."""
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return self.__index
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def Proto(self):
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"""Returns the variable protobuf."""
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return self.__var
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def __str__(self):
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if not self.__var.name:
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if len(self.__var.domain
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) == 2 and self.__var.domain[0] == self.__var.domain[1]:
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# Special case for constants.
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return str(self.__var.domain[0])
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else:
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return 'unnamed_var_%i' % self.__index
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return self.__var.name
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def __repr__(self):
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return '%s(%s)' % (self.__var.name, DisplayBounds(self.__var.domain))
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def Name(self):
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return self.__var.name
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def Not(self):
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"""Returns the negation of a Boolean variable.
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This method implements the logical negation of a Boolean variable.
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It is only valid if the variable has a Boolean domain (0 or 1).
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Note that this method is nilpotent: `x.Not().Not() == x`.
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"""
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for bound in self.__var.domain:
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if bound < 0 or bound > 1:
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raise TypeError(
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'Cannot call Not on a non boolean variable: %s' % self)
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if not self.__negation:
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self.__negation = _NotBooleanVariable(self)
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return self.__negation
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class _NotBooleanVariable(LinearExpr):
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"""Negation of a boolean variable."""
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def __init__(self, boolvar):
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self.__boolvar = boolvar
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def Index(self):
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return -self.__boolvar.Index() - 1
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def Not(self):
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return self.__boolvar
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def __str__(self):
|
|
return 'not(%s)' % str(self.__boolvar)
|
|
|
|
|
|
class BoundedLinearExpression(object):
|
|
"""Represents a linear constraint: `lb <= linear expression <= ub`.
|
|
|
|
The only use of this class is to be added to the CpModel through
|
|
`CpModel.Add(expression)`, as in:
|
|
|
|
model.Add(x + 2 * y -1 >= z)
|
|
"""
|
|
|
|
def __init__(self, expr, bounds):
|
|
self.__expr = expr
|
|
self.__bounds = bounds
|
|
|
|
def __str__(self):
|
|
if len(self.__bounds) == 2:
|
|
lb = self.__bounds[0]
|
|
ub = self.__bounds[1]
|
|
if lb > INT_MIN and ub < INT_MAX:
|
|
if lb == ub:
|
|
return str(self.__expr) + ' == ' + str(lb)
|
|
else:
|
|
return str(lb) + ' <= ' + str(
|
|
self.__expr) + ' <= ' + str(ub)
|
|
elif lb > INT_MIN:
|
|
return str(self.__expr) + ' >= ' + str(lb)
|
|
elif ub < INT_MAX:
|
|
return str(self.__expr) + ' <= ' + str(ub)
|
|
else:
|
|
return 'True (unbounded expr ' + str(self.__expr) + ')'
|
|
else:
|
|
return str(self.__expr) + ' in [' + DisplayBounds(
|
|
self.__bounds) + ']'
|
|
|
|
def Expression(self):
|
|
return self.__expr
|
|
|
|
def Bounds(self):
|
|
return self.__bounds
|
|
|
|
|
|
class Constraint(object):
|
|
"""Base class for constraints.
|
|
|
|
Constraints are built by the CpModel through the Add<XXX> methods.
|
|
Once created by the CpModel class, they are automatically added to the model.
|
|
The purpose of this class is to allow specification of enforcement literals
|
|
for this constraint.
|
|
|
|
b = model.NewBoolVar('b')
|
|
x = model.NewIntVar(0, 10, 'x')
|
|
y = model.NewIntVar(0, 10, 'y')
|
|
|
|
model.Add(x + 2 * y == 5).OnlyEnforceIf(b.Not())
|
|
"""
|
|
|
|
def __init__(self, constraints):
|
|
self.__index = len(constraints)
|
|
self.__constraint = constraints.add()
|
|
|
|
def OnlyEnforceIf(self, boolvar):
|
|
"""Adds an enforcement literal to the constraint.
|
|
|
|
This method adds one or more literals (that is, a boolean variable or its
|
|
negation) as enforcement literals. The conjunction of all these literals
|
|
determines whether the constraint is active or not. It acts as an
|
|
implication, so if the conjunction is true, it implies that the constraint
|
|
must be enforced. If it is false, then the constraint is ignored.
|
|
|
|
BoolOr, BoolAnd, and linear constraints all support enforcement literals.
|
|
|
|
Args:
|
|
boolvar: A boolean literal or a list of boolean literals.
|
|
|
|
Returns:
|
|
self.
|
|
"""
|
|
|
|
if isinstance(boolvar, numbers.Integral) and boolvar == 1:
|
|
# Always true. Do nothing.
|
|
pass
|
|
elif isinstance(boolvar, list):
|
|
for b in boolvar:
|
|
if isinstance(b, numbers.Integral) and b == 1:
|
|
pass
|
|
else:
|
|
self.__constraint.enforcement_literal.append(b.Index())
|
|
else:
|
|
self.__constraint.enforcement_literal.append(boolvar.Index())
|
|
return self
|
|
|
|
def Index(self):
|
|
"""Returns the index of the constraint in the model."""
|
|
return self.__index
|
|
|
|
def Proto(self):
|
|
"""Returns the constraint protobuf."""
|
|
return self.__constraint
|
|
|
|
|
|
class IntervalVar(object):
|
|
"""Represents an Interval variable.
|
|
|
|
An interval variable is both a constraint and a variable. It is defined by
|
|
three integer variables: start, size, and end.
|
|
|
|
It is a constraint because, internally, it enforces that start + size == end.
|
|
|
|
It is also a variable as it can appear in specific scheduling constraints:
|
|
NoOverlap, NoOverlap2D, Cumulative.
|
|
|
|
Optionally, an enforcement literal can be added to this constraint, in which
|
|
case these scheduling constraints will ignore interval variables with
|
|
enforcement literals assigned to false. Conversely, these constraints will
|
|
also set these enforcement literals to false if they cannot fit these
|
|
intervals into the schedule.
|
|
"""
|
|
|
|
def __init__(self, model, start_index, size_index, end_index,
|
|
is_present_index, name):
|
|
self.__model = model
|
|
self.__index = len(model.constraints)
|
|
self.__ct = self.__model.constraints.add()
|
|
self.__ct.interval.start = start_index
|
|
self.__ct.interval.size = size_index
|
|
self.__ct.interval.end = end_index
|
|
if is_present_index is not None:
|
|
self.__ct.enforcement_literal.append(is_present_index)
|
|
if name:
|
|
self.__ct.name = name
|
|
|
|
def Index(self):
|
|
"""Returns the index of the interval constraint in the model."""
|
|
return self.__index
|
|
|
|
def Proto(self):
|
|
"""Returns the interval protobuf."""
|
|
return self.__ct.interval
|
|
|
|
def __str__(self):
|
|
return self.__ct.name
|
|
|
|
def __repr__(self):
|
|
interval = self.__ct.interval
|
|
if self.__ct.enforcement_literal:
|
|
return '%s(start = %s, size = %s, end = %s, is_present = %s)' % (
|
|
self.__ct.name, ShortName(self.__model, interval.start),
|
|
ShortName(self.__model,
|
|
interval.size), ShortName(self.__model, interval.end),
|
|
ShortName(self.__model, self.__ct.enforcement_literal[0]))
|
|
else:
|
|
return '%s(start = %s, size = %s, end = %s)' % (
|
|
self.__ct.name, ShortName(self.__model, interval.start),
|
|
ShortName(self.__model,
|
|
interval.size), ShortName(self.__model, interval.end))
|
|
|
|
def Name(self):
|
|
return self.__ct.name
|
|
|
|
|
|
class CpModel(object):
|
|
"""Methods for building a CP model.
|
|
|
|
Methods beginning with:
|
|
|
|
* ```New``` create integer, boolean, or interval variables.
|
|
* ```Add``` create new constraints and add them to the model.
|
|
"""
|
|
|
|
def __init__(self):
|
|
self.__model = cp_model_pb2.CpModelProto()
|
|
self.__constant_map = {}
|
|
self.__optional_constant_map = {}
|
|
|
|
# Integer variable.
|
|
|
|
def NewIntVar(self, lb, ub, name):
|
|
"""Create an integer variable with domain [lb, ub].
|
|
|
|
The CP-SAT solver is limited to integer variables. If you have fractional
|
|
values, scale them up so that they become integers; if you have strings,
|
|
encode them as integers.
|
|
|
|
Args:
|
|
lb: Lower bound for the variable.
|
|
ub: Upper bound for the variable.
|
|
name: The name of the variable.
|
|
|
|
Returns:
|
|
a variable whose domain is [lb, ub].
|
|
"""
|
|
|
|
return IntVar(self.__model, Domain(lb, ub), name)
|
|
|
|
def NewIntVarFromDomain(self, domain, name):
|
|
"""Create an integer variable from a domain.
|
|
|
|
A domain is a set of integers specified by a collection of intervals.
|
|
For example, `model.NewIntVarFromDomain(cp_model.
|
|
Domain.FromIntervals([[1, 2], [4, 6]]), 'x')`
|
|
|
|
Args:
|
|
domain: An instance of the Domain class.
|
|
name: The name of the variable.
|
|
|
|
Returns:
|
|
a variable whose domain is the given domain.
|
|
"""
|
|
return IntVar(self.__model, domain, name)
|
|
|
|
def NewBoolVar(self, name):
|
|
"""Creates a 0-1 variable with the given name."""
|
|
return IntVar(self.__model, Domain(0, 1), name)
|
|
|
|
def NewConstant(self, value):
|
|
"""Declares a constant integer."""
|
|
return IntVar(self.__model, Domain(value, value), '')
|
|
|
|
# Linear constraints.
|
|
|
|
def AddLinearConstraint(self, linear_expr, lb, ub):
|
|
"""Adds the constraint: `lb <= linear_expr <= ub`."""
|
|
return self.AddLinearExpressionInDomain(linear_expr, Domain(lb, ub))
|
|
|
|
def AddLinearExpressionInDomain(self, linear_expr, domain):
|
|
"""Adds the constraint: `linear_expr` in `domain`."""
|
|
if isinstance(linear_expr, LinearExpr):
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
coeffs_map, constant = linear_expr.GetVarValueMap()
|
|
for t in iteritems(coeffs_map):
|
|
if not isinstance(t[0], IntVar):
|
|
raise TypeError('Wrong argument' + str(t))
|
|
cp_model_helper.AssertIsInt64(t[1])
|
|
model_ct.linear.vars.append(t[0].Index())
|
|
model_ct.linear.coeffs.append(t[1])
|
|
model_ct.linear.domain.extend([
|
|
cp_model_helper.CapSub(x, constant)
|
|
for x in domain.FlattenedIntervals()
|
|
])
|
|
return ct
|
|
elif isinstance(linear_expr, numbers.Integral):
|
|
if not domain.Contains(linear_expr):
|
|
return self.AddBoolOr([]) # Evaluate to false.
|
|
# Nothing to do otherwise.
|
|
else:
|
|
raise TypeError(
|
|
'Not supported: CpModel.AddLinearExpressionInDomain(' +
|
|
str(linear_expr) + ' ' + str(domain) + ')')
|
|
|
|
def Add(self, ct):
|
|
"""Adds a `BoundedLinearExpression` to the model.
|
|
|
|
Args:
|
|
ct: A [`BoundedLinearExpression`](#boundedlinearexpression).
|
|
|
|
Returns:
|
|
An instance of the `Constraint` class.
|
|
"""
|
|
if isinstance(ct, BoundedLinearExpression):
|
|
return self.AddLinearExpressionInDomain(
|
|
ct.Expression(), Domain.FromFlatIntervals(ct.Bounds()))
|
|
elif ct and isinstance(ct, bool):
|
|
return self.AddBoolOr([True])
|
|
elif not ct and isinstance(ct, bool):
|
|
return self.AddBoolOr([]) # Evaluate to false.
|
|
else:
|
|
raise TypeError('Not supported: CpModel.Add(' + str(ct) + ')')
|
|
|
|
# General Integer Constraints.
|
|
|
|
def AddAllDifferent(self, variables):
|
|
"""Adds AllDifferent(variables).
|
|
|
|
This constraint forces all variables to have different values.
|
|
|
|
Args:
|
|
variables: a list of integer variables.
|
|
|
|
Returns:
|
|
An instance of the `Constraint` class.
|
|
"""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.all_diff.vars.extend(
|
|
[self.GetOrMakeIndex(x) for x in variables])
|
|
return ct
|
|
|
|
def AddElement(self, index, variables, target):
|
|
"""Adds the element constraint: `variables[index] == target`."""
|
|
|
|
if not variables:
|
|
raise ValueError('AddElement expects a non-empty variables array')
|
|
|
|
if isinstance(index, numbers.Integral):
|
|
return self.Add(list(variables)[index] == target)
|
|
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.element.index = self.GetOrMakeIndex(index)
|
|
model_ct.element.vars.extend(
|
|
[self.GetOrMakeIndex(x) for x in variables])
|
|
model_ct.element.target = self.GetOrMakeIndex(target)
|
|
return ct
|
|
|
|
def AddCircuit(self, arcs):
|
|
"""Adds Circuit(arcs).
|
|
|
|
Adds a circuit constraint from a sparse list of arcs that encode the graph.
|
|
|
|
A circuit is a unique Hamiltonian path in a subgraph of the total
|
|
graph. In case a node 'i' is not in the path, then there must be a
|
|
loop arc 'i -> i' associated with a true literal. Otherwise
|
|
this constraint will fail.
|
|
|
|
Args:
|
|
arcs: a list of arcs. An arc is a tuple (source_node, destination_node,
|
|
literal). The arc is selected in the circuit if the literal is true.
|
|
Both source_node and destination_node must be integers between 0 and the
|
|
number of nodes - 1.
|
|
|
|
Returns:
|
|
An instance of the `Constraint` class.
|
|
|
|
Raises:
|
|
ValueError: If the list of arcs is empty.
|
|
"""
|
|
if not arcs:
|
|
raise ValueError('AddCircuit expects a non-empty array of arcs')
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
for arc in arcs:
|
|
cp_model_helper.AssertIsInt32(arc[0])
|
|
cp_model_helper.AssertIsInt32(arc[1])
|
|
lit = self.GetOrMakeBooleanIndex(arc[2])
|
|
model_ct.circuit.tails.append(arc[0])
|
|
model_ct.circuit.heads.append(arc[1])
|
|
model_ct.circuit.literals.append(lit)
|
|
return ct
|
|
|
|
def AddAllowedAssignments(self, variables, tuples_list):
|
|
"""Adds AllowedAssignments(variables, tuples_list).
|
|
|
|
An AllowedAssignments constraint is a constraint on an array of variables,
|
|
which requires that when all variables are assigned values, the resulting
|
|
array equals one of the tuples in `tuple_list`.
|
|
|
|
Args:
|
|
variables: A list of variables.
|
|
tuples_list: A list of admissible tuples. Each tuple must have the same
|
|
length as the variables, and the ith value of a tuple corresponds to the
|
|
ith variable.
|
|
|
|
Returns:
|
|
An instance of the `Constraint` class.
|
|
|
|
Raises:
|
|
TypeError: If a tuple does not have the same size as the list of
|
|
variables.
|
|
ValueError: If the array of variables is empty.
|
|
"""
|
|
|
|
if not variables:
|
|
raise ValueError(
|
|
'AddAllowedAssignments expects a non-empty variables '
|
|
'array')
|
|
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.table.vars.extend([self.GetOrMakeIndex(x) for x in variables])
|
|
arity = len(variables)
|
|
for t in tuples_list:
|
|
if len(t) != arity:
|
|
raise TypeError('Tuple ' + str(t) + ' has the wrong arity')
|
|
for v in t:
|
|
cp_model_helper.AssertIsInt64(v)
|
|
model_ct.table.values.extend(t)
|
|
return ct
|
|
|
|
def AddForbiddenAssignments(self, variables, tuples_list):
|
|
"""Adds AddForbiddenAssignments(variables, [tuples_list]).
|
|
|
|
A ForbiddenAssignments constraint is a constraint on an array of variables
|
|
where the list of impossible combinations is provided in the tuples list.
|
|
|
|
Args:
|
|
variables: A list of variables.
|
|
tuples_list: A list of forbidden tuples. Each tuple must have the same
|
|
length as the variables, and the *i*th value of a tuple corresponds to
|
|
the *i*th variable.
|
|
|
|
Returns:
|
|
An instance of the `Constraint` class.
|
|
|
|
Raises:
|
|
TypeError: If a tuple does not have the same size as the list of
|
|
variables.
|
|
ValueError: If the array of variables is empty.
|
|
"""
|
|
|
|
if not variables:
|
|
raise ValueError(
|
|
'AddForbiddenAssignments expects a non-empty variables '
|
|
'array')
|
|
|
|
index = len(self.__model.constraints)
|
|
ct = self.AddAllowedAssignments(variables, tuples_list)
|
|
self.__model.constraints[index].table.negated = True
|
|
return ct
|
|
|
|
def AddAutomaton(self, transition_variables, starting_state, final_states,
|
|
transition_triples):
|
|
"""Adds an automaton constraint.
|
|
|
|
An automaton constraint takes a list of variables (of size *n*), an initial
|
|
state, a set of final states, and a set of transitions. A transition is a
|
|
triplet (*tail*, *transition*, *head*), where *tail* and *head* are states,
|
|
and *transition* is the label of an arc from *head* to *tail*,
|
|
corresponding to the value of one variable in the list of variables.
|
|
|
|
This automaton will be unrolled into a flow with *n* + 1 phases. Each phase
|
|
contains the possible states of the automaton. The first state contains the
|
|
initial state. The last phase contains the final states.
|
|
|
|
Between two consecutive phases *i* and *i* + 1, the automaton creates a set
|
|
of arcs. For each transition (*tail*, *transition*, *head*), it will add
|
|
an arc from the state *tail* of phase *i* and the state *head* of phase
|
|
*i* + 1. This arc is labeled by the value *transition* of the variables
|
|
`variables[i]`. That is, this arc can only be selected if `variables[i]`
|
|
is assigned the value *transition*.
|
|
|
|
A feasible solution of this constraint is an assignment of variables such
|
|
that, starting from the initial state in phase 0, there is a path labeled by
|
|
the values of the variables that ends in one of the final states in the
|
|
final phase.
|
|
|
|
Args:
|
|
transition_variables: A non-empty list of variables whose values
|
|
correspond to the labels of the arcs traversed by the automaton.
|
|
starting_state: The initial state of the automaton.
|
|
final_states: A non-empty list of admissible final states.
|
|
transition_triples: A list of transitions for the automaton, in the
|
|
following format (current_state, variable_value, next_state).
|
|
|
|
Returns:
|
|
An instance of the `Constraint` class.
|
|
|
|
Raises:
|
|
ValueError: if `transition_variables`, `final_states`, or
|
|
`transition_triples` are empty.
|
|
"""
|
|
|
|
if not transition_variables:
|
|
raise ValueError(
|
|
'AddAutomaton expects a non-empty transition_variables '
|
|
'array')
|
|
if not final_states:
|
|
raise ValueError('AddAutomaton expects some final states')
|
|
|
|
if not transition_triples:
|
|
raise ValueError('AddAutomaton expects some transtion triples')
|
|
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.automaton.vars.extend(
|
|
[self.GetOrMakeIndex(x) for x in transition_variables])
|
|
cp_model_helper.AssertIsInt64(starting_state)
|
|
model_ct.automaton.starting_state = starting_state
|
|
for v in final_states:
|
|
cp_model_helper.AssertIsInt64(v)
|
|
model_ct.automaton.final_states.append(v)
|
|
for t in transition_triples:
|
|
if len(t) != 3:
|
|
raise TypeError('Tuple ' + str(t) +
|
|
' has the wrong arity (!= 3)')
|
|
cp_model_helper.AssertIsInt64(t[0])
|
|
cp_model_helper.AssertIsInt64(t[1])
|
|
cp_model_helper.AssertIsInt64(t[2])
|
|
model_ct.automaton.transition_tail.append(t[0])
|
|
model_ct.automaton.transition_label.append(t[1])
|
|
model_ct.automaton.transition_head.append(t[2])
|
|
return ct
|
|
|
|
def AddInverse(self, variables, inverse_variables):
|
|
"""Adds Inverse(variables, inverse_variables).
|
|
|
|
An inverse constraint enforces that if `variables[i]` is assigned a value
|
|
`j`, then `inverse_variables[j]` is assigned a value `i`. And vice versa.
|
|
|
|
Args:
|
|
variables: An array of integer variables.
|
|
inverse_variables: An array of integer variables.
|
|
|
|
Returns:
|
|
An instance of the `Constraint` class.
|
|
|
|
Raises:
|
|
TypeError: if variables and inverse_variables have different lengths, or
|
|
if they are empty.
|
|
"""
|
|
|
|
if not variables or not inverse_variables:
|
|
raise TypeError(
|
|
'The Inverse constraint does not accept empty arrays')
|
|
if len(variables) != len(inverse_variables):
|
|
raise TypeError(
|
|
'In the inverse constraint, the two array variables and'
|
|
' inverse_variables must have the same length.')
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.inverse.f_direct.extend(
|
|
[self.GetOrMakeIndex(x) for x in variables])
|
|
model_ct.inverse.f_inverse.extend(
|
|
[self.GetOrMakeIndex(x) for x in inverse_variables])
|
|
return ct
|
|
|
|
def AddReservoirConstraint(self, times, demands, min_level, max_level):
|
|
"""Adds Reservoir(times, demands, min_level, max_level).
|
|
|
|
Maintains a reservoir level within bounds. The water level starts at 0, and
|
|
at any time >= 0, it must be between min_level and max_level. Furthermore,
|
|
this constraint expects all times variables to be >= 0.
|
|
If the variable `times[i]` is assigned a value t, then the current level
|
|
changes by `demands[i]`, which is constant, at time t.
|
|
|
|
Note that level min can be > 0, or level max can be < 0. It just forces
|
|
some demands to be executed at time 0 to make sure that we are within those
|
|
bounds with the executed demands. Therefore, at any time t >= 0:
|
|
|
|
sum(demands[i] if times[i] <= t) in [min_level, max_level]
|
|
|
|
Args:
|
|
times: A list of positive integer variables which specify the time of the
|
|
filling or emptying the reservoir.
|
|
demands: A list of integer values that specifies the amount of the
|
|
emptying or filling.
|
|
min_level: At any time >= 0, the level of the reservoir must be greater of
|
|
equal than the min level.
|
|
max_level: At any time >= 0, the level of the reservoir must be less or
|
|
equal than the max level.
|
|
|
|
Returns:
|
|
An instance of the `Constraint` class.
|
|
|
|
Raises:
|
|
ValueError: if max_level < min_level.
|
|
"""
|
|
|
|
if max_level < min_level:
|
|
return ValueError(
|
|
'Reservoir constraint must have a max_level >= min_level')
|
|
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.reservoir.times.extend([self.GetOrMakeIndex(x) for x in times])
|
|
model_ct.reservoir.demands.extend(demands)
|
|
model_ct.reservoir.min_level = min_level
|
|
model_ct.reservoir.max_level = max_level
|
|
return ct
|
|
|
|
def AddReservoirConstraintWithActive(self, times, demands, actives,
|
|
min_level, max_level):
|
|
"""Adds Reservoir(times, demands, actives, min_level, max_level).
|
|
|
|
Maintain a reservoir level within bounds. The water level starts at 0, and
|
|
at
|
|
any time >= 0, it must be within min_level, and max_level. Furthermore, this
|
|
constraints expect all times variables to be >= 0.
|
|
If `actives[i]` is true, and if `times[i]` is assigned a value t, then the
|
|
level of the reservoir changes by `demands[i]`, which is constant, at
|
|
time t.
|
|
|
|
Note that level_min can be > 0, or level_max can be < 0. It just forces
|
|
some demands to be executed at time 0 to make sure that we are within those
|
|
bounds with the executed demands. Therefore, at any time t >= 0:
|
|
|
|
sum(demands[i] * actives[i] if times[i] <= t) in [min_level, max_level]
|
|
|
|
The array of boolean variables 'actives', if defined, indicates which
|
|
actions are actually performed.
|
|
|
|
Args:
|
|
times: A list of positive integer variables which specify the time of the
|
|
filling or emptying the reservoir.
|
|
demands: A list of integer values that specifies the amount of the
|
|
emptying or filling.
|
|
actives: a list of boolean variables. They indicates if the
|
|
emptying/refilling events actually take place.
|
|
min_level: At any time >= 0, the level of the reservoir must be greater of
|
|
equal than the min level.
|
|
max_level: At any time >= 0, the level of the reservoir must be less or
|
|
equal than the max level.
|
|
|
|
Returns:
|
|
An instance of the `Constraint` class.
|
|
|
|
Raises:
|
|
ValueError: if max_level < min_level.
|
|
"""
|
|
|
|
if max_level < min_level:
|
|
return ValueError(
|
|
'Reservoir constraint must have a max_level >= min_level')
|
|
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.reservoir.times.extend([self.GetOrMakeIndex(x) for x in times])
|
|
model_ct.reservoir.demands.extend(demands)
|
|
model_ct.reservoir.actives.extend(
|
|
[self.GetOrMakeIndex(x) for x in actives])
|
|
model_ct.reservoir.min_level = min_level
|
|
model_ct.reservoir.max_level = max_level
|
|
return ct
|
|
|
|
def AddMapDomain(self, var, bool_var_array, offset=0):
|
|
"""Adds `var == i + offset <=> bool_var_array[i] == true for all i`."""
|
|
|
|
for i, bool_var in enumerate(bool_var_array):
|
|
b_index = bool_var.Index()
|
|
var_index = var.Index()
|
|
model_ct = self.__model.constraints.add()
|
|
model_ct.linear.vars.append(var_index)
|
|
model_ct.linear.coeffs.append(1)
|
|
model_ct.linear.domain.extend([offset + i, offset + i])
|
|
model_ct.enforcement_literal.append(b_index)
|
|
|
|
model_ct = self.__model.constraints.add()
|
|
model_ct.linear.vars.append(var_index)
|
|
model_ct.linear.coeffs.append(1)
|
|
model_ct.enforcement_literal.append(-b_index - 1)
|
|
if offset + i - 1 >= INT_MIN:
|
|
model_ct.linear.domain.extend([INT_MIN, offset + i - 1])
|
|
if offset + i + 1 <= INT_MAX:
|
|
model_ct.linear.domain.extend([offset + i + 1, INT_MAX])
|
|
|
|
def AddImplication(self, a, b):
|
|
"""Adds `a => b` (`a` implies `b`)."""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.bool_or.literals.append(self.GetOrMakeBooleanIndex(b))
|
|
model_ct.enforcement_literal.append(self.GetOrMakeBooleanIndex(a))
|
|
return ct
|
|
|
|
def AddBoolOr(self, literals):
|
|
"""Adds `Or(literals) == true`."""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.bool_or.literals.extend(
|
|
[self.GetOrMakeBooleanIndex(x) for x in literals])
|
|
return ct
|
|
|
|
def AddBoolAnd(self, literals):
|
|
"""Adds `And(literals) == true`."""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.bool_and.literals.extend(
|
|
[self.GetOrMakeBooleanIndex(x) for x in literals])
|
|
return ct
|
|
|
|
def AddBoolXOr(self, literals):
|
|
"""Adds `XOr(literals) == true`."""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.bool_xor.literals.extend(
|
|
[self.GetOrMakeBooleanIndex(x) for x in literals])
|
|
return ct
|
|
|
|
def AddMinEquality(self, target, variables):
|
|
"""Adds `target == Min(variables)`."""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.int_min.vars.extend(
|
|
[self.GetOrMakeIndex(x) for x in variables])
|
|
model_ct.int_min.target = self.GetOrMakeIndex(target)
|
|
return ct
|
|
|
|
def AddMaxEquality(self, target, variables):
|
|
"""Adds `target == Max(variables)`."""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.int_max.vars.extend(
|
|
[self.GetOrMakeIndex(x) for x in variables])
|
|
model_ct.int_max.target = self.GetOrMakeIndex(target)
|
|
return ct
|
|
|
|
def AddDivisionEquality(self, target, num, denom):
|
|
"""Adds `target == num // denom` (integer division rounded towards 0)."""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.int_div.vars.extend(
|
|
[self.GetOrMakeIndex(num),
|
|
self.GetOrMakeIndex(denom)])
|
|
model_ct.int_div.target = self.GetOrMakeIndex(target)
|
|
return ct
|
|
|
|
def AddAbsEquality(self, target, var):
|
|
"""Adds `target == Abs(var)`."""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
index = self.GetOrMakeIndex(var)
|
|
model_ct.int_max.vars.extend([index, -index - 1])
|
|
model_ct.int_max.target = self.GetOrMakeIndex(target)
|
|
return ct
|
|
|
|
def AddModuloEquality(self, target, var, mod):
|
|
"""Adds `target = var % mod`."""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.int_mod.vars.extend(
|
|
[self.GetOrMakeIndex(var),
|
|
self.GetOrMakeIndex(mod)])
|
|
model_ct.int_mod.target = self.GetOrMakeIndex(target)
|
|
return ct
|
|
|
|
def AddMultiplicationEquality(self, target, variables):
|
|
"""Adds `target == variables[0] * .. * variables[n]`."""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.int_prod.vars.extend(
|
|
[self.GetOrMakeIndex(x) for x in variables])
|
|
model_ct.int_prod.target = self.GetOrMakeIndex(target)
|
|
return ct
|
|
|
|
def AddProdEquality(self, target, variables):
|
|
"""Deprecated, use AddMultiplicationEquality."""
|
|
return self.AddMultiplicationEquality(target, variables)
|
|
|
|
# Scheduling support
|
|
|
|
def NewIntervalVar(self, start, size, end, name):
|
|
"""Creates an interval variable from start, size, and end.
|
|
|
|
An interval variable is a constraint, that is itself used in other
|
|
constraints like NoOverlap.
|
|
|
|
Internally, it ensures that `start + size == end`.
|
|
|
|
Args:
|
|
start: The start of the interval. It can be an integer value, or an
|
|
integer variable.
|
|
size: The size of the interval. It can be an integer value, or an integer
|
|
variable.
|
|
end: The end of the interval. It can be an integer value, or an integer
|
|
variable.
|
|
name: The name of the interval variable.
|
|
|
|
Returns:
|
|
An `IntervalVar` object.
|
|
"""
|
|
|
|
start_index = self.GetOrMakeIndex(start)
|
|
size_index = self.GetOrMakeIndex(size)
|
|
end_index = self.GetOrMakeIndex(end)
|
|
return IntervalVar(self.__model, start_index, size_index, end_index,
|
|
None, name)
|
|
|
|
def NewOptionalIntervalVar(self, start, size, end, is_present, name):
|
|
"""Creates an optional interval var from start, size, end, and is_present.
|
|
|
|
An optional interval variable is a constraint, that is itself used in other
|
|
constraints like NoOverlap. This constraint is protected by an is_present
|
|
literal that indicates if it is active or not.
|
|
|
|
Internally, it ensures that `is_present` implies `start + size == end`.
|
|
|
|
Args:
|
|
start: The start of the interval. It can be an integer value, or an
|
|
integer variable.
|
|
size: The size of the interval. It can be an integer value, or an integer
|
|
variable.
|
|
end: The end of the interval. It can be an integer value, or an integer
|
|
variable.
|
|
is_present: A literal that indicates if the interval is active or not. A
|
|
inactive interval is simply ignored by all constraints.
|
|
name: The name of the interval variable.
|
|
|
|
Returns:
|
|
An `IntervalVar` object.
|
|
"""
|
|
is_present_index = self.GetOrMakeBooleanIndex(is_present)
|
|
start_index = self.GetOrMakeIndex(start)
|
|
size_index = self.GetOrMakeIndex(size)
|
|
end_index = self.GetOrMakeIndex(end)
|
|
return IntervalVar(self.__model, start_index, size_index, end_index,
|
|
is_present_index, name)
|
|
|
|
def AddNoOverlap(self, interval_vars):
|
|
"""Adds NoOverlap(interval_vars).
|
|
|
|
A NoOverlap constraint ensures that all present intervals do not overlap
|
|
in time.
|
|
|
|
Args:
|
|
interval_vars: The list of interval variables to constrain.
|
|
|
|
Returns:
|
|
An instance of the `Constraint` class.
|
|
"""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.no_overlap.intervals.extend(
|
|
[self.GetIntervalIndex(x) for x in interval_vars])
|
|
return ct
|
|
|
|
def AddNoOverlap2D(self, x_intervals, y_intervals):
|
|
"""Adds NoOverlap2D(x_intervals, y_intervals).
|
|
|
|
A NoOverlap2D constraint ensures that all present rectangles do not overlap
|
|
on a plane. Each rectangle is aligned with the X and Y axis, and is defined
|
|
by two intervals which represent its projection onto the X and Y axis.
|
|
|
|
Args:
|
|
x_intervals: The X coordinates of the rectangles.
|
|
y_intervals: The Y coordinates of the rectangles.
|
|
|
|
Returns:
|
|
An instance of the `Constraint` class.
|
|
"""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.no_overlap_2d.x_intervals.extend(
|
|
[self.GetIntervalIndex(x) for x in x_intervals])
|
|
model_ct.no_overlap_2d.y_intervals.extend(
|
|
[self.GetIntervalIndex(x) for x in y_intervals])
|
|
return ct
|
|
|
|
def AddCumulative(self, intervals, demands, capacity):
|
|
"""Adds Cumulative(intervals, demands, capacity).
|
|
|
|
This constraint enforces that:
|
|
|
|
for all t:
|
|
sum(demands[i]
|
|
if (start(intervals[t]) <= t < end(intervals[t])) and
|
|
(t is present)) <= capacity
|
|
|
|
Args:
|
|
intervals: The list of intervals.
|
|
demands: The list of demands for each interval. Each demand must be >= 0.
|
|
Each demand can be an integer value, or an integer variable.
|
|
capacity: The maximum capacity of the cumulative constraint. It must be a
|
|
positive integer value or variable.
|
|
|
|
Returns:
|
|
An instance of the `Constraint` class.
|
|
"""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.cumulative.intervals.extend(
|
|
[self.GetIntervalIndex(x) for x in intervals])
|
|
model_ct.cumulative.demands.extend(
|
|
[self.GetOrMakeIndex(x) for x in demands])
|
|
model_ct.cumulative.capacity = self.GetOrMakeIndex(capacity)
|
|
return ct
|
|
|
|
# Helpers.
|
|
|
|
def __str__(self):
|
|
return str(self.__model)
|
|
|
|
def Proto(self):
|
|
"""Returns the underlying CpModelProto."""
|
|
return self.__model
|
|
|
|
def Negated(self, index):
|
|
return -index - 1
|
|
|
|
def GetOrMakeIndex(self, arg):
|
|
"""Returns the index of a variable, its negation, or a number."""
|
|
if isinstance(arg, IntVar):
|
|
return arg.Index()
|
|
elif (isinstance(arg, _ProductCst) and
|
|
isinstance(arg.Expression(), IntVar) and arg.Coefficient() == -1):
|
|
return -arg.Expression().Index() - 1
|
|
elif isinstance(arg, numbers.Integral):
|
|
cp_model_helper.AssertIsInt64(arg)
|
|
return self.GetOrMakeIndexFromConstant(arg)
|
|
else:
|
|
raise TypeError('NotSupported: model.GetOrMakeIndex(' + str(arg) +
|
|
')')
|
|
|
|
def GetOrMakeBooleanIndex(self, arg):
|
|
"""Returns an index from a boolean expression."""
|
|
if isinstance(arg, IntVar):
|
|
self.AssertIsBooleanVariable(arg)
|
|
return arg.Index()
|
|
elif isinstance(arg, _NotBooleanVariable):
|
|
self.AssertIsBooleanVariable(arg.Not())
|
|
return arg.Index()
|
|
elif isinstance(arg, numbers.Integral):
|
|
cp_model_helper.AssertIsBoolean(arg)
|
|
return self.GetOrMakeIndexFromConstant(arg)
|
|
else:
|
|
raise TypeError('NotSupported: model.GetOrMakeBooleanIndex(' +
|
|
str(arg) + ')')
|
|
|
|
def GetIntervalIndex(self, arg):
|
|
if not isinstance(arg, IntervalVar):
|
|
raise TypeError('NotSupported: model.GetIntervalIndex(%s)' % arg)
|
|
return arg.Index()
|
|
|
|
def GetOrMakeIndexFromConstant(self, value):
|
|
if value in self.__constant_map:
|
|
return self.__constant_map[value]
|
|
index = len(self.__model.variables)
|
|
var = self.__model.variables.add()
|
|
var.domain.extend([value, value])
|
|
self.__constant_map[value] = index
|
|
return index
|
|
|
|
def VarIndexToVarProto(self, var_index):
|
|
if var_index > 0:
|
|
return self.__model.variables[var_index]
|
|
else:
|
|
return self.__model.variables[-var_index - 1]
|
|
|
|
def _SetObjective(self, obj, minimize):
|
|
"""Sets the objective of the model."""
|
|
if isinstance(obj, IntVar):
|
|
self.__model.ClearField('objective')
|
|
self.__model.objective.coeffs.append(1)
|
|
self.__model.objective.offset = 0
|
|
if minimize:
|
|
self.__model.objective.vars.append(obj.Index())
|
|
self.__model.objective.scaling_factor = 1
|
|
else:
|
|
self.__model.objective.vars.append(self.Negated(obj.Index()))
|
|
self.__model.objective.scaling_factor = -1
|
|
elif isinstance(obj, LinearExpr):
|
|
coeffs_map, constant = obj.GetVarValueMap()
|
|
self.__model.ClearField('objective')
|
|
if minimize:
|
|
self.__model.objective.scaling_factor = 1
|
|
self.__model.objective.offset = constant
|
|
else:
|
|
self.__model.objective.scaling_factor = -1
|
|
self.__model.objective.offset = -constant
|
|
for v, c, in iteritems(coeffs_map):
|
|
self.__model.objective.coeffs.append(c)
|
|
if minimize:
|
|
self.__model.objective.vars.append(v.Index())
|
|
else:
|
|
self.__model.objective.vars.append(self.Negated(v.Index()))
|
|
elif isinstance(obj, numbers.Integral):
|
|
self.__model.objective.offset = obj
|
|
self.__model.objective.scaling_factor = 1
|
|
else:
|
|
raise TypeError('TypeError: ' + str(obj) +
|
|
' is not a valid objective')
|
|
|
|
def Minimize(self, obj):
|
|
"""Sets the objective of the model to minimize(obj)."""
|
|
self._SetObjective(obj, minimize=True)
|
|
|
|
def Maximize(self, obj):
|
|
"""Sets the objective of the model to maximize(obj)."""
|
|
self._SetObjective(obj, minimize=False)
|
|
|
|
def HasObjective(self):
|
|
return self.__model.HasField('objective')
|
|
|
|
def AddDecisionStrategy(self, variables, var_strategy, domain_strategy):
|
|
"""Adds a search strategy to the model.
|
|
|
|
Args:
|
|
variables: a list of variables this strategy will assign.
|
|
var_strategy: heuristic to choose the next variable to assign.
|
|
domain_strategy: heuristic to reduce the domain of the selected variable.
|
|
Currently, this is advanced code: the union of all strategies added to
|
|
the model must be complete, i.e. instantiates all variables.
|
|
Otherwise, Solve() will fail.
|
|
"""
|
|
|
|
strategy = self.__model.search_strategy.add()
|
|
for v in variables:
|
|
strategy.variables.append(v.Index())
|
|
strategy.variable_selection_strategy = var_strategy
|
|
strategy.domain_reduction_strategy = domain_strategy
|
|
|
|
def ModelStats(self):
|
|
"""Returns a string containing some model statistics."""
|
|
return pywrapsat.SatHelper.ModelStats(self.__model)
|
|
|
|
def Validate(self):
|
|
"""Returns a string indicating that the model is invalid."""
|
|
return pywrapsat.SatHelper.ValidateModel(self.__model)
|
|
|
|
def AssertIsBooleanVariable(self, x):
|
|
if isinstance(x, IntVar):
|
|
var = self.__model.variables[x.Index()]
|
|
if len(var.domain) != 2 or var.domain[0] < 0 or var.domain[1] > 1:
|
|
raise TypeError('TypeError: ' + str(x) +
|
|
' is not a boolean variable')
|
|
elif not isinstance(x, _NotBooleanVariable):
|
|
raise TypeError('TypeError: ' + str(x) +
|
|
' is not a boolean variable')
|
|
|
|
def AddHint(self, var, value):
|
|
self.__model.solution_hint.vars.append(self.GetOrMakeIndex(var))
|
|
self.__model.solution_hint.values.append(value)
|
|
|
|
|
|
def EvaluateLinearExpr(expression, solution):
|
|
"""Evaluate a linear expression against a solution."""
|
|
if isinstance(expression, numbers.Integral):
|
|
return expression
|
|
if not isinstance(expression, LinearExpr):
|
|
raise TypeError('Cannot interpret %s as a linear expression.' %
|
|
expression)
|
|
|
|
value = 0
|
|
to_process = [(expression, 1)]
|
|
while to_process:
|
|
expr, coef = to_process.pop()
|
|
if isinstance(expr, _ProductCst):
|
|
to_process.append((expr.Expression(), coef * expr.Coefficient()))
|
|
elif isinstance(expr, _SumArray):
|
|
for e in expr.Expressions():
|
|
to_process.append((e, coef))
|
|
value += expr.Constant() * coef
|
|
elif isinstance(expr, _ScalProd):
|
|
for e, c in zip(expr.Expressions(), expr.Coefficients()):
|
|
to_process.append((e, coef * c))
|
|
value += expr.Constant() * coef
|
|
elif isinstance(expr, IntVar):
|
|
value += coef * solution.solution[expr.Index()]
|
|
elif isinstance(expr, _NotBooleanVariable):
|
|
value += coef * (1 - solution.solution[expr.Not().Index()])
|
|
return value
|
|
|
|
|
|
def EvaluateBooleanExpression(literal, solution):
|
|
"""Evaluate a boolean expression against a solution."""
|
|
if isinstance(literal, numbers.Integral):
|
|
return bool(literal)
|
|
elif isinstance(literal, IntVar) or isinstance(literal,
|
|
_NotBooleanVariable):
|
|
index = literal.Index()
|
|
if index >= 0:
|
|
return bool(solution.solution[index])
|
|
else:
|
|
return not solution.solution[-index - 1]
|
|
else:
|
|
raise TypeError('Cannot interpret %s as a boolean expression.' %
|
|
literal)
|
|
|
|
|
|
class CpSolver(object):
|
|
"""Main solver class.
|
|
|
|
The purpose of this class is to search for a solution to the model provided
|
|
to the Solve() method.
|
|
|
|
Once Solve() is called, this class allows inspecting the solution found
|
|
with the Value() and BooleanValue() methods, as well as general statistics
|
|
about the solve procedure.
|
|
"""
|
|
|
|
def __init__(self):
|
|
self.__model = None
|
|
self.__solution = None
|
|
self.parameters = sat_parameters_pb2.SatParameters()
|
|
|
|
def Solve(self, model):
|
|
"""Solves the given model and returns the solve status."""
|
|
self.__solution = pywrapsat.SatHelper.SolveWithParameters(
|
|
model.Proto(), self.parameters)
|
|
return self.__solution.status
|
|
|
|
def SolveWithSolutionCallback(self, model, callback):
|
|
"""Solves a problem and passes each solution found to the callback."""
|
|
self.__solution = (
|
|
pywrapsat.SatHelper.SolveWithParametersAndSolutionCallback(
|
|
model.Proto(), self.parameters, callback))
|
|
return self.__solution.status
|
|
|
|
def SearchForAllSolutions(self, model, callback):
|
|
"""Search for all solutions of a satisfiability problem.
|
|
|
|
This method searches for all feasible solutions of a given model.
|
|
Then it feeds the solution to the callback.
|
|
|
|
Note that the model cannot contain an objective.
|
|
|
|
Args:
|
|
model: The model to solve.
|
|
callback: The callback that will be called at each solution.
|
|
|
|
Returns:
|
|
The status of the solve:
|
|
|
|
* *FEASIBLE* if some solutions have been found
|
|
* *INFEASIBLE* if the solver has proved there are no solution
|
|
* *OPTIMAL* if all solutions have been found
|
|
"""
|
|
if model.HasObjective():
|
|
raise TypeError('Search for all solutions is only defined on '
|
|
'satisfiability problems')
|
|
# Store old values.
|
|
enumerate_all = self.parameters.enumerate_all_solutions
|
|
self.parameters.enumerate_all_solutions = True
|
|
self.__solution = (
|
|
pywrapsat.SatHelper.SolveWithParametersAndSolutionCallback(
|
|
model.Proto(), self.parameters, callback))
|
|
# Restore parameters.
|
|
self.parameters.enumerate_all_solutions = enumerate_all
|
|
return self.__solution.status
|
|
|
|
def Value(self, expression):
|
|
"""Returns the value of a linear expression after solve."""
|
|
if not self.__solution:
|
|
raise RuntimeError('Solve() has not be called.')
|
|
return EvaluateLinearExpr(expression, self.__solution)
|
|
|
|
def BooleanValue(self, literal):
|
|
"""Returns the boolean value of a literal after solve."""
|
|
if not self.__solution:
|
|
raise RuntimeError('Solve() has not be called.')
|
|
return EvaluateBooleanExpression(literal, self.__solution)
|
|
|
|
def ObjectiveValue(self):
|
|
"""Returns the value of the objective after solve."""
|
|
return self.__solution.objective_value
|
|
|
|
def BestObjectiveBound(self):
|
|
"""Returns the best lower (upper) bound found when min(max)imizing."""
|
|
return self.__solution.best_objective_bound
|
|
|
|
def StatusName(self, status=None):
|
|
"""Returns the name of the status returned by Solve()."""
|
|
if status is None:
|
|
status = self.__solution.status
|
|
return cp_model_pb2.CpSolverStatus.Name(status)
|
|
|
|
def NumBooleans(self):
|
|
"""Returns the number of boolean variables managed by the SAT solver."""
|
|
return self.__solution.num_booleans
|
|
|
|
def NumConflicts(self):
|
|
"""Returns the number of conflicts since the creation of the solver."""
|
|
return self.__solution.num_conflicts
|
|
|
|
def NumBranches(self):
|
|
"""Returns the number of search branches explored by the solver."""
|
|
return self.__solution.num_branches
|
|
|
|
def WallTime(self):
|
|
"""Returns the wall time in seconds since the creation of the solver."""
|
|
return self.__solution.wall_time
|
|
|
|
def UserTime(self):
|
|
"""Returns the user time in seconds since the creation of the solver."""
|
|
return self.__solution.user_time
|
|
|
|
def ResponseStats(self):
|
|
"""Returns some statistics on the solution found as a string."""
|
|
return pywrapsat.SatHelper.SolverResponseStats(self.__solution)
|
|
|
|
def ResponseProto(self):
|
|
"""Returns the response object."""
|
|
return self.__solution
|
|
|
|
|
|
class CpSolverSolutionCallback(pywrapsat.SolutionCallback):
|
|
"""Solution callback.
|
|
|
|
This class implements a callback that will be called at each new solution
|
|
found during search.
|
|
|
|
The method OnSolutionCallback() will be called by the solver, and must be
|
|
implemented. The current solution can be queried using the BooleanValue()
|
|
and Value() methods.
|
|
|
|
It inherits the following methods from its base class:
|
|
|
|
* `ObjectiveValue(self)`
|
|
* `BestObjectiveBound(self)`
|
|
* `NumBooleans(self)`
|
|
* `NumConflicts(self)`
|
|
* `NumBranches(self)`
|
|
* `WallTime(self)`
|
|
* `UserTime(self)`
|
|
|
|
These methods returns the same information as their counterpart in the
|
|
`CpSolver` class.
|
|
"""
|
|
|
|
def __init__(self):
|
|
pywrapsat.SolutionCallback.__init__(self)
|
|
|
|
def OnSolutionCallback(self):
|
|
"""Proxy for the same method in snake case."""
|
|
self.on_solution_callback()
|
|
|
|
def BooleanValue(self, lit):
|
|
"""Returns the boolean value of a boolean literal.
|
|
|
|
Args:
|
|
lit: A boolean variable or its negation.
|
|
|
|
Returns:
|
|
The Boolean value of the literal in the solution.
|
|
|
|
Raises:
|
|
RuntimeError: if `lit` is not a boolean variable or its negation.
|
|
"""
|
|
if not self.HasResponse():
|
|
raise RuntimeError('Solve() has not be called.')
|
|
if isinstance(lit, numbers.Integral):
|
|
return bool(lit)
|
|
elif isinstance(lit, IntVar) or isinstance(lit, _NotBooleanVariable):
|
|
index = lit.Index()
|
|
return self.SolutionBooleanValue(index)
|
|
else:
|
|
raise TypeError('Cannot interpret %s as a boolean expression.' %
|
|
lit)
|
|
|
|
def Value(self, expression):
|
|
"""Evaluates an linear expression in the current solution.
|
|
|
|
Args:
|
|
expression: a linear expression of the model.
|
|
|
|
Returns:
|
|
An integer value equal to the evaluation of the linear expression
|
|
against the current solution.
|
|
|
|
Raises:
|
|
RuntimeError: if 'expression' is not a LinearExpr.
|
|
"""
|
|
if not self.HasResponse():
|
|
raise RuntimeError('Solve() has not be called.')
|
|
if isinstance(expression, numbers.Integral):
|
|
return expression
|
|
if not isinstance(expression, LinearExpr):
|
|
raise TypeError('Cannot interpret %s as a linear expression.' %
|
|
expression)
|
|
|
|
value = 0
|
|
to_process = [(expression, 1)]
|
|
while to_process:
|
|
expr, coef = to_process.pop()
|
|
if isinstance(expr, _ProductCst):
|
|
to_process.append(
|
|
(expr.Expression(), coef * expr.Coefficient()))
|
|
elif isinstance(expr, _SumArray):
|
|
for e in expr.Expressions():
|
|
to_process.append((e, coef))
|
|
value += expr.Constant() * coef
|
|
elif isinstance(expr, _ScalProd):
|
|
for e, c in zip(expr.Expressions(), expr.Coefficients()):
|
|
to_process.append((e, coef * c))
|
|
value += expr.Constant() * coef
|
|
elif isinstance(expr, IntVar):
|
|
value += coef * self.SolutionIntegerValue(expr.Index())
|
|
elif isinstance(expr, _NotBooleanVariable):
|
|
value += coef * (1 -
|
|
self.SolutionIntegerValue(expr.Not().Index()))
|
|
return value
|
|
|
|
|
|
class ObjectiveSolutionPrinter(CpSolverSolutionCallback):
|
|
"""Display the objective value and time of intermediate solutions."""
|
|
|
|
def __init__(self):
|
|
CpSolverSolutionCallback.__init__(self)
|
|
self.__solution_count = 0
|
|
self.__start_time = time.time()
|
|
|
|
def on_solution_callback(self):
|
|
"""Called on each new solution."""
|
|
current_time = time.time()
|
|
obj = self.ObjectiveValue()
|
|
print('Solution %i, time = %0.2f s, objective = %i' %
|
|
(self.__solution_count, current_time - self.__start_time, obj))
|
|
self.__solution_count += 1
|
|
|
|
def solution_count(self):
|
|
"""Returns the number of solutions found."""
|
|
return self.__solution_count
|
|
|
|
|
|
class VarArrayAndObjectiveSolutionPrinter(CpSolverSolutionCallback):
|
|
"""Print intermediate solutions (objective, variable values, time)."""
|
|
|
|
def __init__(self, variables):
|
|
CpSolverSolutionCallback.__init__(self)
|
|
self.__variables = variables
|
|
self.__solution_count = 0
|
|
self.__start_time = time.time()
|
|
|
|
def on_solution_callback(self):
|
|
"""Called on each new solution."""
|
|
current_time = time.time()
|
|
obj = self.ObjectiveValue()
|
|
print('Solution %i, time = %0.2f s, objective = %i' %
|
|
(self.__solution_count, current_time - self.__start_time, obj))
|
|
for v in self.__variables:
|
|
print(' %s = %i' % (v, self.Value(v)), end=' ')
|
|
print()
|
|
self.__solution_count += 1
|
|
|
|
def solution_count(self):
|
|
"""Returns the number of solutions found."""
|
|
return self.__solution_count
|
|
|
|
|
|
class VarArraySolutionPrinter(CpSolverSolutionCallback):
|
|
"""Print intermediate solutions (variable values, time)."""
|
|
|
|
def __init__(self, variables):
|
|
CpSolverSolutionCallback.__init__(self)
|
|
self.__variables = variables
|
|
self.__solution_count = 0
|
|
self.__start_time = time.time()
|
|
|
|
def on_solution_callback(self):
|
|
"""Called on each new solution."""
|
|
current_time = time.time()
|
|
print('Solution %i, time = %0.2f s' %
|
|
(self.__solution_count, current_time - self.__start_time))
|
|
for v in self.__variables:
|
|
print(' %s = %i' % (v, self.Value(v)), end=' ')
|
|
print()
|
|
self.__solution_count += 1
|
|
|
|
def solution_count(self):
|
|
"""Returns the number of solutions found."""
|
|
return self.__solution_count
|