125 lines
7.0 KiB
Python
125 lines
7.0 KiB
Python
__author__: str = "Jeremy Saklad"
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from collections.abc import Iterable
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from functools import cache, partialmethod, reduce, singledispatch, singledispatchmethod
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from numbers import Integral, Number
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from typing import Final
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from ortools.sat.python import cp_model
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class BoneMarketModel(cp_model.CpModel):
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"""A CpModel with additional functions for common constraints and enhanced enforcement literal support."""
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__slots__: tuple[()] = ()
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def AddAllowedAssignments(self, variables: Iterable[Iterable], tuples_list: Iterable[Iterable]) -> tuple:
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# Used for variable names
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invocation: Final[str] = repr((variables, tuples_list))
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intermediate_variables, constraints = zip(*(self.NewIntermediateIntVar(variable, f'{invocation}: {variable}') for variable in variables))
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super().AddAllowedAssignments(intermediate_variables, tuples_list)
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return constraints
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def AddApproximateExponentiationEquality(self, target, var, exp: Number, upto: Integral) -> tuple:
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"""Add an approximate exponentiation equality using a lookup table.
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Set `upto` to a value that is unlikely to come into play.
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Each parameter is interpreted as a BoundedLinearExpression, and a layer of indirection is applied such that each Constraint in the returned tuple can accept an enforcement literal."""
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return self.AddAllowedAssignments((target, var), ((int(base**exp), base) for base in range(upto + 1)))
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def AddDivisionEquality(self, target, num, denom) -> tuple:
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"""Adds `target == num // denom` (integer division rounded towards 0).
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Each parameter is interpreted as a BoundedLinearExpression, and a layer of indirection is applied such that each Constraint in the returned tuple can accept an enforcement literal."""
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# Used for variable names
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invocation: Final[str] = f'{repr(target)} == {repr(num)} // {repr(denom)}'
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intermediate_target, target_constraint = self.NewIntermediateIntVar(target, f'{invocation}: target')
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intermediate_num, num_constraint = self.NewIntermediateIntVar(num, f'{invocation}: num', lb=0)
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intermediate_denom, denom_constraint = self.NewIntermediateIntVar(denom, f'{invocation}: denom', lb=1)
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super().AddDivisionEquality(intermediate_target, intermediate_num, intermediate_denom)
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return (target_constraint, num_constraint, denom_constraint)
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def AddIf(self, variable, *constraints: tuple) -> frozenset:
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"""Add constraints to the model, only enforced if the specified variable is true.
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Each item in `constraints` must be either a BoundedLinearExpression, a Constraint compatible with OnlyEnforceIf, a 0-arity partial method of CpModel returning a valid item, or an iterable containing valid items."""
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@singledispatch
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def Add(constraint: Iterable) -> frozenset:
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return frozenset((Add(element) for element in constraint))
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@Add.register
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def _(constraint: cp_model.Constraint) -> cp_model.Constraint:
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return constraint.OnlyEnforceIf(variable)
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@Add.register
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def _(constraint: cp_model.BoundedLinearExpression) -> cp_model.Constraint:
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return Add(self.Add(constraint))
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@Add.register
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def _(constraint: partialmethod):
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return Add(constraint.__get__(self)())
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return frozenset((Add(constraint) for constraint in constraints))
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def AddMultiplicationEquality(self, target, variables: Iterable) -> tuple:
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"""Adds `target == variables[0] * .. * variables[n]`.
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Each parameter is interpreted as a BoundedLinearExpression, and a layer of indirection is applied such that each Constraint in the returned tuple can accept an enforcement literal."""
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superclass: Final = super()
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def Multiply(end, stack: list) -> tuple:
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intermediate_variable, variable_constraint = self.NewIntermediateIntVar(stack.pop(), f'{repr(end)} == {"*".join((repr(variable) for variable in stack))}: last variable')
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partial_target: Final[cp_model.IntVar] = self.NewIntVar(f'{repr(end)} == {"*".join((repr(variable) for variable in stack))}: partial target')
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recursive_constraints: Final[tuple] = self.AddMultiplicationEquality(partial_target, stack) if len(stack) > 1 else (self.Add(partial_target == stack.pop()),)
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intermediate_target, target_constraint = self.NewIntermediateIntVar(end, f'{repr(end)} == {"*".join((repr(variable) for variable in stack))}: target')
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superclass.AddMultiplicationEquality(intermediate_target, (partial_target, intermediate_variable))
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return (variable_constraint, *recursive_constraints, target_constraint)
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# Avoid mutating parameter directly
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return Multiply(target, variables.copy() if isinstance(variables, list) else list(variables))
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@cache
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def BoolExpression(self, bounded_linear_exp: cp_model.BoundedLinearExpression) -> cp_model.IntVar:
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"""Add a fully-reified implication using an intermediate Boolean variable."""
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intermediate: Final[cp_model.IntVar] = self.NewBoolVar(str(bounded_linear_exp))
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linear_exp: Final[cp_model.LinearExp] = bounded_linear_exp.Expression()
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domain: Final[cp_model.Domain] = cp_model.Domain(*bounded_linear_exp.Bounds())
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self.AddLinearExpressionInDomain(linear_exp, domain).OnlyEnforceIf(intermediate)
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self.AddLinearExpressionInDomain(linear_exp, domain.Complement()).OnlyEnforceIf(intermediate.Not())
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return intermediate
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@singledispatchmethod
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def NewIntermediateIntVar(self, expression: cp_model.LinearExpr, name: str, *, lb: Integral = cp_model.INT32_MIN, ub: Integral = cp_model.INT32_MAX) -> tuple:
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"""Creates an integer variable equivalent to the given expression and returns a tuple consisting of the variable and constraints for use with enforcement literals.
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`equality` must be either a LinearExp or a unary partialmethod that accepts a target integer variable and returns Constraints."""
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# If expression is either an integer variable with the specified bounds or an integer constant, just pass it through
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if isinstance(expression, cp_model.IntVar) and (lambda domain : domain == [lb, ub] or domain[0] == domain[1])(cp_model.IntVar.Proto(expression).domain):
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return (expression, ())
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else:
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intermediate: Final[cp_model.IntVar] = super().NewIntVar(lb, ub, name)
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return (intermediate, self.Add(intermediate == expression))
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@NewIntermediateIntVar.register
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def _(self, expression: partialmethod, name: str, *, lb: Integral = cp_model.INT32_MIN, ub: Integral = cp_model.INT32_MAX) -> tuple:
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intermediate: Final[cp_model.IntVar] = super().NewIntVar(lb, ub, name)
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return (intermediate, expression.__get__(self)(intermediate))
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@NewIntermediateIntVar.register
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def _(self, expression: Integral, *args, **kwargs) -> tuple:
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return (self.NewConstant(expression), ())
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def NewIntVar(self, name: str, *, lb: Integral = cp_model.INT32_MIN, ub: Integral = cp_model.INT32_MAX) -> cp_model.IntVar:
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return super().NewIntVar(lb, ub, name)
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