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# csp.py
# From Classic Computer Science Problems in Python Chapter 3
# Copyright 2018 David Kopec
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from typing import Generic, TypeVar, Dict, List, Optional
from abc import ABC, abstractmethod
V = TypeVar('V') # variable type
D = TypeVar('D') # domain type
# Base class for all constraints
class Constraint(Generic[V, D], ABC):
# The variables that the constraint is between
def __init__(self, variables: List[V]) -> None:
self.variables = variables
# Must be overridden by subclasses
@abstractmethod
def satisfied(self, assignment: Dict[V, D]) -> bool:
...
# A constraint satisfaction problem consists of variables of type V
# that have ranges of values known as domains of type D and constraints
# that determine whether a particular variable's domain selection is valid
class CSP(Generic[V, D]):
def __init__(self, variables: List[V], domains: Dict[V, List[D]]) -> None:
self.variables: List[V] = variables # variables to be constrained
self.domains: Dict[V, List[D]] = domains # domain of each variable
self.constraints: Dict[V, List[Constraint[V, D]]] = {}
for variable in self.variables:
self.constraints[variable] = []
if variable not in self.domains:
raise LookupError("Every variable should have a domain assigned to it.")
def add_constraint(self, constraint: Constraint[V, D]) -> None:
for variable in constraint.variables:
if variable not in self.variables:
raise LookupError("Variable in constraint not in CSP")
else:
self.constraints[variable].append(constraint)
# Check if the value assignment is consistent by checking all constraints
# for the given variable against it
def consistent(self, variable: V, assignment: Dict[V, D]) -> bool:
for constraint in self.constraints[variable]:
if not constraint.satisfied(assignment):
return False
return True
def backtracking_search(self, assignment: Dict[V, D] = {}) -> Optional[Dict[V, D]]:
# assignment is complete if every variable is assigned (our base case)
if len(assignment) == len(self.variables):
return assignment
# get all variables in the CSP but not in the assignment
unassigned: List[V] = [v for v in self.variables if v not in assignment]
# get the every possible domain value of the first unassigned variable
first: V = unassigned[0]
for value in self.domains[first]:
local_assignment = assignment.copy()
local_assignment[first] = value
# if we're still consistent, we recurse (continue)
if self.consistent(first, local_assignment):
result: Optional[Dict[V, D]] = self.backtracking_search(local_assignment)
# if we didn't find the result, we will end up backtracking
if result is not None:
return result
return None