def tree_csp_solver(constraint_problem: ConstraintProblem, with_history: bool = False) \
-> Optional[Deque[Tuple[Variable, Any]]]:
actions_history = None
if with_history:
actions_history = deque()
topological_sorted_unassigned_variables = __kahn_topological_sort(constraint_problem)
if not topological_sorted_unassigned_variables:
return actions_history
for i in range(len(topological_sorted_unassigned_variables) - 1, 0, -1):
for value in topological_sorted_unassigned_variables[i].domain:
topological_sorted_unassigned_variables[i].assign(value)
if not constraint_problem.get_consistent_domain(topological_sorted_unassigned_variables[i-1]):
topological_sorted_unassigned_variables[i].remove_from_domain(value)
topological_sorted_unassigned_variables[i].unassign()
if not topological_sorted_unassigned_variables[i].domain:
return actions_history
for variable in topological_sorted_unassigned_variables:
consistent_domain = constraint_problem.get_consistent_domain(variable)
if not consistent_domain:
return actions_history
value, *_ = consistent_domain
variable.assign(value)
if with_history:
actions_history.append((variable, value))
return actions_history
def ac3(constraint_problem: ConstraintProblem,
assigned_variable: Variable = None) -> bool:
if assigned_variable is not None: # usage of ac3 as part of Maintaining Arc Consistency (MAC) algorithm
unassigned_neighbors = constraint_problem.get_unassigned_neighbors(
assigned_variable)
arcs = {(unassigned_neighbor, assigned_variable)
for unassigned_neighbor in unassigned_neighbors}
else:
arcs = {(variable, neighbor)
for variable in constraint_problem.get_unassigned_variables()
for neighbor in constraint_problem.get_neighbors(variable)}
while arcs:
variable, neighbor = arcs.pop()
if __revise(constraint_problem, variable, neighbor):
if not constraint_problem.get_consistent_domain(variable):
return False
rest_of_neighbors = constraint_problem.get_neighbors(variable) - {
neighbor
}
if rest_of_neighbors:
for other_neighbor in rest_of_neighbors:
arcs.add((other_neighbor, variable))
for var in constraint_problem.get_variables():
if not var.domain or not constraint_problem.get_consistent_domain(var):
return False
return True
def minimum_remaining_values(
constraint_problem: ConstraintProblem,
variables: Optional[FrozenSet[Variable]] = None
) -> FrozenSet[Variable]:
if variables is not None: # then we're using minimum_remaining_values as secondary key
min_variable = min(
variables,
key=lambda variable: len(
constraint_problem.get_consistent_domain(variable)))
return frozenset({min_variable})
unassigned_variables = constraint_problem.get_unassigned_variables()
min_variable = min(
unassigned_variables,
key=lambda var: len(constraint_problem.get_consistent_domain(var)))
min_remaining_values = len(
constraint_problem.get_consistent_domain(min_variable))
min_variables = filter(
lambda var: len(constraint_problem.get_consistent_domain(var)) ==
min_remaining_values, unassigned_variables)
return frozenset(min_variables)
def naive_cycle_cutset(constraint_problem: ConstraintProblem, with_history: bool = False) \
-> Optional[Deque[Tuple[Variable, Any]]]:
actions_history = None
if with_history:
actions_history = deque()
variables = constraint_problem.get_variables()
read_only_variables = constraint_problem.get_assigned_variables()
constraints = list(constraint_problem.get_constraints())
constraints.sort(key=lambda constraint: len(constraint.variables), reverse=True)
constraint_graph = constraint_problem.get_constraint_graph_as_adjacency_list()
for i in range(1, len(constraints)):
cutset_constraints = constraints[:i]
cutset_variables = set()
for cutset_const in cutset_constraints:
cutset_variables.update(cutset_const.variables)
reduced_graph = {var: neighbors for var, neighbors in constraint_graph.items() if var not in cutset_variables}
for var in reduced_graph:
reduced_graph[var] -= cutset_variables
if __is_tree(reduced_graph):
consistent_assignments_list = __get_consistent_assignments(cutset_variables, cutset_constraints,
read_only_variables)
non_cutset_variables = variables - cutset_variables
non_cutset_vars_to_original_domains_map = {var: var.domain for var in non_cutset_variables}
for consist_assignment in consistent_assignments_list:
for var, value in zip(cutset_variables, consist_assignment):
if var not in read_only_variables:
var.assign(value)
if with_history:
actions_history.append((var, value))
for non_cutset_var in non_cutset_variables:
if non_cutset_var not in read_only_variables:
non_cutset_var.domain = list(constraint_problem.get_consistent_domain(non_cutset_var))
tree_csp_action_history = tree_csp_solver(constraint_problem, with_history)
if with_history:
actions_history.extend(tree_csp_action_history)
if constraint_problem.is_completely_consistently_assigned():
return actions_history
for var in variables:
if var not in read_only_variables:
var.unassign()
if with_history:
actions_history.append((var, None))
for var in non_cutset_vars_to_original_domains_map:
if var not in read_only_variables:
var.domain = non_cutset_vars_to_original_domains_map[var]
return actions_history
def least_constraining_value(constraint_problem: ConstraintProblem,
variable: Variable) -> list:
unassigned_neighbors = constraint_problem.get_unassigned_neighbors(
variable)
def neighbors_consistent_domain_lengths(value) -> int:
variable.assign(value)
consistent_domain_lengths = map(
lambda neighbor: len(
(constraint_problem.get_consistent_domain(neighbor))),
unassigned_neighbors)
variable.unassign()
return sum(consistent_domain_lengths)
return sorted(constraint_problem.get_consistent_domain(variable),
key=neighbors_consistent_domain_lengths,
reverse=True)
def i_consistency(constraint_problem: ConstraintProblem, i: int) -> bool:
variables = constraint_problem.get_variables()
assert 0 < i <= len(variables), "for i = {0}: i <= 0 or (number of variables in constraint_problem) < i.".format(i)
i_minus_one_sized_subsets = combinations(variables, i - 1)
i_subsets_consistent_assignments = __initialize_i_consistency(variables, i_minus_one_sized_subsets)
reducing_domains = True
while reducing_domains:
reducing_domains = False
for subset, ith_variable in i_subsets_consistent_assignments:
if __revise_i(constraint_problem, subset, ith_variable, i_subsets_consistent_assignments):
reducing_domains = True
for var in constraint_problem.get_variables():
if not var.domain or not constraint_problem.get_consistent_domain(var):
return False
return True
def ac4(constraint_problem: ConstraintProblem) -> bool:
support_counter = collections.Counter()
variable_value_pairs_supported_by = collections.defaultdict(set)
unsupported_variable_value_pairs = collections.deque()
__initialize_ac4(constraint_problem.get_constraints(), support_counter, variable_value_pairs_supported_by,
unsupported_variable_value_pairs)
while unsupported_variable_value_pairs:
second_variable, second_value = unsupported_variable_value_pairs.popleft()
for first_variable, first_value in variable_value_pairs_supported_by[(second_variable, second_value)]:
if first_value in first_variable.domain:
support_counter[(first_variable, first_value, second_variable)] -= 1
if support_counter[(first_variable, first_value, second_variable)] == 0:
first_variable.remove_from_domain(first_value)
unsupported_variable_value_pairs.append((first_variable, first_value))
for var in constraint_problem.get_variables():
if not var.domain or not constraint_problem.get_consistent_domain(var):
return False
return True
def do_not_sort(constraint_problem: ConstraintProblem,
variable: Variable) -> list:
return list(constraint_problem.get_consistent_domain(variable))
def __optimized_heuristic_backtrack(constraint_problem: ConstraintProblem,
find_all_solutions: bool = False,
with_history: bool = False):
unassigned_variables = constraint_problem.get_unassigned_variables()
min_variable = min(
unassigned_variables,
key=lambda var: len(constraint_problem.get_consistent_domain(var)))
min_remaining_values = len(
constraint_problem.get_consistent_domain(min_variable))
min_variables = filter(
lambda var: len(constraint_problem.get_consistent_domain(var)) ==
min_remaining_values, unassigned_variables)
selected_unassigned_vars = frozenset(min_variables)
if len(selected_unassigned_vars) > 1:
selected_variable = max(
selected_unassigned_vars,
key=lambda var: len(
constraint_problem.get_unassigned_neighbors(var)))
else:
selected_variable, *_ = selected_unassigned_vars
unassigned_neighbors = constraint_problem.get_unassigned_neighbors(
selected_variable)
def neighbors_consistent_domain_lengths(val) -> int:
selected_variable.assign(val)
consistent_domain_lengths = map(
lambda neighbor: len(
(constraint_problem.get_consistent_domain(neighbor))),
unassigned_neighbors)
selected_variable.unassign()
return sum(consistent_domain_lengths)
sorted_domain = sorted(
constraint_problem.get_consistent_domain(selected_variable),
key=neighbors_consistent_domain_lengths,
reverse=True)
for value in sorted_domain:
selected_variable.assign(value)
if with_history:
__actions_history.append((selected_variable, value))
if constraint_problem.is_completely_assigned():
if constraint_problem.is_consistently_assigned():
if find_all_solutions:
yield constraint_problem.get_current_assignment()
else:
yield None
selected_variable.unassign()
if with_history:
__actions_history.append((selected_variable, None))
continue
if constraint_problem.is_consistently_assigned():
for solution_assignment in __optimized_heuristic_backtrack(
constraint_problem, find_all_solutions, with_history):
yield solution_assignment
selected_variable.unassign()
if with_history:
__actions_history.append((selected_variable, None))