def __build_nfa(self):
op_stack = []
self.nfa = Digraph(len(self.pat) + 1)
# tracks the last left parenthesis
leftPar = -1
for i in range(self.end_state):
ch = self.pat[i]
if ch == '(':
# add an epsilon transition to the next character and push the operator for later processing
self.nfa.add_edge(i, i+1)
op_stack.append(i)
leftPar = i
elif ch == '|' and leftPar >= 0:
# add a transition from the left parenthesis node to the first node after the OR (|) operator
self.nfa.add_edge(leftPar, i+1)
op_stack.append(i)
elif ch == ')':
# add a transition from the node right after the | operator to the right parenthesis node
last_op = op_stack.pop()
while self.pat[last_op] == '|':
self.nfa.add_edge(last_op, i)
last_op = op_stack.pop()
leftPar = last_op
self.nfa.add_edge(i, i+1)
# handles the case (...)*
if i < self.end_state - 1 and self.pat[i+1] == '*':
self.nfa.add_edge(leftPar, i+1)
self.nfa.add_edge(i+1, leftPar)
elif ch == '*':
# always add a transition to the next node as the star operator can match a zero input
self.nfa.add_edge(i, i+1)
# handles the case of a star operator after a simple symbol, e.g. ab*
if i > 0 and self.pat[i-1] != ')':
self.nfa.add_edge(i, i-1)
self.nfa.add_edge(i-1, i+1)
assert len(op_stack) == 0
class SimpleRegEx:
def __init__(self, pattern):
self.pat = pattern
self.end_state = len(pattern)
self.__build_nfa()
# stores a flag per node indicating if the last DFS operation reached the corresponding node
self._marked = [False for _ in range(self.nfa.V())]
def matches(self, text):
# find the epsilon transitions from the origin state
self.__dfs_cycle([0])
current_states = self.__get_reachable_states()
if self.end_state in current_states:
return True
# compute the next set of reachable states for each input character
for i in range(len(text)):
new_states = []
for state in current_states:
if text[i] == self.pat[state] or self.pat[state] == '.':
new_states.append(state+1)
self.__dfs_cycle(new_states)
current_states = self.__get_reachable_states()
if self.end_state in current_states:
return True
if len(current_states) == 0:
return False
return self.end_state in current_states
def __get_reachable_states(self):
return [i for i in range(self.end_state + 1) if self._marked[i]]
def __build_nfa(self):
op_stack = []
self.nfa = Digraph(len(self.pat) + 1)
# tracks the last left parenthesis
leftPar = -1
for i in range(self.end_state):
ch = self.pat[i]
if ch == '(':
# add an epsilon transition to the next character and push the operator for later processing
self.nfa.add_edge(i, i+1)
op_stack.append(i)
leftPar = i
elif ch == '|' and leftPar >= 0:
# add a transition from the left parenthesis node to the first node after the OR (|) operator
self.nfa.add_edge(leftPar, i+1)
op_stack.append(i)
elif ch == ')':
# add a transition from the node right after the | operator to the right parenthesis node
last_op = op_stack.pop()
while self.pat[last_op] == '|':
self.nfa.add_edge(last_op, i)
last_op = op_stack.pop()
leftPar = last_op
self.nfa.add_edge(i, i+1)
# handles the case (...)*
if i < self.end_state - 1 and self.pat[i+1] == '*':
self.nfa.add_edge(leftPar, i+1)
self.nfa.add_edge(i+1, leftPar)
elif ch == '*':
# always add a transition to the next node as the star operator can match a zero input
self.nfa.add_edge(i, i+1)
# handles the case of a star operator after a simple symbol, e.g. ab*
if i > 0 and self.pat[i-1] != ')':
self.nfa.add_edge(i, i-1)
self.nfa.add_edge(i-1, i+1)
assert len(op_stack) == 0
def __dfs_cycle(self, states):
self._marked = [False for _ in range(self.nfa.V())]
for s in states:
self.__dfs(s)
def __dfs(self, v):
self._marked[v] = True
for w in self.nfa.edges(v):
if not self._marked[w]:
self.__dfs(w)
