编写一个可以将正规式:((ab)|b)(a|(ba)*)a转化为NFA图的python代码
时间: 2023-12-14 21:39:14 浏览: 170
以下是一个简单的 Python 代码示例,实现将给定的正则表达式转换为NFA图:
```python
class State:
"""
状态类
"""
def __init__(self, label):
self.label = label
self.edges = []
self.epsilon_edges = []
self.accepts = False
class NFA:
"""
NFA类
"""
def __init__(self, regex):
self.start = None # 开始状态
self.end = None # 结束状态
self.states = [] # 所有状态
self.build(regex)
def build(self, regex):
"""
构建NFA图
"""
stack = []
index = 0
while index < len(regex):
if regex[index] == '(':
stack.append(index)
elif regex[index] == ')':
start_index = stack.pop()
if len(stack) == 0:
if start_index == 0 and index == len(regex) - 1:
# 整个正则表达式都被括号包含
self.build(regex[1:-1])
return
else:
# 括号内的表达式
self.build(regex[start_index+1:index])
elif regex[index] == '|':
if len(stack) == 0:
# 添加新状态
state1 = State(len(self.states))
state2 = State(len(self.states) + 1)
self.states.append(state1)
self.states.append(state2)
# 连接状态
state1.epsilon_edges.append(state2)
if self.start is None:
self.start = state1
if len(stack) == 0:
self.end = state2
else:
stack.append(len(self.states) - 1)
elif regex[index] == '*':
# 添加新状态
state1 = State(len(self.states))
state2 = State(len(self.states) + 1)
self.states.append(state1)
self.states.append(state2)
# 连接状态
if len(stack) == 0:
state1.epsilon_edges.append(state2)
state1.epsilon_edges.append(self.start)
self.start = state1
self.end = state2
else:
state1.epsilon_edges.append(state2)
state1.epsilon_edges.append(self.states[stack[-1]])
self.states[stack[-1]].epsilon_edges.append(state1)
stack[-1] = len(self.states) - 1
else:
# 添加新状态
state1 = State(len(self.states))
state2 = State(len(self.states) + 1)
self.states.append(state1)
self.states.append(state2)
# 连接状态
state1.edges.append((regex[index], state2))
if self.start is None:
self.start = state1
if len(stack) == 0:
self.end = state2
index += 1
# 设置结束状态
if self.end is not None:
self.end.accepts = True
def match(self, string):
"""
匹配字符串
"""
current_states = set()
next_states = set()
current_states.add(self.start)
for char in string:
next_states.clear()
for state in current_states:
for edge in state.edges:
if edge[0] == char:
next_states.add(edge[1])
current_states.clear()
current_states.update(next_states)
return self.end in current_states
def print(self):
"""
打印NFA图
"""
print('Start: ', self.start.label)
for state in self.states:
if state.accepts:
print('Accept: ', state.label)
for edge in state.edges:
print(state.label, ' --', edge[0], '--> ', edge[1].label)
for epsilon_edge in state.epsilon_edges:
print(state.label, ' --epsilon--> ', epsilon_edge.label)
# 测试
nfa = NFA('((ab)|b)(a|(ba)*)a')
nfa.print()
print(nfa.match('aba')) # True
print(nfa.match('baa')) # True
print(nfa.match('bbba')) # False
```
该代码使用了栈来处理括号和或运算符,使用了状态来表示NFA图中的节点,并使用边和 epsilon 边来表示节点之间的连接。在构建NFA图时,每遇到一个字符或星号就会创建两个新状态,并将它们连接起来。在处理或运算符时,将创建两个新状态并将它们与前面的状态连接起来。最后,添加一个结束状态来表示匹配的终点。可以使用 `match` 方法来测试给定字符串是否匹配NFA图。
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