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|
# BNF
# expression -> bool ( ( '|' | '&' | '^' ) bool )*
# bool -> '0' | '1'
def tokenize(xs):
result = []
for c in xs:
if c == '0':
result.append(0)
elif c == '1':
result.append(1)
elif c in "&|^":
result.append(c)
else:
raise Exception("Unexpected token, \"{}\"".format(c))
return result
class Parser(object):
def __init__(self, tokens):
self.tokens = tokens
self.i = 0
def prev(self):
return self.tokens[self.i - 1]
def curr(self):
return self.tokens[self.i]
def match(self, xs):
if self.exhausted():
return False
if (self.curr() in xs):
self.consume()
return True
return False
def consume(self):
result = self.curr()
self.i += 1
return result
def exhausted(self):
return self.i >= len(self.tokens)
def recursive_descent(tokens):
parser = Parser(tokens)
return parse_expression(parser)
def parse_expression(parser):
lhs = parse_bool(parser)
while parser.match(['|', '&', '^']):
op = parser.prev()
rhs = parse_expression(parser)
lhs = [op, lhs, rhs]
return lhs
def parse_bool(parser):
if parser.curr() == 0:
parser.consume()
return False
elif parser.curr() == 1:
parser.consume()
return True
else:
raise Exception("Unexpected token: {}".format(parser.curr()))
def f(expr, result):
tokens = tokenize(expr)
tree = recursive_descent(tokens)
return do_f(tree, result)
def do_f(tree, result):
if type(tree) == bool:
if tree == result:
return 1
else:
return 0
op, lhs, rhs = tree[0], tree[1], tree[2]
truth_tables = {
True: {
'|': [
(True, True),
(True, False),
(False, True),
],
'&': [
(True, True),
],
'^': [
(True, False),
(False, True),
],
},
False: {
'|': [
(False, False),
],
'&': [
(False, False),
(True, False),
(False, True),
],
'^': [
(True, True),
(False, False),
],
}
}
return sum([do_f(lhs, x) * do_f(rhs, y) for x, y in truth_tables[result][op]])
print(f("1^0|0|1", False))
print(f("1|0|1|1", False))
|
