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import sys
boolean_true = "T"
boolean_false = "F"
operator_gt = "+"
operator_lt = "-"
operator_eq = "="
operator_and = "&"
operator_or = "|"
operator_not = "!"
operator_left_paran = "("
operator_right_paran = ")"
operator_association = {
operator_gt: "left",
operator_lt: "left",
operator_eq: "left",
operator_and: "left",
operator_or: "left",
operator_not: "right"
operator_precedence = {
operator_not: 4,
operator_gt: 3,
operator_lt: 3,
operator_eq: 2,
operator_and: 1,
operator_or: 0,
operator_left_paran: -1,
operator_right_paran: -1
def precedence(op):
return operator_precedence[op]
def associativity(op):
return operator_association[op]
def is_boolean(c):
return c == boolean_true or c == boolean_false
def is_op(c):
return operator_precedence.has_key(c) and not (is_left_paran(c) or is_right_paran(c))
def is_left_paran(c):
return c == operator_left_paran
def is_right_paran(c):
return c == operator_right_paran
def append_token(token, l):
if token != "":
return ""
def tokenize(expr):
tokens = []
last_token = ""
in_token = False
for c in expr:
if c == " ":
in_token = False
last_token = append_token(last_token, tokens)
elif is_op(c) or is_right_paran(c) or is_left_paran(c):
in_token = False
last_token = append_token(last_token, tokens)
in_token = True
last_token += c
if not in_token and last_token != "":
last_token = append_token(last_token, tokens)
if in_token:
append_token(last_token, tokens)
return tokens
# notes are taken from
def infix_to_prefix(expr):
"""converts the infix expression to prefix using the shunting yard algorithm"""
ops = []
results = []
for token in tokenize(expr):
#print ops, results
if is_op(token):
#If the token is an operator, o1, then:
#while there is an operator token, o2, at the top of the stack, and
#either o1 is left-associative and its precedence is less than or equal to that of o2,
#or o1 is right-associative and its precedence is less than that of o2,
#pop o2 off the stack, onto the output queue;
#push o1 onto the stack.
while len(ops) > 0 and is_op(ops[-1]) and \
( (associativity(token) == 'left' and precedence(token) <= precedence(ops[-1])) \
or (associativity(token) == 'right' and precedence(token) < precedence(ops[-1])) ):
#If the token is a left parenthesis, then push it onto the stack.
elif is_left_paran(token):
#If the token is a right parenthesis:
elif is_right_paran(token):
#Until the token at the top of the stack is a left parenthesis, pop operators off the stack onto the output queue.
while len(ops) > 0 and not is_left_paran(ops[-1]):
#Pop the left parenthesis from the stack, but not onto the output queue.
#If the stack runs out without finding a left parenthesis, then there are mismatched parentheses.
if len(ops) == 0:
print "error: mismatched parentheses"
if is_left_paran(ops[-1]):
#If the token is a number, then add it to the output queue.
#When there are no more tokens to read:
#While there are still operator tokens in the stack:
while len(ops) > 0:
#If the operator token on the top of the stack is a parenthesis, then there are mismatched parentheses.
if is_right_paran(ops[-1]) or is_left_paran(ops[-1]):
print "error: mismatched parentheses"
#Pop the operator onto the output queue.
return results
if __name__ == '__main__':
if len(sys.argv) == 1:
print "usage", sys.argv[0], "\"infix boolean expression\""
print "e.g. \"( true & false | ( true & ! true ) )\""
print ' '.join(infix_to_prefix(sys.argv[1]))
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