Mapytex/expression.py

430 lines
13 KiB
Python
Raw Normal View History

2013-08-09 09:35:14 +00:00
#!/usr/bin/env python
# encoding: utf-8
2013-11-01 21:58:42 +00:00
from generic import Stack, flatten_list, expand_list
from fraction import Fraction
2013-08-09 09:35:14 +00:00
class Expression(object):
"""A calculus expression. Today it can andle only expression with numbers later it will be able to manipulate unknown"""
2013-11-01 21:58:42 +00:00
PRIORITY = {"*" : 3, "/": 3, "+": 2, "-":2, "(": 1}
2013-08-09 11:08:24 +00:00
2013-08-09 09:35:14 +00:00
def __init__(self, exp):
2013-11-01 11:42:42 +00:00
""" Initiate the expression
2013-08-09 09:35:14 +00:00
:param exp: the expression. It can be a string or a list of tokens. It can be infix or postfix expression
"""
2013-11-01 21:58:42 +00:00
if type(exp) == str:
self._exp = exp
self.tokens = self.str2tokens(exp) # les tokens seront alors stockés dans self.tokens temporairement
elif type(exp) == list:
self.tokens = exp
2013-08-09 09:35:14 +00:00
2013-11-08 09:05:28 +00:00
self._infix_tokens = None
self._postfix_tokens = None
self.feed_fix() # Determine le fix et range la liste dans self.[fix]_tokens
2013-11-01 21:58:42 +00:00
## ---------------------
## Mechanism functions
def simplify(self, render = lambda x:str(x)):
""" Generator which return steps for computing the expression
2013-11-08 09:05:28 +00:00
2013-11-01 21:58:42 +00:00
@param render: function which render the list of token (postfix form now)
2013-11-08 09:05:28 +00:00
2013-11-01 21:58:42 +00:00
"""
if not self.can_go_further():
2013-11-02 15:36:08 +00:00
yield render(self.postfix_tokens)
else:
2013-11-02 15:36:08 +00:00
self.compute_exp()
2013-11-16 20:39:13 +00:00
old_s = ''
2013-11-01 21:58:42 +00:00
for s in self.steps:
2013-11-16 20:39:13 +00:00
new_s = render(s)
# Astuce pour éviter d'avoir deux fois la même étape (par exemple pour la transfo d'une division en fraction)
2013-11-16 20:39:13 +00:00
if new_s != old_s:
old_s = new_s
yield new_s
2013-11-02 15:36:08 +00:00
for s in self.child.simplify(render = render):
if old_s != s:
yield s
2013-11-01 21:58:42 +00:00
def can_go_further(self):
2013-11-02 15:36:08 +00:00
"""Check whether it's a last step or not. If not create self.child the next expression.
2013-11-01 21:58:42 +00:00
:returns: 1 if it's not the last step, 0 otherwise
"""
if len(self.tokens) == 1:
return 0
else:
return 1
def compute_exp(self):
2013-11-02 15:36:08 +00:00
""" Create self.child with self.steps to go up to it """
2013-11-01 21:58:42 +00:00
self.steps = [self.postfix_tokens]
tokenList = self.postfix_tokens.copy()
tmpTokenList = []
while len(tokenList) > 2:
# on va chercher les motifs du genre A B + pour les calculer
2013-11-02 15:36:08 +00:00
if self.isNumber(tokenList[0]) and self.isNumber(tokenList[1]) and self.isOperator(tokenList[2]):
2013-11-01 21:58:42 +00:00
# S'il y a une opération à faire
op1 = tokenList[0]
op2 = tokenList[1]
token = tokenList[2]
2013-11-02 15:36:08 +00:00
res = self.doMath(token, op1, op2)
2013-11-01 21:58:42 +00:00
tmpTokenList.append(res)
# Comme on vient de faire le calcul, on peut détruire aussi les deux prochains termes
del tokenList[0:3]
else:
tmpTokenList.append(tokenList[0])
del tokenList[0]
tmpTokenList += tokenList
2013-11-02 15:36:08 +00:00
steps = expand_list(tmpTokenList)
2013-11-01 21:58:42 +00:00
if len(steps[:-1]) > 0:
self.steps += [flatten_list(s) for s in steps[:-1]]
2013-11-02 15:36:08 +00:00
self.child = Expression(steps[-1])
2013-11-01 11:42:42 +00:00
## ---------------------
## String parsing
## @classmethod ????
2013-11-01 21:58:42 +00:00
def str2tokens(self, exp):
""" Parse the expression, ie tranform a string into a list of tokens
2013-11-01 11:42:42 +00:00
2013-11-01 21:58:42 +00:00
:param exp: The expression (a string)
:returns: list of token
2013-11-01 11:42:42 +00:00
2013-11-01 21:58:42 +00:00
"""
2013-11-02 15:36:08 +00:00
tokens = exp.split(" ")
for (i,t) in enumerate(tokens):
try:
tokens[i] = int(t)
except ValueError:
pass
return tokens
2013-11-01 11:42:42 +00:00
2013-11-01 21:58:42 +00:00
# ---------------------
# "fix" recognition
2013-11-01 11:42:42 +00:00
2013-11-01 21:58:42 +00:00
@classmethod
def get_fix(self, tokens):
""" Give the "fix" of an expression
2013-11-08 09:05:28 +00:00
[A, +, B] -> infix, or if there is parenthesis it is infix
2013-11-01 21:58:42 +00:00
[+, A, B] -> prefix
[A, B, +] -> postfix
/!\ does not verify if the expression is correct/computable!
:param exp: the expression (list of token)
:returns: the "fix" (infix, postfix, prefix)
"""
if self.isOperator(tokens[0]):
return "prefix"
2013-11-08 09:05:28 +00:00
elif "(" in tokens:
return "infix"
2013-11-01 21:58:42 +00:00
elif not self.isOperator(tokens[0]) and not self.isOperator(tokens[1]):
return "postfix"
else:
return "infix"
2013-11-08 09:05:28 +00:00
def feed_fix(self):
2013-11-01 21:58:42 +00:00
""" Recognize the fix of self.tokens and stock tokens in self.[fix]_tokens """
2013-11-02 15:36:08 +00:00
if len(self.tokens) > 1:
fix = self.get_fix(self.tokens)
else:
fix = "postfix" # Completement arbitraire mais on s'en fiche!
2013-11-01 21:58:42 +00:00
setattr(self, fix+"_tokens", self.tokens)
2013-11-08 09:05:28 +00:00
2013-11-01 21:58:42 +00:00
# ----------------------
# Expressions - tokens manipulation
@property
def infix_tokens(self):
""" Return infix list of tokens. Verify if it has already been computed and compute it if not
:returns: infix list of tokens
"""
2013-11-08 09:05:28 +00:00
if self._infix_tokens:
2013-11-01 21:58:42 +00:00
return self._infix_tokens
2013-11-08 09:05:28 +00:00
elif self._postfix_tokens:
self._infix_tokens = self.post2in_fix(self._postfix_tokens)
2013-11-01 21:58:42 +00:00
return self._infix_tokens
else:
raise ValueError("Unkown fix")
@infix_tokens.setter
def infix_tokens(self, val):
self._infix_tokens = val
@property
def postfix_tokens(self):
""" Return postfix list of tokens. Verify if it has already been computed and compute it if not
:returns: postfix list of tokens
"""
2013-11-08 09:05:28 +00:00
if self._postfix_tokens:
2013-11-01 21:58:42 +00:00
return self._postfix_tokens
2013-11-08 09:05:28 +00:00
elif self._infix_tokens:
self._postfix_tokens = self.in2post_fix(self._infix_tokens)
2013-11-01 21:58:42 +00:00
return self._postfix_tokens
else:
raise ValueError("Unkown fix")
@postfix_tokens.setter
def postfix_tokens(self, val):
self._postfix_tokens = val
# ----------------------
# "fix" tranformations
@classmethod
def in2post_fix(self, infix_tokens):
""" From the infix_tokens list compute the corresponding postfix_tokens list
2013-11-08 09:05:28 +00:00
@param infix_tokens: the infix list of tokens to transform into postfix form.
@return: the corresponding postfix list of tokens.
2013-11-08 09:05:28 +00:00
>>> Expression.in2post_fix(['(', 2, '+', 5, '-', 1, ')', '/', '(', 3, '*', 4, ')'])
[2, 5, '+', 1, '-', 3, 4, '*', '/']
"""
2013-11-01 21:58:42 +00:00
opStack = Stack()
postfixList = []
2013-11-08 09:05:28 +00:00
for token in infix_tokens:
2013-11-01 21:58:42 +00:00
if token == "(":
opStack.push(token)
elif token == ")":
topToken = opStack.pop()
while topToken != "(":
postfixList.append(topToken)
topToken = opStack.pop()
elif self.isOperator(token):
# On doit ajouter la condition == str sinon python ne veut pas tester l'appartenance à la chaine de caractère.
while (not opStack.isEmpty()) and (self.PRIORITY[opStack.peek()] >= self.PRIORITY[token]):
postfixList.append(opStack.pop())
opStack.push(token)
else:
postfixList.append(token)
while not opStack.isEmpty():
postfixList.append(opStack.pop())
return postfixList
2013-11-08 09:05:28 +00:00
@classmethod
def post2in_fix(self, postfix_tokens):
""" From the postfix_tokens list compute the corresponding infix_tokens list
2013-11-08 09:05:28 +00:00
@param postfix_tokens: the postfix list of tokens to transform into infix form.
@return: the corresponding infix list of tokens if postfix_tokens.
2013-11-08 09:05:28 +00:00
>>> Expression.post2in_fix([2, 5, '+', 1, '-', 3, 4, '*', '/'])
['( ', 2, '+', 5, '-', 1, ' )', '/', '( ', 3, '*', 4, ' )']
>>> Expression.post2in_fix([2])
[2]
2013-11-08 09:05:28 +00:00
"""
2013-11-01 21:58:42 +00:00
operandeStack = Stack()
2013-11-08 09:05:28 +00:00
for token in postfix_tokens:
2013-11-01 21:58:42 +00:00
if self.isOperator(token):
op2 = operandeStack.pop()
2013-11-01 21:58:42 +00:00
if self.needPar(op2, token, "after"):
op2 = ["( ", op2, " )"]
op1 = operandeStack.pop()
2013-11-01 21:58:42 +00:00
if self.needPar(op1, token, "before"):
op1 = ["( ", op1, " )"]
res = [op1, token, op2]
operandeStack.push(res)
else:
operandeStack.push(token)
# Manip pour gerer les cas similaires au deuxième exemple
infix_tokens = operandeStack.pop()
if type(infix_tokens) == list:
infix_tokens = flatten_list(infix_tokens)
elif self.isNumber(infix_tokens):
infix_tokens = [infix_tokens]
2013-11-08 09:05:28 +00:00
return infix_tokens
2013-11-01 21:58:42 +00:00
# ---------------------
# Tools for placing parenthesis in infix notation
@classmethod
def needPar(self, operande, operator, posi = "after"):
"""Says whether or not the operande needs parenthesis
:param operande: the operande
:param operator: the operator
:param posi: "after"(default) if the operande will be after the operator, "before" othewise
:returns: bollean
"""
2013-11-02 15:36:08 +00:00
if self.isNumber(operande) and operande < 0:
2013-11-01 21:58:42 +00:00
return 1
2013-11-02 15:36:08 +00:00
elif not self.isNumber(operande):
2013-11-01 21:58:42 +00:00
# Si c'est une grande expression ou un chiffre négatif
stand_alone = self.get_main_op(operande)
# Si la priorité de l'operande est plus faible que celle de l'opérateur
minor_priority = self.PRIORITY[self.get_main_op(operande)] < self.PRIORITY[operator]
# Si l'opérateur est -/ pour after ou juste / pour before
special = (operator in "-/" and posi == "after") or (operator in "/" and posi == "before")
return stand_alone and (minor_priority or special)
else:
return 0
@classmethod
def get_main_op(self, tokens):
"""Getting the main operation of the list of tokens
:param exp: the list of tokens
:returns: the main operation (+, -, * or /) or 0 if the expression is only one element
"""
parStack = Stack()
if len(tokens) == 1:
# Si l'expression n'est qu'un élément
return 0
main_op = []
for token in tokens:
if token == "(":
parStack.push(token)
elif token == ")":
parStack.pop()
elif self.isOperator(token) and parStack.isEmpty():
main_op.append(token)
return min(main_op, key = lambda s: self.PRIORITY[s])
2013-11-01 11:42:42 +00:00
## ---------------------
## Computing the expression
@staticmethod
def doMath(op, op1, op2):
2013-11-01 21:58:42 +00:00
"""Compute "op1 op op2" or create a fraction
2013-11-01 11:42:42 +00:00
2013-11-01 21:58:42 +00:00
:param op: operator
:param op1: first operande
:param op2: second operande
:returns: string representing the result
2013-11-01 11:42:42 +00:00
2013-11-01 21:58:42 +00:00
"""
operations = {"+": "__add__", "-": "__sub__", "*": "__mul__"}
if op == "/":
ans = [Fraction(op1, op2)]
ans += ans[0].simplify()
return ans
else:
return getattr(op1,operations[op])(op2)
## ---------------------
## Recognize numbers and operators
2013-11-01 11:42:42 +00:00
@staticmethod
def isNumber(exp):
2013-11-01 21:58:42 +00:00
"""Check if the expression can be a number
:param exp: an expression
:returns: True if the expression can be a number and false otherwise
"""
return type(exp) == int or type(exp) == Fraction
@staticmethod
def isOperator(exp):
2013-11-01 21:58:42 +00:00
"""Check if the expression is an opération in "+-*/"
:param exp: an expression
:returns: boolean
"""
return (type(exp) == str and exp in "+-*/")
2013-11-01 11:42:42 +00:00
def test(exp):
a = Expression(exp)
#for i in a.simplify():
for i in a.simplify(render = render):
2013-11-01 11:42:42 +00:00
print(i)
2013-08-09 09:35:14 +00:00
2013-11-08 09:05:28 +00:00
print("\n")
def render(tokens):
post_tokens = Expression.post2in_fix(tokens)
return ' '.join([str(t) for t in post_tokens])
2013-11-08 09:05:28 +00:00
if __name__ == '__main__':
exp = "1 + 3 * 5"
test(exp)
2013-11-08 09:05:28 +00:00
#exp = "2 * 3 * 3 * 5"
#test(exp)
exp = "2 * 3 + 3 * 5"
test(exp)
2013-11-08 09:05:28 +00:00
exp = "2 * ( 3 + 4 ) + 3 * 5"
test(exp)
#exp = "2 * ( 3 + 4 ) + ( 3 - 4 ) * 5"
#test(exp)
#
#exp = "2 * ( 2 - ( 3 + 4 ) ) + ( 3 - 4 ) * 5"
#test(exp)
#
#exp = "2 * ( 2 - ( 3 + 4 ) ) + 5 * ( 3 - 4 )"
#test(exp)
#
#exp = "2 + 5 * ( 3 - 4 )"
#test(exp)
2013-11-08 09:05:28 +00:00
#exp = "( 2 + 5 ) * ( 3 - 4 )"
#test(exp)
2013-11-08 09:05:28 +00:00
#exp = "( 2 + 5 ) * ( 3 * 4 )"
#test(exp)
2013-11-08 09:05:28 +00:00
exp = "( 2 + 5 - 1 ) / ( 3 * 4 )"
test(exp)
exp = "( 2 + 5 ) / ( 3 * 4 ) + 1 / 12"
test(exp)
exp = "( 2 + 5 ) / ( 3 * 4 ) + 1 / 2"
test(exp)
exp = "( 2 + 5 ) / ( 3 * 4 ) + 1 / 12 + 5 * 5"
test(exp)
import doctest
doctest.testmod()
2013-08-09 09:35:14 +00:00
# -----------------------------
# Reglages pour 'vim'
# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
# cursor: 16 del