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