337 lines
11 KiB
Python
337 lines
11 KiB
Python
#!/usr/bin/env python
|
|
# encoding: utf-8
|
|
|
|
from generic import Stack, flatten_list, expand_list
|
|
from fraction import Fraction
|
|
|
|
def trace(f):
|
|
""" Permet de visualiser des appels récursifs à la fonction décorée """
|
|
f.indent = 0
|
|
def g(x):
|
|
print('| ' * f.indent + '|--', f.__name__, x)
|
|
f.indent += 1
|
|
value = f(x)
|
|
print( '| ' * f.indent + '|--', 'return', repr(value))
|
|
f.indent -= 1
|
|
return value
|
|
return g
|
|
|
|
class Expression(object):
|
|
"""A calculus expression. Today it can andle only expression with numbers later it will be able to manipulate unknown"""
|
|
|
|
PRIORITY = {"*" : 3, "/": 3, "+": 2, "-":2, "(": 1}
|
|
|
|
def __init__(self, exp):
|
|
""" Initiate the expression
|
|
|
|
:param exp: the expression. It can be a string or a list of tokens. It can be infix or postfix expression
|
|
"""
|
|
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
|
|
|
|
self.find_fix() # Determine le fix et range la liste dans self.[fix]_tokens
|
|
|
|
## ---------------------
|
|
## Mechanism functions
|
|
|
|
def simplify(self, render = lambda x:str(x)):
|
|
""" Generator which return steps for computing the expression
|
|
@param render: function which render the list of token (postfix form now)
|
|
"""
|
|
if not self.can_go_further():
|
|
yield render(self.postfix_tokens) # self.postfix_tokens devra être une propriété pour vérifier que quand on y accède, on a bien la forme voulu et si non, la calculer.
|
|
else:
|
|
self.compute_exp() # crée self.children et éventuellement les étapes intermédiaires pour y arriver. /!\ les étapes sont sous la forme de listes de tokens en postfix
|
|
for s in self.steps:
|
|
yield render(s)
|
|
for s in self.children.simplify(render = render):
|
|
yield render(s)
|
|
|
|
def can_go_further(self):
|
|
"""Check whether it's a last step or not. If not create self.children the next expression.
|
|
: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):
|
|
""" Create self.children with self.steps to go up to it """
|
|
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
|
|
if isNumber(tokenList[0]) and isNumber(tokenList[1]) and self.isOperator(tokenList[2]):
|
|
|
|
# S'il y a une opération à faire
|
|
op1 = tokenList[0]
|
|
op2 = tokenList[1]
|
|
token = tokenList[2]
|
|
|
|
res = doMath(token, op1, op2)
|
|
|
|
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
|
|
|
|
steps += expand_list(tmpTokenList)
|
|
|
|
self.steps += [steps[:-1]]
|
|
self.children = Expression(steps[-1])
|
|
|
|
|
|
## ---------------------
|
|
## String parsing
|
|
|
|
## @classmethod ????
|
|
def str2tokens(self, exp):
|
|
""" Parse the expression, ie tranform a string into a list of tokens
|
|
|
|
:param exp: The expression (a string)
|
|
:returns: list of token
|
|
|
|
"""
|
|
return exp.split(" ")
|
|
|
|
# ---------------------
|
|
# "fix" recognition
|
|
|
|
@classmethod
|
|
def get_fix(self, tokens):
|
|
""" Give the "fix" of an expression
|
|
[A, +, B] -> infix
|
|
[+, 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"
|
|
elif not self.isOperator(tokens[0]) and not self.isOperator(tokens[1]):
|
|
return "postfix"
|
|
else:
|
|
return "infix"
|
|
|
|
def find_fix(self):
|
|
""" Recognize the fix of self.tokens and stock tokens in self.[fix]_tokens """
|
|
fix = self.get_fix(self.tokens)
|
|
|
|
setattr(self, fix+"_tokens", self.tokens)
|
|
|
|
# ----------------------
|
|
# 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
|
|
"""
|
|
if hasattr(self, "_infix_tokens"):
|
|
return self._infix_tokens
|
|
|
|
elif hasattr(self, "_postfix_tokens"):
|
|
self.infix_tokens = self.post2in_fix()
|
|
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
|
|
"""
|
|
if hasattr(self, "_postfix_tokens"):
|
|
return self._postfix_tokens
|
|
|
|
elif hasattr(self,"_infix_tokens"):
|
|
self.postfix_tokens = self.in2post_fix()
|
|
return self._postfix_tokens
|
|
|
|
else:
|
|
raise ValueError("Unkown fix")
|
|
|
|
@postfix_tokens.setter
|
|
def postfix_tokens(self, val):
|
|
self._postfix_tokens = val
|
|
|
|
# ----------------------
|
|
# "fix" tranformations
|
|
|
|
def in2post_fix(self):
|
|
""" From the self.infix_tokens list compute the corresponding self.postfix_tokens list """
|
|
|
|
opStack = Stack()
|
|
postfixList = []
|
|
|
|
for token in self.infix_tokens:
|
|
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())
|
|
|
|
self.postfix_tokens = postfixList
|
|
|
|
def post2in_fix(self):
|
|
""" From the self.postfix_tokens list compute the corresponding self.infix_tokens list """
|
|
operandeStack = Stack()
|
|
|
|
for token in postfixTokens:
|
|
if self.isOperator(token):
|
|
op2 = operandeStack.pop()
|
|
if self.needPar(op2, token, "after"):
|
|
op2 = ["( ", op2, " )"]
|
|
op1 = operandeStack.pop()
|
|
if self.needPar(op1, token, "before"):
|
|
op1 = ["( ", op1, " )"]
|
|
res = [op1, token, op2]
|
|
|
|
operandeStack.push(res)
|
|
|
|
else:
|
|
operandeStack.push(token)
|
|
|
|
self.infix_tokens = flatten_list(operandeStack.pop())
|
|
|
|
# ---------------------
|
|
# 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
|
|
"""
|
|
|
|
if isNumber(operande) and operande < 0:
|
|
return 1
|
|
elif not isNumber(operande):
|
|
# 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])
|
|
|
|
## ---------------------
|
|
## Computing the expression
|
|
|
|
@classmethod
|
|
def doMath(self, op, op1, op2):
|
|
"""Compute "op1 op op2" or create a fraction
|
|
|
|
:param op: operator
|
|
:param op1: first operande
|
|
:param op2: second operande
|
|
:returns: string representing the result
|
|
|
|
"""
|
|
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
|
|
|
|
@classmethod
|
|
def isNumber(self, exp):
|
|
"""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
|
|
|
|
@classmethod
|
|
def isOperator(self, exp):
|
|
"""Check if the expression is an opération in "+-*/"
|
|
|
|
:param exp: an expression
|
|
:returns: boolean
|
|
|
|
"""
|
|
return (type(exp) == str and exp in "+-*/")
|
|
|
|
if __name__ == '__main__':
|
|
a = Expression("10 + 1 * 3")
|
|
for i in a.simplify():
|
|
print(i)
|
|
|
|
# -----------------------------
|
|
# Reglages pour 'vim'
|
|
# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
|
|
# cursor: 16 del
|