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lafrite 2014-01-15 17:04:24 +01:00
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calculus.py
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#!/usr/bin/env python
# encoding: utf-8
from generic import Stack
from fraction import Fraction
def str2tokens(exp):
"""Convert an expression into a list of tokens
:param exp: The expression
:returns: the list of tokens
>>> str2tokens("1 + 2")
[1, '+', 2]
"""
tokens = exp.split(" ")
for (i,t) in enumerate(tokens):
try:
tokens[i] = int(t)
except ValueError:
pass
return tokens
def infixToPostfix(infixTokens):
"""Transform an infix list of tokens into postfix tokens
:param infixTokens: an infix list of tokens
:returns: the corresponding postfix list of tokens
:Example:
>>> infixToPostfix([1, "+", 2])
[1, 2, '+']
>>> infixToPostfix([1, "*", 2, "+", 3])
[1, 2, '*', 3, '+']
"""
priority = {"*" : 3, "/": 3, "+": 2, "-":2, "(": 1}
opStack = Stack()
postfixList = []
#infixTokens = infixExp.split(" ")
for token in infixTokens:
if token == "(":
opStack.push(token)
elif token == ")":
topToken = opStack.pop()
while topToken != "(":
postfixList.append(topToken)
topToken = opStack.pop()
elif isOperation(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 (priority[opStack.peek()] >= priority[token]):
postfixList.append(opStack.pop())
opStack.push(token)
else:
postfixList.append(token)
while not opStack.isEmpty():
postfixList.append(opStack.pop())
return postfixList
def computePostfix(postfixTokens):
"""Compute a postfix list of tokens
:param postfixTokens: a postfix list of tokens
:returns: the result of the calculus
"""
#print(postfixToInfix(postfixExp))
# where to save numbers or
operandeStack = Stack()
#tokenList = postfixExp.split(" ")
for (i,token) in enumerate(postfixTokens):
if isOperation(token):
op2 = operandeStack.pop()
op1 = operandeStack.pop()
res = doMath(token, op1, op2)
operandeStack.push(res)
#print("Operation: {op1} {op} {op2}".format(op1 = op1, op = token, op2 = op2))
#print(operandeStack)
#print(postfixTokens[i+1:])
newPostfix = " ".join(operandeStack + postfixTokens[i+1:])
#print(postfixToInfix(newPostfix))
else:
operandeStack.push(token)
return operandeStack.pop()
def computePostfixBis(postfixTokens):
"""Compute a postfix list of tokens like a good student
:param postfixTokens: a postfix list of tokens
:returns: the result of the expression
"""
# where to save numbers or
operandeStack = Stack()
#tokenList = postfixExp.split(" ")
tokenList = postfixTokens.copy()
steps = []
steps = []
# On fait le calcul jusqu'à n'avoir plus qu'un élément
while len(tokenList) > 1:
tmpTokenList = []
# on va chercher les motifs du genre A B + pour les calculer
while len(tokenList) > 2:
if isNumber(tokenList[0]) and isNumber(tokenList[1]) and isOperation(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)
tokenList = steps[-1].copy()
return steps
def isNumber(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
def isOperation(exp):
"""Check if the expression is an opération in "+-*/"
:param exp: an expression
:returns: boolean
"""
return (type(exp) == str and exp in "+-*/")
def doMath(op, op1, op2):
"""Compute "op1 op op2"
: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)
def postfixToInfix(postfixTokens):
"""Transforms postfix list of tokens into infix string
:param postfixTokens: a postfix list of tokens
:returns: the corresponding infix string
"""
operandeStack = Stack()
#print(postfixTokens)
#tokenList = postfixExp.split(" ")
for (i,token) in enumerate(postfixTokens):
if isOperation(token):
op2 = operandeStack.pop()
if needPar(op2, token, "after"):
op2 = "( " + str(op2) + " )"
op1 = operandeStack.pop()
if needPar(op1, token, "before"):
op1 = "( " + str(op1) + " )"
res = "{op1} {op} {op2}".format(op1 = op1, op = token, op2 = op2)
operandeStack.push(res)
else:
operandeStack.push(token)
return operandeStack.pop()
def needPar(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
"""
priority = {"*" : 3, "/": 3, "+": 2, "-":2}
if isNumber(operande) and operande < 0:
return 1
elif not isNumber(operande):
# Si c'est une grande expression ou un chiffre négatif
stand_alone = get_main_op(operande)
# Si la priorité de l'operande est plus faible que celle de l'opérateur
#debug_var("stand_alone",stand_alone)
#debug_var("operande", type(operande))
minor_priority = priority[get_main_op(operande)] < 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
def get_main_op(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
"""
priority = {"*" : 3, "/": 3, "+": 2, "-":2}
parStack = Stack()
#tokenList = exp.split(" ")
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 isOperation(token) and parStack.isEmpty():
main_op.append(token)
return min(main_op, key = lambda s: priority[s])
def expand_list(list_list):
"""Expand list of list
:param list: the list to expande
:returns: list of expanded lists
:Example:
>>> expand_list([1,2,[3,4],5,[6,7,8]])
[[1, 2, 3, 5, 6], [1, 2, 4, 5, 7], [1, 2, 4, 5, 8]]
>>> expand_list([1,2,4,5,6,7,8])
[[1, 2, 4, 5, 6, 7, 8]]
"""
list_in_list = [i for i in list_list if type(i) == list].copy()
try:
nbr_ans_list = max([len(i) for i in list_in_list])
ans = [list_list.copy() for i in range(nbr_ans_list)]
for (i,l) in enumerate(ans):
for (j,e) in enumerate(l):
if type(e) == list:
ans[i][j] = e[min(i,len(e)-1)]
# S'il n'y a pas eut d'étapes intermédiaires (2e exemple)
except ValueError:
ans = [list_list]
return ans
def print_steps(steps):
"""Juste print a list
:param steps: @todo
:returns: @todo
"""
print("{first} \t = {sec}".format(first = str_from_postfix(steps[0]), sec = str_from_postfix(steps[1])))
for i in steps[2:]:
print("\t\t = {i}".format(i=str_from_postfix(i)))
def str_from_postfix(postfix):
"""Return the string representing the expression
:param postfix: a postfix ordered list of tokens
:returns: the corresponding string expression
"""
infix = postfixToInfix(postfix)
return infix
def debug_var(name, var):
"""print the name of the variable and the value
:param name: the name of the variable
:param var: the variable we want information
"""
print(name, ": ", var)
def test(exp):
"""Make various test on an expression
"""
print("-------------")
print("Expression ",exp)
tokens = str2tokens(exp)
postfix = infixToPostfix(tokens)
#print("Postfix " , postfix)
#print(computePostfix(postfix))
#print("Bis")
steps = [postfix]
steps += computePostfixBis(postfix)
print_steps(steps)
#print(postfixToInfix(postfix))
#print(get_main_op(exp))
if __name__ == '__main__':
exp = "1 + 3 * 5"
test(exp)
#exp = "2 * 3 * 3 * 5"
#test(exp)
#exp = "2 * 3 + 3 * 5"
#test(exp)
#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)
#
#exp = "( 2 + 5 ) * ( 3 - 4 )"
#test(exp)
#
#exp = "( 2 + 5 ) * ( 3 * 4 )"
#test(exp)
#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)
#print(expand_list([1,2,['a','b','c'], 3, ['d','e']]))
## Ce denier pose un soucis. Pour le faire marcher il faudrai implémenter le calcul avec les fractions
#exp = "( 2 + 5 ) / 3 * 4"
#test(exp)
import doctest
doctest.testmod()
# -----------------------------
# Reglages pour 'vim'
# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
# cursor: 16 del

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expression.py.back
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#!/usr/bin/env python
# encoding: utf-8
from generic import Stack
from calculus import isNumber, doMath
class Expression(object):
"""An arithmetic expression"""
priority = {"*" : 3, "/": 3, "+": 2, "-":2, "(": 1}
def __init__(self, exp, fix = "infix"):
"""Initiate the expression.
:param exp: the string representing the expression (infx form by default)
:param fix: form of the expression infix (default) - postfix - prefix
"""
if fix == "infix":
self._exp_infix = exp
self._token_infix = exp.split(" ")
elif fix == "postfix":
self._token_postfix = exp
else:
print("Pas encore fait!")
def infixToPostfix(self):
"""Convert the infix expression into postfix expression.
"""
#@todo importer les exemples
opStack = Stack()
postfixList = []
for token in self._token_infix:
if token == "(":
opStack.push(token)
elif token == ")":
topToken = opStack.pop()
while topToken != "(":
postfixList.append(topToken)
topToken = opStack.pop()
elif token in "+-*/":
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._token_postfix = postfixList
self._exp_postfix = " ".join(postfixList)
def computePostfix(self):
"""Compute a postfix expression like a good student
:returns: list of steps to reach the result (postfix form)
"""
tokenList = self._token_postfix.copy()
tmpTokenList = []
# on va chercher les motifs du genre A B + pour les calculer
while len(tokenList) > 2:
#print(tokenList[2])
if isNumber(tokenList[0]) and isNumber(tokenList[1]) and tokenList[2] in "+-*/":
# 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
if len(tmpTokenList) > 1:
next_steps = Expression(tmpTokenList, fix = "postfix").computePostfix()
else:
next_steps = tmpTokenList
print(self._exp_postfix)
return [self._exp_postfix] + next_steps
def test(exp):
"""Make various test on an expression
"""
print("-------------")
print("Expression ",exp)
expression = Expression(exp)
expression.infixToPostfix()
print(expression.computePostfix())
if __name__ == '__main__':
exp = "1 + 3 * 5"
test(exp)
exp = "2 * 3 * 3 * 5"
test(exp)
exp = "2 * 3 + 3 * 5"
test(exp)
# -----------------------------
# Reglages pour 'vim'
# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
# cursor: 16 del

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expression.py_back
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#!/usr/bin/env python
# encoding: utf-8
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
"""
self._tokens = {}
self._strings = {}
if type(exp) == list:
fix = self.get_fix(exp)
self._tokens[fix] = exp
elif type(exp) == str:
tokens = self.parseExp(exp)
fix = self.get_fix(tokens)
self._tokens[fix] = tokens
self._strings[fix] = exp
else:
raise ValueError("The expression needs to be a string or a list of token")
# ---------------------
# String parsing
# @classmethod ????
def parseExp(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
def get_fix(self, tokens):
""" Give the "fix" of an expression
infix -> A + B
prefix -> + A B
postfix -> A B +
:param exp: the expression (list of token)
:returns: the "fix" (infix, postfix, prefix)
"""
if tokens[0] in "+-*/":
return "prefix"
elif token[0] not in "+-*/" ans token[1] not in "+-*/":
return "postfix"
else:
return "infix"
# ----------------------
# Expressions - tokens getters
def tokens(self, fix = "infix"):
"""Get the list of tokens with the wanted fix
:param fix: the fix wanted (infix default)
:returns: list of tokens
"""
# Si ce fix n'a pas encore été enregistré
if fix not in self._tokens:
# Il peut venir de la version string
if fix in self._string:
self._tokens[fix] = self.parseExp(self._string[fix])
# Sinon il faut le calculer à partir d'une autre forme
else:
fix_transfo = "to" + fix.capitalize()
getattr(self,fix_transfo)()
return self._tokens[fix]
##### On en est là,il faudra faire attention à bien vérifier ce que les "to..." enregistre (string ou tokens)
def string(self, fix = "infix"):
"""Get the string with the wanted fix
:param fix: the fix wanted (infix default)
:returns: the string representing the expression
"""
# Si ce fix n'a pas encore été enregistré
if fix not in self._string:
# Il peut venir de la version string
if fix in self._tokens:
self._string[fix] = self.parseExp(self._string[fix])
# Sinon il faut le calculer à partir d'une autre forme
else:
fix_transfo = "to" + fix.capitalize()
getattr(self,fix_transfo)()
return self._string[fix]
# ----------------------
# "fix" tranformations
def toPostfix(self):
""" Transorm the expression into postfix form using the infix form"""
pass
def toInfix(self):
""" Tranform the expression into infix form using postfix form"""
pass
# ---------------------
# Tools for placing parenthesis in infix notation
def needPar(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 "-" in operande:
return 1
elif not isNumber(operande):
# Si c'est une grande expression ou un chiffre négatif
stand_alone = get_main_op(operande)
# Si la priorité de l'operande est plus faible que celle de l'opérateur
minor_priority = self.priority[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
# J'aime pas bien cette endroit faudrait que ce soit une méthode qui s'applique uniquement à l'expression en question (self) pas à n'importe quel string, ça serait plus propre.
def get_main_op(exp):
""" Gives the main operation of the expression
:param exp: the expression
:returns: the main operation (+, -, * or /) or 0 if the expression is only one element
"""
parStack = Stack()
tokenList = exp.split(" ")
if len(tokenList) == 1:
# Si l'expression n'est qu'un élément
return 0
main_op = []
for token in tokenList:
if token == "(":
parStack.push(token)
elif token == ")":
parStack.pop()
elif token in "+-*/" and parStack.isEmpty():
main_op.append(token)
return min(main_op, key = lambda s: priority[s])
# ---------------------
# Computing the expression
def compute(self):
""" Recursive method for computing as a student the expression
:returns: list of steps needed to reach the result
"""
pass
def doMath(op, op1, op2):
"""Compute "op1 op op2"
:param op: operator
:param op1: first operande
:param op2: second operande
:returns: string representing the result
"""
return str(eval(op1 + op + op2))
# -----------------------------
# Reglages pour 'vim'
# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
# cursor: 16 del