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calculus.py
409
calculus.py
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#!/usr/bin/env python
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# encoding: utf-8
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from generic import Stack
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from fraction import Fraction
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def str2tokens(exp):
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"""Convert an expression into a list of tokens
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:param exp: The expression
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:returns: the list of tokens
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>>> str2tokens("1 + 2")
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[1, '+', 2]
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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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def infixToPostfix(infixTokens):
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"""Transform an infix list of tokens into postfix tokens
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:param infixTokens: an infix list of tokens
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:returns: the corresponding postfix list of tokens
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:Example:
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>>> infixToPostfix([1, "+", 2])
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[1, 2, '+']
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>>> infixToPostfix([1, "*", 2, "+", 3])
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[1, 2, '*', 3, '+']
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"""
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priority = {"*" : 3, "/": 3, "+": 2, "-":2, "(": 1}
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opStack = Stack()
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postfixList = []
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#infixTokens = infixExp.split(" ")
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for token in infixTokens:
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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 isOperation(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 (priority[opStack.peek()] >= 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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def computePostfix(postfixTokens):
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"""Compute a postfix list of tokens
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:param postfixTokens: a postfix list of tokens
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:returns: the result of the calculus
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"""
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#print(postfixToInfix(postfixExp))
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# where to save numbers or
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operandeStack = Stack()
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#tokenList = postfixExp.split(" ")
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for (i,token) in enumerate(postfixTokens):
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if isOperation(token):
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op2 = operandeStack.pop()
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op1 = operandeStack.pop()
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res = doMath(token, op1, op2)
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operandeStack.push(res)
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#print("Operation: {op1} {op} {op2}".format(op1 = op1, op = token, op2 = op2))
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#print(operandeStack)
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#print(postfixTokens[i+1:])
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newPostfix = " ".join(operandeStack + postfixTokens[i+1:])
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#print(postfixToInfix(newPostfix))
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else:
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operandeStack.push(token)
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return operandeStack.pop()
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def computePostfixBis(postfixTokens):
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"""Compute a postfix list of tokens like a good student
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:param postfixTokens: a postfix list of tokens
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:returns: the result of the expression
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"""
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# where to save numbers or
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operandeStack = Stack()
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#tokenList = postfixExp.split(" ")
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tokenList = postfixTokens.copy()
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steps = []
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steps = []
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# On fait le calcul jusqu'à n'avoir plus qu'un élément
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while len(tokenList) > 1:
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tmpTokenList = []
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# on va chercher les motifs du genre A B + pour les calculer
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while len(tokenList) > 2:
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if isNumber(tokenList[0]) and isNumber(tokenList[1]) and isOperation(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 = 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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tokenList = steps[-1].copy()
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return steps
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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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def isOperation(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 doMath(op, op1, op2):
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"""Compute "op1 op op2"
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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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def postfixToInfix(postfixTokens):
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"""Transforms postfix list of tokens into infix string
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:param postfixTokens: a postfix list of tokens
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:returns: the corresponding infix string
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"""
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operandeStack = Stack()
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#print(postfixTokens)
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#tokenList = postfixExp.split(" ")
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for (i,token) in enumerate(postfixTokens):
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if isOperation(token):
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op2 = operandeStack.pop()
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if needPar(op2, token, "after"):
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op2 = "( " + str(op2) + " )"
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op1 = operandeStack.pop()
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if needPar(op1, token, "before"):
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op1 = "( " + str(op1) + " )"
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res = "{op1} {op} {op2}".format(op1 = op1, op = token, op2 = op2)
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operandeStack.push(res)
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else:
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operandeStack.push(token)
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return operandeStack.pop()
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def needPar(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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priority = {"*" : 3, "/": 3, "+": 2, "-":2}
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if isNumber(operande) and operande < 0:
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return 1
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elif not isNumber(operande):
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# Si c'est une grande expression ou un chiffre négatif
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stand_alone = 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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#debug_var("stand_alone",stand_alone)
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#debug_var("operande", type(operande))
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minor_priority = priority[get_main_op(operande)] < 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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def get_main_op(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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priority = {"*" : 3, "/": 3, "+": 2, "-":2}
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parStack = Stack()
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#tokenList = exp.split(" ")
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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 isOperation(token) and parStack.isEmpty():
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main_op.append(token)
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return min(main_op, key = lambda s: priority[s])
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def expand_list(list_list):
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"""Expand list of list
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:param list: the list to expande
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:returns: list of expanded lists
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:Example:
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>>> expand_list([1,2,[3,4],5,[6,7,8]])
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[[1, 2, 3, 5, 6], [1, 2, 4, 5, 7], [1, 2, 4, 5, 8]]
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>>> expand_list([1,2,4,5,6,7,8])
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[[1, 2, 4, 5, 6, 7, 8]]
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"""
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list_in_list = [i for i in list_list if type(i) == list].copy()
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try:
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nbr_ans_list = max([len(i) for i in list_in_list])
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ans = [list_list.copy() for i in range(nbr_ans_list)]
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for (i,l) in enumerate(ans):
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for (j,e) in enumerate(l):
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if type(e) == list:
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ans[i][j] = e[min(i,len(e)-1)]
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# S'il n'y a pas eut d'étapes intermédiaires (2e exemple)
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except ValueError:
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ans = [list_list]
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return ans
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def print_steps(steps):
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"""Juste print a list
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:param steps: @todo
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:returns: @todo
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"""
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print("{first} \t = {sec}".format(first = str_from_postfix(steps[0]), sec = str_from_postfix(steps[1])))
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for i in steps[2:]:
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print("\t\t = {i}".format(i=str_from_postfix(i)))
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def str_from_postfix(postfix):
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"""Return the string representing the expression
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:param postfix: a postfix ordered list of tokens
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:returns: the corresponding string expression
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"""
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infix = postfixToInfix(postfix)
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return infix
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def debug_var(name, var):
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"""print the name of the variable and the value
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:param name: the name of the variable
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:param var: the variable we want information
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"""
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print(name, ": ", var)
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def test(exp):
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"""Make various test on an expression
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"""
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print("-------------")
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print("Expression ",exp)
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tokens = str2tokens(exp)
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postfix = infixToPostfix(tokens)
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#print("Postfix " , postfix)
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#print(computePostfix(postfix))
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#print("Bis")
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steps = [postfix]
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steps += computePostfixBis(postfix)
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print_steps(steps)
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#print(postfixToInfix(postfix))
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#print(get_main_op(exp))
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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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#
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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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#
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#exp = "( 2 + 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 - 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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#print(expand_list([1,2,['a','b','c'], 3, ['d','e']]))
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## Ce denier pose un soucis. Pour le faire marcher il faudrai implémenter le calcul avec les fractions
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#exp = "( 2 + 5 ) / 3 * 4"
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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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@ -1,115 +0,0 @@
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#!/usr/bin/env python
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# encoding: utf-8
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from generic import Stack
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from calculus import isNumber, doMath
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class Expression(object):
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"""An arithmetic expression"""
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priority = {"*" : 3, "/": 3, "+": 2, "-":2, "(": 1}
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def __init__(self, exp, fix = "infix"):
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"""Initiate the expression.
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:param exp: the string representing the expression (infx form by default)
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:param fix: form of the expression infix (default) - postfix - prefix
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"""
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if fix == "infix":
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self._exp_infix = exp
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self._token_infix = exp.split(" ")
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elif fix == "postfix":
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self._token_postfix = exp
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else:
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print("Pas encore fait!")
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def infixToPostfix(self):
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"""Convert the infix expression into postfix expression.
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"""
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#@todo importer les exemples
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opStack = Stack()
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postfixList = []
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for token in self._token_infix:
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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 token in "+-*/":
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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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self._token_postfix = postfixList
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self._exp_postfix = " ".join(postfixList)
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def computePostfix(self):
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"""Compute a postfix expression like a good student
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:returns: list of steps to reach the result (postfix form)
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"""
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tokenList = self._token_postfix.copy()
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tmpTokenList = []
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# on va chercher les motifs du genre A B + pour les calculer
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while len(tokenList) > 2:
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#print(tokenList[2])
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if isNumber(tokenList[0]) and isNumber(tokenList[1]) and tokenList[2] in "+-*/":
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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 = 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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if len(tmpTokenList) > 1:
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next_steps = Expression(tmpTokenList, fix = "postfix").computePostfix()
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else:
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next_steps = tmpTokenList
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print(self._exp_postfix)
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return [self._exp_postfix] + next_steps
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def test(exp):
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"""Make various test on an expression
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"""
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print("-------------")
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print("Expression ",exp)
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expression = Expression(exp)
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expression.infixToPostfix()
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print(expression.computePostfix())
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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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# -----------------------------
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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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@ -1,191 +0,0 @@
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#!/usr/bin/env python
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# encoding: utf-8
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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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self._tokens = {}
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self._strings = {}
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if type(exp) == list:
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fix = self.get_fix(exp)
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self._tokens[fix] = exp
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elif type(exp) == str:
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tokens = self.parseExp(exp)
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fix = self.get_fix(tokens)
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self._tokens[fix] = tokens
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self._strings[fix] = exp
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else:
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raise ValueError("The expression needs to be a string or a list of token")
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# ---------------------
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# String parsing
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# @classmethod ????
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def parseExp(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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return exp.split(" ")
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# ---------------------
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# "fix" recognition
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def get_fix(self, tokens):
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""" Give the "fix" of an expression
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infix -> A + B
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||||
prefix -> + A B
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postfix -> A B +
|
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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 tokens[0] in "+-*/":
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return "prefix"
|
||||
elif token[0] not in "+-*/" ans token[1] not in "+-*/":
|
||||
return "postfix"
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||||
else:
|
||||
return "infix"
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||||
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# ----------------------
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# Expressions - tokens getters
|
||||
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||||
def tokens(self, fix = "infix"):
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"""Get the list of tokens with the wanted fix
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:param fix: the fix wanted (infix default)
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:returns: list of tokens
|
||||
|
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"""
|
||||
# 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
|
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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
|
||||
Loading…
Reference in New Issue