Python implements a simple four step calculator
- 2020-05-17 05:46:59
- OfStack
1. The algorithm
1. The main idea of the algorithm is to convert an infix expression (Infix expression) into an easy-to-handle suffix expression (Postfix expression), and then calculate the result of the expression with the help of the simple data structure of the stack.
2, about how to talk about ordinary expressions into postfix expressions, and how to deal with postfix expressions and calculate the results of the specific algorithm description is not described here, the book has a detailed explanation.
2. Simple calculator
Directions for use
A simple example of using the calculator class is as follows:
# usage
c = Calculator()
print('result: {:f}'.formart(c.get_result('1.11+2.22-3.33*4.44/5.55')))
# output:
result: 0.666000The test case
In order to test the calculator effectively, several test cases are designed. The test results are as follows:
Test No.1: (1.11) = 1.110000
Test No.2: 1.11+2.22-3.33*4.44/5.55 = 0.666000
Test No.3: 1.11+(2.22-3.33)*4.44/5.55 = 0.222000
Test No.4: 1.11+(2.22-3.33)*(4.44+5.55)/6.66 = -0.555000
Test No.5: 1.11*((2.22-3.33)*(4.44+5.55))/(6.66+7.77) = -0.852992
Test No.6: (1.11+2.22)*(3.33+4.44)/5.55*6.66 = 31.048920
Test No.7: (1.11-2.22)/(3.33+4.44)/5.55*(6.66+7.77)/(8.88) = -0.041828
Test No.8: Error: (1.11+2.22)*(3.33+4.44: missing ")", please check your expression
Test No.9: Error: (1.11+2.22)*3.33/0+(34-45): divisor cannot be zero
Test No.10: Error: 12+89^7: invalid character: ^The implementation code
The realization of the stack
The stack is actually a restricted operation table, all operations can only be at the top of the stack (push, push, etc.), the following is a simple stack using Python code:
class Stack(object):
"""
The structure of a Stack.
The user don't have to know the definition.
"""
def __init__(self):
self.__container = list()
def __is_empty(self):
"""
Test if the stack is empty or not
:return: True or False
"""
return len(self.__container) == 0
def push(self, element):
"""
Add a new element to the stack
:param element: the element you want to add
:return: None
"""
self.__container.append(element)
def top(self):
"""
Get the top element of the stack
:return: top element
"""
if self.__is_empty():
return None
return self.__container[-1]
def pop(self):
"""
Remove the top element of the stack
:return: None or the top element of the stack
"""
return None if self.__is_empty() else self.__container.pop()
def clear(self):
"""
We'll make an empty stack
:return: self
"""
self.__container.clear()
return selfThe implementation of the calculator class
In the calculator class, we put the validation of the expression in a single function, but in practice, we can do it in a function that turns infix expressions into postfix expressions if we want, so that we can perform both validation and conversion by traversing the expression once. However, in order to keep the structure clear, it is better to implement it separately, and it is more realistic to do the best thing possible for each function.
In this calculator class, there are many extreme cases that are not taken into account because there would be more code for the entire implementation. However, you can continue to extend the entire class at a later stage, and it is possible to add new functionality. The current implementation is the main framework, including basic error detection and computation, with the emphasis on learning how to solve problems using the stack, a seemingly simple but powerful data structure.
class Calculator(object):
"""
A simple calculator, just for fun
"""
def __init__(self):
self.__exp = ''
def __validate(self):
"""
We have to make sure the expression is legal.
1. We only accept the `()` to specify the priority of a sub-expression. Notes: `[ {` and `] }` will be
replaced by `(` and `)` respectively.
2. Valid characters should be `+`, `-`, `*`, `/`, `(`, `)` and numbers(int, float)
- Invalid expression examples, but we can only handle the 4th case. The implementation will
be much more sophisticated if we want to handle all the possible cases.:
1. `a+b-+c`
2. `a+b+-`
3. `a+(b+c`
4. `a+(+b-)`
5. etc
:return: True or False
"""
if not isinstance(self.__exp, str):
print('Error: {}: expression should be a string'.format(self.__exp))
return False
# Save the non-space expression
val_exp = ''
s = Stack()
for x in self.__exp:
# We should ignore the space characters
if x == ' ':
continue
if self.__is_bracket(x) or self.__is_digit(x) or self.__is_operators(x) \
or x == '.':
if x == '(':
s.push(x)
elif x == ')':
s.pop()
val_exp += x
else:
print('Error: {}: invalid character: {}'.format(self.__exp, x))
return False
if s.top():
print('Error: {}: missing ")", please check your expression'.format(self.__exp))
return False
self.__exp = val_exp
return True
def __convert2postfix_exp(self):
"""
Convert the infix expression to a postfix expression
:return: the converted expression
"""
# highest priority: ()
# middle: * /
# lowest: + -
converted_exp = ''
stk = Stack()
for x in self.__exp:
if self.__is_digit(x) or x == '.':
converted_exp += x
elif self.__is_operators(x):
converted_exp += ' '
tp = stk.top()
if tp:
if tp == '(':
stk.push(x)
continue
x_pri = self.__get_priority(x)
tp_pri = self.__get_priority(tp)
if x_pri > tp_pri:
stk.push(x)
elif x_pri == tp_pri:
converted_exp += stk.pop() + ' '
stk.push(x)
else:
while stk.top():
if self.__get_priority(stk.top()) != x_pri:
converted_exp += stk.pop() + ' '
else:
break
stk.push(x)
else:
stk.push(x)
elif self.__is_bracket(x):
converted_exp += ' '
if x == '(':
stk.push(x)
else:
while stk.top() and stk.top() != '(':
converted_exp += stk.pop() + ' '
stk.pop()
# pop all the operators
while stk.top():
converted_exp += ' ' + stk.pop() + ' '
return converted_exp
def __get_result(self, operand_2, operand_1, operator):
if operator == '+':
return operand_1 + operand_2
elif operator == '-':
return operand_1 - operand_2
elif operator == '*':
return operand_1 * operand_2
elif operator == '/':
if operand_2 != 0:
return operand_1 / operand_2
else:
print('Error: {}: divisor cannot be zero'.format(self.__exp))
return None
def __calc_postfix_exp(self, exp):
"""
Get the result from a converted postfix expression
e.g. 6 5 2 3 + 8 * + 3 + *
:return: result
"""
assert isinstance(exp, str)
stk = Stack()
exp_split = exp.strip().split()
for x in exp_split:
if self.__is_operators(x):
# pop two top numbers in the stack
r = self.__get_result(stk.pop(), stk.pop(), x)
if r is None:
return None
else:
stk.push(r)
else:
# push the converted number to the stack
stk.push(float(x))
return stk.pop()
def __calc(self):
"""
Try to get the result of the expression
:return: None or result
"""
# Validate
if self.__validate():
# Convert, then run the algorithm to get the result
return self.__calc_postfix_exp(self.__convert2postfix_exp())
else:
return None
def get_result(self, expression):
"""
Get the result of an expression
Suppose we have got a valid expression
:return: None or result
"""
self.__exp = expression.strip()
return self.__calc()
"""
Utilities
"""
@staticmethod
def __is_operators(x):
return x in ['+', '-', '*', '/']
@staticmethod
def __is_bracket(x):
return x in ['(', ')']
@staticmethod
def __is_digit(x):
return x.isdigit()
@staticmethod
def __get_priority(op):
if op in ['+', '-']:
return 0
elif op in ['*', '/']:
return 1
conclusion
Above is the use of Python to achieve a simple 4 computing calculator all content, I hope the content of this article to your learning or work can be helpful, if you have questions you can leave a message to communicate.
reference
Data structure and algorithms (C language)