python 表达式计算

说明

本文是针对符合中缀表达式的式子,才能得出正确的计算结果,这里不讲解中缀表达式.

要计算一个表达式分下面几个步骤:
1: 中缀表达式转成前缀表达式思路如下图:

2:计算前缀表达式
前缀表达式的计算有下面几步:

• a:从右至左扫描表达式，遇到数字时，将数字压入堆栈.

• b:遇到运算符时，弹出栈顶的两个数，用运算符对它们做相应的计算并将结果入栈

• c:重复上述过程，最后栈中就只有一个值,这个值就是计算结果.。

代码

import re


# 自定义堆栈
class Stack:
    def __init__(self):
        self.items = []
        self.index = -1

    # def __iter__(self):
    #     return self

    def iter(self):
        for i in self.items:
            yield i

    def isEmpty(self):
        return self.items == []

    def push(self, item):
        self.items.append(item)

    def pop(self):
        return self.items.pop()

    def peek(self):
        return self.items[len(self.items) - 1]

    def size(self):
        return len(self.items)





# 获取前缀表达式
def get_pre_exp(str):
    num_stact = Stack()
    flag_stack = Stack()
    exp = re.sub(r"\s+", "", str)
    re_exp = exp[::-1]  # 反转字符串
    for i in re_exp:
        if i.isdigit():
            num_stact.push(i)
        else:
            if i in [")", "+", "×", "/", "-", "*"]:
                flag_stack.push(i)
            if i == "(":

                while True:
                    if ")" not in flag_stack.iter():
                        raise Exception("表达式括号不匹配")
                    flag = flag_stack.pop()
                    if flag == ")":
                        break
                    else:
                        num_stact.push(flag)
    while True:
        if flag_stack.size() > 0:
            f = flag_stack.pop()
            num_stact.push(f)
        else:
            break
    return num_stact


# 计算前缀表达式
def caculate(sta):
    t = Stack()
    for i in sta.iter():
        if i.isdigit():
            t.push(i)
        else:
            flag = i
            if t.size() >= 2:
                left_num = t.pop()
                right_num = t.pop()
                if flag == "+":
                    tmp = int(left_num) + int(right_num)
                    t.push(tmp)
                elif flag in ["*", "×"]:
                    tmp = int(left_num) * int(right_num)
                    t.push(tmp)
                elif flag == "/":
                    tmp = int(left_num) / int(right_num)
                    t.push(tmp)
                elif flag == "-":
                    tmp = int(left_num) - int(right_num)
                    t.push(tmp)
    return t.pop()

s = "1 + ((2 + 3) × 4) - 5"
pre_expression = get_pre_exp(s)
print(caculate(pre_expression))