思路：
优先级处理
思路一：正则表达式+递归（计算时间慢）
思路二：堆栈的方式
队列：先进先出
电梯--》队列
上电梯（入队123）：第三个人3，第二个人2，第一个人1
>>> li = []
>>> li.insert(0,'p1')#进队列
>>> li.insert(0,'p2')
>>> li.insert(0,'p3')
>>> li
['p3', 'p2', 'p1']
或者用append('元素')
下电梯（出队123）：第一个人，第二个人，第三个人
>>> li.pop()#出队列
'p1'
>>> li.pop()
'p2'
>>> li.pop()
'p3'
>>>
如果用append方法，就用li.pop(0)
堆栈：先进后出
衣服箱子--》堆栈
装衣服（入栈123）：第三件衣服3，第二件衣服2，第一件衣服1
>>> li = []
>>> li.insert(0,'a1')#进栈
>>> li.insert(0,'a2')
>>> li.insert(0,'a3')
>>> li
['a3', 'a2', 'a1']
>>>
取衣服（出栈321）：第三件衣服，第二件衣服，第一件衣服
>>> li.pop(0)#出栈
'a3'
>>> li.pop(0)
'a2'
>>> li.pop(0)
'a1'
>>>
数字栈
运算符栈
拼接成表达式运算
实例：
#!/usr/bin/env python
#_*_coding:utf-8_*_
import re
#判断是数字还是符号的函数
def is_symbo(element):#遍历元素
res = False#判断运算符
symbol=['+','-','*','/','(',')']
if element in symbol:
res=True
return res
#exp优先级比较
def priority(top_sym,wait_sym):
#print('from the priotry:',top_sym,wait_sym)
level1=['+','-']
level2=['*','/']
level3 = ['(']
level4 = [')']
#运算符栈栈顶元素为+-
if top_sym in level1:
# if wait_sym in level1:
# return '>'
# elif wait_sym in level2:#top_sym='-' wait_sym='*'
# return '<'
# elif wait_sym in level3:#top_sym='-' wait_sym='('
# return '<'
# elif wait_sym in level4:#top_sym='-' wait_sym=')'
# return '>'
# else:
# return '>'
#优化
if wait_sym in level2 or wait_sym in level3:
return '<'
else:
return '>'
# 运算符栈栈顶元素为*/
elif top_sym in level2:
# if wait_sym in level1:#top_sym='*' wait_sym='+'
# return '>'
# if wait_sym in level2:#top_sym='*' wait_sym='*'
# return '>'
# elif top_sym in level3:#top_sym='-' wait_sym='('
# return '<'
# elif top_sym in level4:#top_sym='-' wait_sym=')'
# return '>'
# else:
# return '>'
#优化
if wait_sym in level3:
return '<'
else:
return '>'
#运算符栈顶元素为（
elif top_sym in level3:
if wait_sym in level4:#右括号)碰到了(，那么左括号应该弹出栈
return '='
else:
return '<'#只要栈顶顶元素为（，等待入栈的元素都应该无条件入栈
# 运算符栈顶元素为)
#用来计算的,执行计算结果
def calculate(num1,symbol,num2):
res=0
if symbol == '+':
res=num1+num2
elif symbol =='-':
res=num1-num2
elif symbol =='*':
res=num1*num2
elif symbol =='/':
res=num1/num2
print('from calculate res is [%s|%s|%s] %s' %(num1,symbol,num2,res))
return res
#接受一个表达式
def init_action(expression):
#print(expression)
#去掉空格，匹配空格，替换为空，目标是expression，重新赋值给expression
expression = re.sub(' ','',expression)
#print(expression)
init_l = [i for i in re.split('(-d+.*d*)',expression)if i]#提取-数字
#print('--->',init_l)
expression_l=[]#格式化列表，初始化为空
while True:
if len(init_l) ==0:break#pop完了结束
exp=init_l.pop(0)#列表左侧弹元素
#print('==>',exp)#打印列表每个元素
if len(expression_l) ==0 and re.search('^-d+.*d*$',exp):#-开头，数字结尾，匹配负数
expression_l.append(exp)
continue#直接进行下次循环，不分割-1
#判断负数出现的情况
if len(expression_l) > 0:
if re.search('[+-*/(]$',expression_l[-1]):
expression_l.append(exp)
continue#不做切分，-2这步
new_l = [i for i in re.split('([+-*/()])',exp) if i]#切分结果
#print(new_l)
expression_l+=new_l
#print(expression_l)
return expression_l
#主函数
def main(expression_l):
#print('from in the main',expression_l)
number_stack=[]#数字栈
symbol_stack=[]#运算符栈
for ele in expression_l:#遍历元素是数字还是运算符
print('-' * 20)
print('数字栈', number_stack)
print('运算符栈', symbol_stack)
print('待入栈运算符', ele)
ret = is_symbo(ele)
#print(ret)
if not ret:
#压入数字栈
ele=float(ele)
number_stack.append(ele)
else:
# 压入运算符栈
while True:
if len(symbol_stack) == 0:
symbol_stack.append(ele)
break
res=priority(symbol_stack[-1],ele)#优先级比较
if res == '<':
symbol_stack.append(ele)
break
elif res == '=':#右括号碰到左括号的情况
symbol_stack.pop()
break
elif res == '>':
symbol = symbol_stack.pop()
num2=number_stack.pop()
num1=number_stack.pop()
number_stack.append(calculate(num1,symbol,num2))
else:
symbol = symbol_stack.pop()
num2 = number_stack.pop()
num1 = number_stack.pop()
number_stack.append(calculate(num1, symbol, num2))
return number_stack,symbol_stack
if __name__ == '__main__':
#用户输入表达式
expression = '-1 - 2 *((-60+30+(-40/5)*(-9-2*-5/30-7/3*99/4*2998+10/-568/14))-(-4*-3)/(16-3*2))+3'
# expression='(1-2*3)-1-2*((-60+30+(-40/5)*(-9-2*-5/30-7/3*99/4*2998+10*568/14))-(-4*-3)/(16-3*2))+3'
#expression='-1 -3*( -2+3)'
#格式化处理，得到一个列表
expression_l = init_action(expression)#把用户输入的表达式格式化成一个列表的形式
#print(expression_l)
#分到数字栈，运算符栈
#主函数，处理格式化后的列表
jieguo=main(expression_l)#数字栈
print('最终结果是:%s' % jieguo[0][0])
结果：
--------------------
数字栈 []
运算符栈 []
待入栈运算符 -1
--------------------
数字栈 [-1.0]
运算符栈 []
待入栈运算符 -
--------------------
数字栈 [-1.0]
运算符栈 ['-']
待入栈运算符 2
--------------------
数字栈 [-1.0, 2.0]
运算符栈 ['-']
待入栈运算符 *
--------------------
数字栈 [-1.0, 2.0]
运算符栈 ['-', '*']
待入栈运算符 (
--------------------
数字栈 [-1.0, 2.0]
运算符栈 ['-', '*', '(']
待入栈运算符 (
--------------------
数字栈 [-1.0, 2.0]
运算符栈 ['-', '*', '(', '(']
待入栈运算符 -60
--------------------
数字栈 [-1.0, 2.0, -60.0]
运算符栈 ['-', '*', '(', '(']
待入栈运算符 +
--------------------
数字栈 [-1.0, 2.0, -60.0]
运算符栈 ['-', '*', '(', '(', '+']
待入栈运算符 30
--------------------
数字栈 [-1.0, 2.0, -60.0, 30.0]
运算符栈 ['-', '*', '(', '(', '+']
待入栈运算符 +
from calculate res is [-60.0|+|30.0] -30.0
--------------------
数字栈 [-1.0, 2.0, -30.0]
运算符栈 ['-', '*', '(', '(', '+']
待入栈运算符 (
--------------------
数字栈 [-1.0, 2.0, -30.0]
运算符栈 ['-', '*', '(', '(', '+', '(']
待入栈运算符 -40
--------------------
数字栈 [-1.0, 2.0, -30.0, -40.0]
运算符栈 ['-', '*', '(', '(', '+', '(']
待入栈运算符 /
--------------------
数字栈 [-1.0, 2.0, -30.0, -40.0]
运算符栈 ['-', '*', '(', '(', '+', '(', '/']
待入栈运算符 5
--------------------
数字栈 [-1.0, 2.0, -30.0, -40.0, 5.0]
运算符栈 ['-', '*', '(', '(', '+', '(', '/']
待入栈运算符 )
from calculate res is [-40.0|/|5.0] -8.0
--------------------
数字栈 [-1.0, 2.0, -30.0, -8.0]
运算符栈 ['-', '*', '(', '(', '+']
待入栈运算符 *
--------------------
数字栈 [-1.0, 2.0, -30.0, -8.0]
运算符栈 ['-', '*', '(', '(', '+', '*']
待入栈运算符 (
--------------------
数字栈 [-1.0, 2.0, -30.0, -8.0]
运算符栈 ['-', '*', '(', '(', '+', '*', '(']
待入栈运算符 -9
--------------------
数字栈 [-1.0, 2.0, -30.0, -8.0, -9.0]
运算符栈 ['-', '*', '(', '(', '+', '*', '(']
待入栈运算符 -
--------------------
数字栈 [-1.0, 2.0, -30.0, -8.0, -9.0]
运算符栈 ['-', '*', '(', '(', '+', '*', '(', '-']
待入栈运算符 2
--------------------
数字栈 [-1.0, 2.0, -30.0, -8.0, -9.0, 2.0]
运算符栈 ['-', '*', '(', '(', '+', '*', '(', '-']
待入栈运算符 *
--------------------
数字栈 [-1.0, 2.0, -30.0, -8.0, -9.0, 2.0]
运算符栈 ['-', '*', '(', '(', '+', '*', '(', '-', '*']
待入栈运算符 -5
--------------------
数字栈 [-1.0, 2.0, -30.0, -8.0, -9.0, 2.0, -5.0]
运算符栈 ['-', '*', '(', '(', '+', '*', '(', '-', '*']
待入栈运算符 /
from calculate res is [2.0|*|-5.0] -10.0
--------------------
数字栈 [-1.0, 2.0, -30.0, -8.0, -9.0, -10.0]
运算符栈 ['-', '*', '(', '(', '+', '*', '(', '-', '/']
待入栈运算符 30
--------------------
数字栈 [-1.0, 2.0, -30.0, -8.0, -9.0, -10.0, 30.0]
运算符栈 ['-', '*', '(', '(', '+', '*', '(', '-', '/']
待入栈运算符 -
from calculate res is [-10.0|/|30.0] -0.3333333333333333
from calculate res is [-9.0|-|-0.3333333333333333] -8.666666666666666
--------------------
数字栈 [-1.0, 2.0, -30.0, -8.0, -8.666666666666666]
运算符栈 ['-', '*', '(', '(', '+', '*', '(', '-']
待入栈运算符 7
--------------------
数字栈 [-1.0, 2.0, -30.0, -8.0, -8.666666666666666, 7.0]
运算符栈 ['-', '*', '(', '(', '+', '*', '(', '-']
待入栈运算符 /
--------------------
数字栈 [-1.0, 2.0, -30.0, -8.0, -8.666666666666666, 7.0]
运算符栈 ['-', '*', '(', '(', '+', '*', '(', '-', '/']
待入栈运算符 3
--------------------
数字栈 [-1.0, 2.0, -30.0, -8.0, -8.666666666666666, 7.0, 3.0]
运算符栈 ['-', '*', '(', '(', '+', '*', '(', '-', '/']
待入栈运算符 *
from calculate res is [7.0|/|3.0] 2.3333333333333335
--------------------
数字栈 [-1.0, 2.0, -30.0, -8.0, -8.666666666666666, 2.3333333333333335]
运算符栈 ['-', '*', '(', '(', '+', '*', '(', '-', '*']
待入栈运算符 99
--------------------
数字栈 [-1.0, 2.0, -30.0, -8.0, -8.666666666666666, 2.3333333333333335, 99.0]
运算符栈 ['-', '*', '(', '(', '+', '*', '(', '-', '*']
待入栈运算符 /
from calculate res is [2.3333333333333335|*|99.0] 231.00000000000003
--------------------
数字栈 [-1.0, 2.0, -30.0, -8.0, -8.666666666666666, 231.00000000000003]
运算符栈 ['-', '*', '(', '(', '+', '*', '(', '-', '/']
待入栈运算符 4
--------------------
数字栈 [-1.0, 2.0, -30.0, -8.0, -8.666666666666666, 231.00000000000003, 4.0]
运算符栈 ['-', '*', '(', '(', '+', '*', '(', '-', '/']
待入栈运算符 *
from calculate res is [231.00000000000003|/|4.0] 57.75000000000001
--------------------
数字栈 [-1.0, 2.0, -30.0, -8.0, -8.666666666666666, 57.75000000000001]
运算符栈 ['-', '*', '(', '(', '+', '*', '(', '-', '*']
待入栈运算符 2998
--------------------
数字栈 [-1.0, 2.0, -30.0, -8.0, -8.666666666666666, 57.75000000000001, 2998.0]
运算符栈 ['-', '*', '(', '(', '+', '*', '(', '-', '*']
待入栈运算符 +
from calculate res is [57.75000000000001|*|2998.0] 173134.50000000003
from calculate res is [-8.666666666666666|-|173134.50000000003] -173143.1666666667
--------------------
数字栈 [-1.0, 2.0, -30.0, -8.0, -173143.1666666667]
运算符栈 ['-', '*', '(', '(', '+', '*', '(', '+']
待入栈运算符 10
--------------------
数字栈 [-1.0, 2.0, -30.0, -8.0, -173143.1666666667, 10.0]
运算符栈 ['-', '*', '(', '(', '+', '*', '(', '+']
待入栈运算符 /
--------------------
数字栈 [-1.0, 2.0, -30.0, -8.0, -173143.1666666667, 10.0]
运算符栈 ['-', '*', '(', '(', '+', '*', '(', '+', '/']
待入栈运算符 -568
--------------------
数字栈 [-1.0, 2.0, -30.0, -8.0, -173143.1666666667, 10.0, -568.0]
运算符栈 ['-', '*', '(', '(', '+', '*', '(', '+', '/']
待入栈运算符 /
from calculate res is [10.0|/|-568.0] -0.017605633802816902
--------------------
数字栈 [-1.0, 2.0, -30.0, -8.0, -173143.1666666667, -0.017605633802816902]
运算符栈 ['-', '*', '(', '(', '+', '*', '(', '+', '/']
待入栈运算符 14
--------------------
数字栈 [-1.0, 2.0, -30.0, -8.0, -173143.1666666667, -0.017605633802816902, 14.0]
运算符栈 ['-', '*', '(', '(', '+', '*', '(', '+', '/']
待入栈运算符 )
from calculate res is [-0.017605633802816902|/|14.0] -0.0012575452716297787
from calculate res is [-173143.1666666667|+|-0.0012575452716297787] -173143.16792421197
--------------------
数字栈 [-1.0, 2.0, -30.0, -8.0, -173143.16792421197]
运算符栈 ['-', '*', '(', '(', '+', '*']
待入栈运算符 )
from calculate res is [-8.0|*|-173143.16792421197] 1385145.3433936958
from calculate res is [-30.0|+|1385145.3433936958] 1385115.3433936958
--------------------
数字栈 [-1.0, 2.0, 1385115.3433936958]
运算符栈 ['-', '*', '(']
待入栈运算符 -
--------------------
数字栈 [-1.0, 2.0, 1385115.3433936958]
运算符栈 ['-', '*', '(', '-']
待入栈运算符 (
--------------------
数字栈 [-1.0, 2.0, 1385115.3433936958]
运算符栈 ['-', '*', '(', '-', '(']
待入栈运算符 -4
--------------------
数字栈 [-1.0, 2.0, 1385115.3433936958, -4.0]
运算符栈 ['-', '*', '(', '-', '(']
待入栈运算符 *
--------------------
数字栈 [-1.0, 2.0, 1385115.3433936958, -4.0]
运算符栈 ['-', '*', '(', '-', '(', '*']
待入栈运算符 -3
--------------------
数字栈 [-1.0, 2.0, 1385115.3433936958, -4.0, -3.0]
运算符栈 ['-', '*', '(', '-', '(', '*']
待入栈运算符 )
from calculate res is [-4.0|*|-3.0] 12.0
--------------------
数字栈 [-1.0, 2.0, 1385115.3433936958, 12.0]
运算符栈 ['-', '*', '(', '-']
待入栈运算符 /
--------------------
数字栈 [-1.0, 2.0, 1385115.3433936958, 12.0]
运算符栈 ['-', '*', '(', '-', '/']
待入栈运算符 (
--------------------
数字栈 [-1.0, 2.0, 1385115.3433936958, 12.0]
运算符栈 ['-', '*', '(', '-', '/', '(']
待入栈运算符 16
--------------------
数字栈 [-1.0, 2.0, 1385115.3433936958, 12.0, 16.0]
运算符栈 ['-', '*', '(', '-', '/', '(']
待入栈运算符 -
--------------------
数字栈 [-1.0, 2.0, 1385115.3433936958, 12.0, 16.0]
运算符栈 ['-', '*', '(', '-', '/', '(', '-']
待入栈运算符 3
--------------------
数字栈 [-1.0, 2.0, 1385115.3433936958, 12.0, 16.0, 3.0]
运算符栈 ['-', '*', '(', '-', '/', '(', '-']
待入栈运算符 *
--------------------
数字栈 [-1.0, 2.0, 1385115.3433936958, 12.0, 16.0, 3.0]
运算符栈 ['-', '*', '(', '-', '/', '(', '-', '*']
待入栈运算符 2
--------------------
数字栈 [-1.0, 2.0, 1385115.3433936958, 12.0, 16.0, 3.0, 2.0]
运算符栈 ['-', '*', '(', '-', '/', '(', '-', '*']
待入栈运算符 )
from calculate res is [3.0|*|2.0] 6.0
from calculate res is [16.0|-|6.0] 10.0
--------------------
数字栈 [-1.0, 2.0, 1385115.3433936958, 12.0, 10.0]
运算符栈 ['-', '*', '(', '-', '/']
待入栈运算符 )
from calculate res is [12.0|/|10.0] 1.2
from calculate res is [1385115.3433936958|-|1.2] 1385114.1433936958
--------------------
数字栈 [-1.0, 2.0, 1385114.1433936958]
运算符栈 ['-', '*']
待入栈运算符 +
from calculate res is [2.0|*|1385114.1433936958] 2770228.2867873916
from calculate res is [-1.0|-|2770228.2867873916] -2770229.2867873916
--------------------
数字栈 [-2770229.2867873916]
运算符栈 ['+']
待入栈运算符 3
from calculate res is [-2770229.2867873916|+|3.0] -2770226.2867873916
最终结果是:-2770226.2867873916