代码：
1 from pythonds.basic.stack import Stack 2 alphabet = "ABCDEFGHIJKLMNOPQRSTUVWXYZ" 3 num = "0123456789" 4 5 def infixToPostfix(infixexpr): # 将中缀表达式转换为后缀表达式 6 prio = {} 7 prio['*'] = 3 # 运算符的优先级 8 prio['/'] = 3 9 prio['+'] = 2 10 prio['-'] = 2 11 prio['('] = 1 12 postExprList = [] 13 tokeList = [] #列表来存储后缀表达式 14 opstack = Stack() # 储存操作符的栈，只有操作符的顺序会发生改变，操作数的顺序是不变的 15 for letter in infixexpr: 16 if letter in "ABCDEFGHIJKLMNOPQRSTUVWXYZ" or letter in "0123456789": 17 postExprList.append(letter) 18 elif letter == '(': # 优先级最低，直接压入 19 opstack.push (letter) 20 elif letter ==')': # 需要把括号内的符号都输出出来 21 topletter = opstack.pop() 22 while topletter != '(': 23 postExprList.append(topletter) 24 topletter = opstack.pop() 25 else: # 判断非括号的符号是否要推入栈，需要比较优先级，当然也要看栈是否为空 26 while (not opstack.isEmpty()) and 27 (prio[opstack.peek()] > prio[letter]): # 如果新符号的优先级低，且栈不为空，就要符号出栈 28 topletter = opstack.pop() 29 postExprList.append(topletter) 30 opstack.push(letter) # 否则就入栈 31 while not opstack.isEmpty(): # 栈顶的优先级永远是最高的，把最后的符号出栈，一定是满足顺需的 32 postExprList.append(opstack.pop()) 33 return "".join(postExprList) # 将列表转换为字符串返回出去（方便输出） 34 35 36 def getValue(postfixexpr): # 利用栈的的特性求后缀表达式的值 37 s = Stack() 38 # print("run here") 39 # print(postfixexpr) 40 for letter in postfixexpr: 41 # print(letter) 42 if letter in num: 43 n = int(letter) # 强制转换的格式，注意是谁在括号了 44 s.push(n) 45 else: 46 op1 = s.pop() 47 op2 = s.pop() 48 if letter == '+': 49 result = op2 + op1 50 elif letter == '-': 51 result = op2 - op1 52 elif letter == '*': 53 result = op2 * op1 54 elif letter == '/': 55 result = op2 / op1 56 s.push(result) 57 return s.pop() 58 postfixstr = infixToPostfix('(3+2)*2+1') 59 #print(postfixstr) 60 print(getValue(postfixstr))
备注：
前缀和后缀表达式：离操作数越近的数先加
思路：先将中缀表达式转换为全括号表达式，再将全括号表达式转换为前缀或者中缀表达式