数据结构与算法-(7)---栈的应用拓展-前缀表达式转换+求值

class Stack :
    def __init__(self):
        self.items = []

    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)

def infix_to_prefix(infix_expr):
    # 定义一个空字典prec{}--记录操作符优先级  -- 优先级由低到高是1~3
    prec = {}
    prec["*"] = 3
    prec["/"] = 3
    prec["+"] = 2
    prec["-"] = 2
    prec[")"] = 1
    opStack = Stack()#初始化操作符栈

    #初始化列表用于储存前缀表达式
    prefixList = []

    #将中缀表达式解析为一个 tokenList 列表,并反转该列表
    tokenList = infix_expr.split()[::-1]#利用split切割成一个一个,然后通过切片转置到列表里
    #列表的元素为:c +  ) B + A (  遇到右括号入栈,左计算

    for token in tokenList:
        #若token是操作数---添加到列表
        if token in "ABCDEFGHIJKLMNOPQRSTUVWXYZ" or token in "0123456789":
            prefixList.append(token)
        # )---压入操作符栈
        elif token == ")":
            opStack.push(token)
        # (---从操作符栈opStack中弹出并返回顶部元素topToken
        elif token == "(":
            topToken = opStack.pop()
            #当topToken不是")"
            while topToken != ")":
                prefixList.append(topToken)
                topToken = opStack.pop()

        # 若token是操作符,通过while循环语句比较他们的优先级,大的操作符添加到式子末端
        else:
            while (not opStack.isEmpty()) and \
                    (prec[opStack.peek()] > prec[token]):
                        #opStack.pop()会直接把栈顶元素弹出并返回
                        prefixList.append(opStack.pop())
            opStack.push(token)

#扫描完后将栈中的元素弹出
    while not opStack.isEmpty():
        #  操作符
        prefixList.append(opStack.pop())
        #  将后缀表达式通过切片转置合成前缀表达式字符串
    return " ".join(prefixList[::-1])
print(infix_to_prefix("A + B * C "))

def postfix_eval(prefix_expr):
    operandStack = Stack()
    tokenList = prefix_expr.split()

    for token in reversed(tokenList):
        if token in "0123456789":#遇到操作数,入栈
            operandStack.push(int(token))
        else:
            operand2 = operandStack.pop()
            operand1 = operandStack.pop()
            result = doMath(token,operand1,operand2)
            operandStack.push(result)
    return operandStack.pop()

def doMath(op, op1, op2):
    if op == "*":
        return op1 * op2
    elif op == "/":
        return op1 / op2
    elif op == "+":
        return op1 + op2
    else:
        return op1 - op2

print(doMath("*", 11, 11))