四则运算表达式二叉树法求后缀表达式

data = """
3+51*4-23/(3+8)-5
(42+33*(2+5))-7*8
"""

nex = []  # 存储括号对应关系
token = []


# 预处理
def pre(s):
    global token
    global nex
    token = []
    nex = []
    stack = []
    i = 0
    while i < len(s):
        if s[i] == '(':
            token.append("(")
            i += 1
        elif s[i] == ')':
            token.append(")")
            i += 1
        elif s[i] in "+-*/":
            token.append(s[i])
            i += 1
        elif s[i].isspace():
            i += 1
        else:
            v = ""
            while i < len(s) and s[i].isdigit():
                v += s[i]
                i += 1
            token.append(v)
    i = 0
    nex = [0] * len(token)
    while i < len(token):
        if token[i] == "(":
            stack.append(i)
            i += 1
        elif token[i] == ")":
            x = stack.pop()
            nex[i] = x
            nex[x] = i
            i += 1
        else:
            i += 1


# 运算符优先级
def priority(op):
    return {"+": 0, "-": 0, "*": 1, "/": 1}[op]


# 计算值
def cal(x, y, op):
    if op == "+":
        return x + y
    elif op == "-":
        return x - y
    elif op == "*":
        return x * y
    else:
        return x / y


# 将token[f:t]转换成结点
def node(token, f, t):
    r = {}
    minOp = -1
    minOpPriority = 0xfffffff
    while token[f] == "(" and token[t] == ")":
        f += 1
        t -= 1
    if f == t:
        r["value"] = int(token[f])
        return r
    i = f
    while i <= t:
        if token[i] == '(':
            i = nex[i] + 1
        elif token[i] in "+-*/":
            op = priority(token[i])
            if op <= minOpPriority:
                minOp = i
                minOpPriority = op
            i += 1
        else:
            i += 1
    r["left"] = node(token, f, minOp - 1)
    r["right"] = node(token, minOp + 1, t)
    r["op"] = token[minOp]
    r["value"] = cal(r["left"]["value"], r["right"]["value"], r["op"])
    return r


# 打印后序
def houxu(node):
    if not "op" in node:
        return [node["value"]]
    l = houxu(node["left"])
    r = houxu(node["right"])
    op = node["op"]
    return l + r + [op]


def main(s):
    s = s.strip()
    pre(s)
    n = node(token, 0, len(token) - 1)
    print(houxu(n))
    return n["value"]


for i in data.split():
    print(i, "=", eval(i), main(i))