二叉树的应用：表达树的代码实现（python语言）

def make_sum(a, b):  # 加
    return ['+', a, b]


def make_prod(a, b):  # 乘
    return ['*', a, b]


def make_diff(a, b):  # 减
    return ['-', a, b]


def make_div(a, b):  # 除
    return ['/', a, b]


def is_basic_exp(a):  # 判别是否为基本表达式
    return not isinstance(a, list)


def eval_exp(e):
    if is_basic_exp(e):
        return e
    op, a, b = e[0], eval_exp(e[1]), eval_exp(e[2])
    if op == '+':
        return eval_sum(a, b)
    elif op == '-':
        return eval_diff(a, b)
    elif op == '*':
        return eval_prod(a, b)
    elif op == '/':
        return eval_div(a, b)
    else:
        raise ValueError("Unkown opterator:", op)


def eval_sum(a, b):  # 加
    if isinstance(a, Number) and isinstance(b, Number):  # 如果a是一个数字并且b也是一个数字
        return a+b
    if isinstance(a, Number) and a == 0:
        return b
    if isinstance(b, Number) and b == 0:
        return a
    return make_sum(a, b)


def eval_div(a, b):  # 除
    if isinstance(a, Number) and isinstance(b, Number):
        return a / b
    if isinstance(a, Number) and a == 0:
        return 0
    if isinstance(b, Number) and b == 1:
        return a
    if isinstance(b, Number) and b ==0:
        raise ZeroDivisionError
    return make_div(a, b)


def eval_prod(a, b):  # 乘
    if isinstance(a, Number) and isinstance(b, Number):
        return a * b
    if isinstance(a, Number) and a == 0:
        return 0
    if isinstance(b, Number) and b == 0:
        return 0
    if isinstance(a, Number) and a == 1:
        return b
    if isinstance(b, Number) and b == 1:
        return a
    return make_prod(a, b)


def eval_diff(a, b):  # 减
    if isinstance(a, Number) and isinstance(b, Number):
        return a - b
    if isinstance(a, Number) and a == 0:
        return -b
    if isinstance(b, Number) and b == 0:
        return a
    return make_diff(a, b)