Python新手如何实现符合指定要求的Polynominal多项式类？

核心问题修复 #

你当前代码打印对象地址的根本原因是：Python类的实例方法第一个参数永远是实例本身，你没有显式声明self，导致*args的第一个元素就是实例对象，遍历拼接时就会出现内存地址输出。

完整实现代码 #

class Polynominal:
    def __init__(self, *args):
        # 校验所有系数都是整数
        for coeff in args:
            if not isinstance(coeff, int):
                raise TypeError("所有系数必须为整数")
        # 存储系数，自动去掉末尾的无效0
        self.coeffs = list(args)
        while len(self.coeffs) > 0 and self.coeffs[-1] == 0:
            self.coeffs.pop()
        # 空多项式处理
        if not self.coeffs:
            self.coeffs = [0]

    @classmethod
    def from_iterable(cls, iterable):
        # 从可迭代对象创建实例
        return cls(*iterable)

    def get_degree(self):
        # 返回多项式次数
        return len(self.coeffs) - 1

    def __str__(self):
        terms = []
        for power, coeff in enumerate(self.coeffs):
            if coeff == 0:
                continue
            # 处理系数绝对值
            abs_coeff = abs(coeff)
            # 处理项的主体部分
            if power == 0:
                term = str(abs_coeff)
            elif power == 1:
                term = f"{abs_coeff}x" if abs_coeff != 1 else "x"
            else:
                term = f"{abs_coeff}x^{power}" if abs_coeff != 1 else f"x^{power}"
            terms.append((coeff > 0, term))
        # 空多项式返回空字符串
        if not terms:
            return ""
        # 拼接符号
        res = []
        for idx, (is_positive, term) in enumerate(terms):
            if idx == 0:
                res.append(term if is_positive else f"-{term}")
            else:
                res.append(f" + {term}" if is_positive else f" - {term}")
        return "".join(res)

    def __call__(self, x):
        # 霍纳法则实现多项式求值
        result = 0
        for coeff in reversed(self.coeffs):
            result = result * x + coeff
        return result

    def __eq__(self, other):
        # 相等判断
        if not isinstance(other, Polynominal):
            return False
        return self.coeffs == other.coeffs

    def __add__(self, other):
        # 多项式相加
        if not isinstance(other, Polynominal):
            raise TypeError("只能与Polynominal实例相加")
        max_len = max(len(self.coeffs), len(other.coeffs))
        # 补0对齐长度
        self_padded = self.coeffs + [0] * (max_len - len(self.coeffs))
        other_padded = other.coeffs + [0] * (max_len - len(other.coeffs))
        new_coeffs = [a + b for a, b in zip(self_padded, other_padded)]
        return Polynominal(*new_coeffs)

    def __mul__(self, other):
        # 多项式相乘
        if not isinstance(other, Polynominal):
            raise TypeError("只能与Polynominal实例相乘")
        new_len = len(self.coeffs) + len(other.coeffs) - 1
        new_coeffs = [0] * new_len
        for i, a in enumerate(self.coeffs):
            for j, b in enumerate(other.coeffs):
                new_coeffs[i + j] += a * b
        return Polynominal(*new_coeffs)

功能验证示例 #

# 字符串转换测试
print(str(Polynominal()))  # 输出空字符串
print(str(Polynominal(1, 2, 3))) # 输出 1 + 2x + 3x^2
print(str(Polynominal(1, -1, 1, -1))) # 输出 1 - x + x^2 - x^3
print(str(Polynominal(0, 2, 0))) # 输出 2x

# 求值测试
p = Polynominal(1, 2)
print(p(1)) # 3
print(p(2)) # 5

# 次数测试
print(Polynominal().get_degree()) # 0
print(Polynominal(1, 2, 3).get_degree()) # 2

# 相等测试
print(Polynominal() == Polynominal(0)) # True
print(Polynominal(1, 2, 3) == Polynominal(1, 2, 3)) # True

# 相加测试
print(Polynominal(1,1,1) + Polynominal(2,2,2) == Polynominal(3,3,3)) # True

# 相乘测试
print(Polynominal(1,1) * Polynominal(2,2) == Polynominal(2,4,2)) # True

# from_iterable测试
print(Polynominal.from_iterable([1,2,3]) == Polynominal(1,2,3)) # True

内容的提问来源于stack exchange，提问作者xyzxyzxyz