将polynomial类用字典表示

可以将一个多项式表示为字典，其中字典的键是指数，字典的值是对应的系数。例如，多项式3x^2 + 2x + 1可以表示为字典{2:3, 1:2, 0:1}。以下是一个示例代码：

class Polynomial:
    def __init__(self, coeffs):
        self.coeffs = coeffs

    def __repr__(self):
        return "Polynomial({})".format(self.coeffs)

    def __add__(self, other):
        new_coeffs = {}
        for exp in set(self.coeffs.keys()) | set(other.coeffs.keys()):
            new_coeffs[exp] = self.coeffs.get(exp, 0) + other.coeffs.get(exp, 0)
        return Polynomial(new_coeffs)

    def __mul__(self, other):
        new_coeffs = {}
        for exp1, coeff1 in self.coeffs.items():
            for exp2, coeff2 in other.coeffs.items():
                new_exp = exp1 + exp2
                new_coeff = coeff1 * coeff2
                if new_exp in new_coeffs:
                    new_coeffs[new_exp] += new_coeff
                else:
                    new_coeffs[new_exp] = new_coeff
        return Polynomial(new_coeffs)

使用这个类，我们可以用以下方式创建和操作多项式：

p1 = Polynomial({2: 3, 1: 2, 0: 1})
p2 = Polynomial({3: 1, 1: 4, 0: 1})
print(p1)  # 输出：Polynomial({2: 3, 1: 2, 0: 1})
print(p2)  # 输出：Polynomial({3: 1, 1: 4, 0: 1})
p3 = p1 + p2
print(p3)  # 输出：Polynomial({3: 1, 2: 3, 1: 6, 0: 2})
p4 = p1 * p2
print(p4)  # 输出：Polynomial({5: 3, 4: 12, 3: 7, 2: 10, 1: 2, 0: 1})