一元多项式的运算数据结构

一元多项式可以使用链表来实现运算的数据结构。每个节点表示多项式中的一个项，包含一个系数和一个指数。链表的每个节点按照指数降序排列，方便进行运算。

具体的数据结构可以设计如下：

class Node:
    def __init__(self, coefficient, exponent):
        self.coefficient = coefficient  # 系数
        self.exponent = exponent  # 指数
        self.next = None  # 下一个节点的指针

class Polynomial:
    def __init__(self):
        self.head = None  # 头节点

    def insert_term(self, coefficient, exponent):
        # 按照指数降序插入节点
        new_node = Node(coefficient, exponent)
        if self.head is None or exponent > self.head.exponent:
            new_node.next = self.head
            self.head = new_node
        else:
            current = self.head
            while current.next and current.next.exponent >= exponent:
                current = current.next
            new_node.next = current.next
            current.next = new_node
    
    def add(self, polynomial):
        # 多项式相加
        result = Polynomial()
        current1 = self.head
        current2 = polynomial.head

        while current1 and current2:
            if current1.exponent > current2.exponent:
                result.insert_term(current1.coefficient, current1.exponent)
                current1 = current1.next
            elif current1.exponent < current2.exponent:
                result.insert_term(current2.coefficient, current2.exponent)
                current2 = current2.next
            else:
                result.insert_term(current1.coefficient + current2.coefficient, current1.exponent)
                current1 = current1.next
                current2 = current2.next

        # 处理剩余的节点
        while current1:
            result.insert_term(current1.coefficient, current1.exponent)
            current1 = current1.next
        while current2:
            result.insert_term(current2.coefficient, current2.exponent)
            current2 = current2.next

        return result

    def multiply(self, polynomial):
        # 多项式相乘
        result = Polynomial()
        current1 = self.head
        while current1:
            current2 = polynomial.head
            while current2:
                result.insert_term(current1.coefficient * current2.coefficient, current1.exponent + current2.exponent)
                current2 = current2.next
            current1 = current1.next
        return result

    def display(self):
        # 打印多项式
        if self.head is None:
            print("Empty polynomial")
        else:
            current = self.head
            while current:
                if current.coefficient == 0:
                    current = current.next
                    continue
                if current.coefficient > 0:
                    print("+", end="")
                print(current.coefficient, end="")
                if current.exponent > 0:
                    print("x^" + str(current.exponent), end="")
                current = current.next
            print()

使用上述数据结构，可以创建两个多项式对象，进行加法和乘法运算，并输出结果。