编写建立链表储存多项式，并实现两多项式相加

创建链表来存储多项式，通常会将每一项作为一个节点，包含系数和指数信息。可以定义一个Node类表示链表中的单个节点，然后构建一个Polynomial类来维护整个链表以及相关的操作。 首先，定义一个`Node`类： ```python class Node: def __init__(self, coefficient, exponent): self.coefficient = coefficient self.exponent = exponent self.next = None ``` 接着，创建`Polynomial`类，用于链表的增删查改和相加： ```python class Polynomial: def __init__(self): self.head = None # 添加新项 def add_term(self, coefficient, exponent): new_node = Node(coefficient, exponent) if not self.head: self.head = new_node else: current = self.head while current.next and current.next.exponent == exponent: current = current.next if current.next and current.next.exponent > exponent: new_node.next = current.next current.next = new_node else: current.next = new_node # 相加两个多项式 @staticmethod def add_poly(poly1, poly2): result = Polynomial() current1 = poly1.head current2 = poly2.head carry = 0 while current1 or current2: coef1 = current1.coefficient if current1 else 0 coef2 = current2.coefficient if current2 else 0 sum_coef = coef1 + coef2 + carry result.add_term(sum_coef, current1.exponent if current1 else current2.exponent) carry = 1 if sum_coef >= 10 else 0 if current1: current1 = current1.next if current2: current2 = current2.next if carry > 0: result.add_term(carry, 0) # 如果还有进位，则添加一个0次幂的项 return result ``` 现在你可以实例化两个`Polynomial`对象并使用`add_poly`方法相加： ```python poly1 = Polynomial() # 添加多项式1的项... poly1.add_term(5, 2) poly1.add_term(3, 1) poly2 = Polynomial() # 添加多项式2的项... poly2.add_term(4, 2) poly2.add_term(7, 1) sum_poly = Polynomial.add_poly(poly1, poly2) ```