编写一个程序用单链表存储多项式,并实现两个一元多项式A与B相加的函数。A,B刚开始指数是递增有序的,A与B之和按降序排列。
时间: 2024-10-11 15:06:23 浏览: 45
为了编写一个程序,我们可以首先定义一个`Node`类表示多项式的项,包括系数和指数。然后创建一个`PolynomialList`类用于管理单链表结构,其中包含一个头部节点和相关的操作方法,如添加项、合并两个多项式等。
```python
class Node:
def __init__(self, coefficient=0, exponent=0):
self.coefficient = coefficient
self.exponent = exponent
self.next = None
class PolynomialList:
def __init__(self):
self.head = None
# 添加项到链表
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
new_node.next = current.next
current.next = new_node
# 合并两个多项式
def merge_polynomials(self, other):
combined_list = PolynomialList()
current_a = self.head
current_b = other.head
while current_a and current_b:
a_coeff = current_a.coefficient
b_coeff = current_b.coefficient
if current_a.exponent > current_b.exponent:
combined_list.add_term(a_coeff, current_a.exponent)
current_a = current_a.next
elif current_a.exponent < current_b.exponent:
combined_list.add_term(b_coeff, current_b.exponent)
current_b = current_b.next
else: # 当两项指数相同时,取较大系数
combined_list.add_term(max(a_coeff, b_coeff), current_a.exponent)
current_a = current_a.next
current_b = current_b.next
# 如果还有剩余的项,则逐个添加
while current_a:
combined_list.add_term(current_a.coefficient, current_a.exponent)
current_a = current_a.next
while current_b:
combined_list.add_term(current_b.coefficient, current_b.exponent)
current_b = current_b.next
return combined_list
# 示例:
polynomial_A = PolynomialList()
polynomial_B = PolynomialList()
# 分别为A和B添加项...
# ...
sum_poly = polynomial_A.merge_polynomials(polynomial_B)
```
这个程序首先定义了单链表中的节点,并实现了多项式链表的基本操作。`merge_polynomials`函数负责合并两个多项式,按照题目要求将结果按降序排列。你可以根据实际需求,补充添加项到`polynomial_A`和`polynomial_B`的具体代码。
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