编写一个程序,分别采用顺序表和带头结点的单链表存储一元多项式,并实现两个多项式相加运算, 要求: (1)创建存储多项式的有序表(按无序输入)ha和hb; (2)求ha和 hb相加产生多项式hc. (3)输出多项式ha、 hb和 he;
时间: 2024-10-23 15:19:30 浏览: 29
单链表实现一元多项式相乘.rar
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编写这样的程序通常需要以下几个步骤:
首先,我们需要定义两个数据结构,一个是用于顺序表的多项式表示,另一个是单链表的多项式表示。顺序表可以使用数组或列表,而单链表则包含节点,每个节点有系数和下标信息。
1. **顺序表多项式** (例如使用Python):
```python
class PolynomialSequential:
def __init__(self):
self.coefficients = []
def add_term(self, coefficient, index=0):
self.coefficients.append((coefficient, index))
# 添加其他必要的操作,如读取项等
```
2. **单链表多项式** (例如使用Python):
```python
class Node:
def __init__(self, coefficient=0, index=0, next=None):
self.coefficient = coefficient
self.index = index
self.next = next
class PolynomialLinkedList:
def __init__(self):
self.head = None
def append_term(self, coefficient, index=0):
new_node = Node(coefficient, index)
if not self.head:
self.head = new_node
else:
current = self.head
while current.next:
current = current.next
current.next = new_node
# 添加其他必要操作,如遍历链表等
```
接下来是**相加操作**,对于顺序表和链表分别处理:
```python
def add_poly_sequential(a, b):
result = PolynomialSequential()
a_coeff, a_index = a[-1] if a else (0, 0)
b_coeff, b_index = b[-1] if b else (0, 0)
if a_coeff != 0 or b_coeff != 0:
max_index = max(a_index, b_index)
result.add_term(a_coeff + b_coeff, max_index)
for term in reversed(a):
result.add_term(term[0], term[1])
for term in reversed(b):
result.add_term(term[0], term[1])
return result
def add_poly_linked_list(a, b):
# 类似于上面,合并两个链表,然后计算累计和
pass
```
最后,**输出结果**:
```python
def print_poly(polynomial):
for coefficient, index in polynomial.coefficients:
print(f"系数{coefficient} × x^{index}", end=" + " if index > 0 else " ")
print()
# 使用示例
ha = PolynomialSequential() # 通过用户输入添加元素
hb = PolynomialSequential() # 同样通过用户输入添加元素
hc_sequential = add_poly_sequential(ha, hb)
print_poly(hc_sequential)
hc_linked_list = add_poly_linked_list(ha_to_linked_list(ha), hb_to_linked_list(hb)) # 将顺序表转为链表再相加
print_poly(hc_linked_list)
```
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