用单链表表示一元多项式,并实现输入、输出、加、减运算。要求实现: (1)创建多项式 (2)多项式加法 (3)输出多项式 (4)多项式减法
时间: 2024-11-16 09:20:41 浏览: 8
在用单链表表示一元多项式时,我们可以将每个节点设计为存储系数和指数的数据结构。例如,可以创建一个名为`Term`的类,包含两个属性:`coefficient`(系数)和`exponent`(指数),以及指向下一个项的指针。
以下是关键的步骤和代码实现:
1. **创建多项式(Constructing a Polynomial)**:
```python
class Term:
def __init__(self, coefficient=0, exponent=0):
self.coefficient = coefficient
self.exponent = exponent
self.next = None
class Polynomial:
def __init__(self):
self.head = None
```
2. **多项式加法/Addition of Polynomials**:
```python
def add_poly(poly1, poly2):
result = Polynomial()
current1 = poly1.head
current2 = poly2.head
while current1 is not None and current2 is not None:
total_coeff = current1.coefficient + current2.coefficient
if total_coeff != 0:
term = Term(total_coeff)
result.append_term(term)
if current1.exponent < current2.exponent:
current1 = current1.next
else:
current2 = current2.next
# 处理剩余的部分
while current1 is not None or current2 is not None:
if current1 is not None:
result.append_term(current1)
current1 = current1.next
if current2 is not None:
result.append_term(current2)
current2 = current2.next
return result
# append_term 函数用于向结果添加新的term
```
3. **输出多项式/Output Polynomial**:
```python
def print_poly(poly):
current = poly.head
while current is not None:
print(f"{current.coefficient}x^{{{current.exponent}}}", end=" + " if current.next else "\n")
current = current.next
# 示例:print_poly(result)
```
4. **多项式减法/Subtraction of Polynomials**:
```python
def subtract_poly(poly1, poly2):
difference = Polynomial()
for term in poly1:
temp = Term(-term.coefficient) # 初始化负值系数
diff_result = add_poly(temp, poly2) # 将负值项与原多项式相加得到差值
difference.append_poly(diff_result)
return difference
```
注意:以上代码是基于Python编写的简略示例,实际项目中可能会有错误检查和优化。对于具体的输入输出,你需要处理用户输入转换成`Term`对象的过程。
阅读全文