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# Python怎么实现环形链表
## 目录
1. [什么是环形链表](#什么是环形链表)
2. [环形链表的基本操作](#环形链表的基本操作)
- [节点定义](#节点定义)
- [创建环形链表](#创建环形链表)
- [遍历环形链表](#遍历环形链表)
- [检测环形链表](#检测环形链表)
- [插入节点](#插入节点)
- [删除节点](#删除节点)
3. [环形链表的应用场景](#环形链表的应用场景)
4. [完整代码示例](#完整代码示例)
5. [常见问题与解决方案](#常见问题与解决方案)
6. [性能分析](#性能分析)
7. [总结](#总结)
## 什么是环形链表
环形链表(Circular Linked List)是一种特殊的链表结构,其中最后一个节点的指针不是指向`None`,而是指向链表的第一个节点,形成一个闭环。与普通单链表相比,环形链表没有真正的"终点"。
```python
普通单链表:A -> B -> C -> None
环形链表: A -> B -> C -> A (循环)
环形链表可以分为: - 单向环形链表:每个节点只有一个指针指向下一个节点 - 双向环形链表:每个节点有前驱和后继两个指针
与普通链表类似,首先需要定义节点类:
class Node:
def __init__(self, data):
self.data = data # 节点存储的数据
self.next = None # 指向下一个节点的指针
创建环形链表的关键在于将尾节点的next
指向头节点:
def create_circular_linked_list(values):
if not values:
return None
# 创建头节点
head = Node(values[0])
current = head
# 添加后续节点
for value in values[1:]:
current.next = Node(value)
current = current.next
# 将尾节点指向头节点形成环
current.next = head
return head
由于环形链表没有终点,遍历时需要特殊处理:
def traverse_circular_list(head):
if not head:
print("空链表")
return
current = head
while True:
print(current.data, end=" -> ")
current = current.next
if current == head: # 回到起点时停止
break
print(f"(回到 {head.data})")
判断链表是否有环的经典方法是”快慢指针法”:
def has_cycle(head):
if not head or not head.next:
return False
slow = head
fast = head.next
while fast and fast.next:
if slow == fast:
return True
slow = slow.next
fast = fast.next.next
return False
在环形链表中插入节点需要考虑多种情况:
def insert_node(head, position, data):
new_node = Node(data)
# 空链表情况
if not head:
new_node.next = new_node
return new_node
current = head
# 在头节点前插入
if position == 0:
new_node.next = head
# 找到尾节点并更新其next
while current.next != head:
current = current.next
current.next = new_node
return new_node # 新的头节点
# 在其他位置插入
count = 1
while count < position and current.next != head:
current = current.next
count += 1
new_node.next = current.next
current.next = new_node
return head
删除操作也需要特殊处理环形结构:
def delete_node(head, key):
if not head:
return None
current = head
prev = None
# 查找要删除的节点
while True:
if current.data == key:
break
if current.next == head: # 遍历完整个环
print(f"未找到值为 {key} 的节点")
return head
prev = current
current = current.next
# 删除头节点的情况
if current == head:
# 找到尾节点
temp = head
while temp.next != head:
temp = temp.next
temp.next = head.next
head = head.next
else:
prev.next = current.next
return head
class Node:
def __init__(self, data):
self.data = data
self.next = None
class CircularLinkedList:
def __init__(self):
self.head = None
def append(self, data):
new_node = Node(data)
if not self.head:
self.head = new_node
new_node.next = self.head
return
current = self.head
while current.next != self.head:
current = current.next
current.next = new_node
new_node.next = self.head
def prepend(self, data):
new_node = Node(data)
current = self.head
new_node.next = self.head
if not self.head:
new_node.next = new_node
else:
while current.next != self.head:
current = current.next
current.next = new_node
self.head = new_node
def remove(self, key):
if not self.head:
return
if self.head.data == key:
current = self.head
while current.next != self.head:
current = current.next
if self.head == self.head.next: # 只有一个节点
self.head = None
else:
current.next = self.head.next
self.head = current.next
else:
current = self.head
prev = None
while current.next != self.head:
prev = current
current = current.next
if current.data == key:
prev.next = current.next
current = current.next
def __len__(self):
if not self.head:
return 0
count = 1
current = self.head
while current.next != self.head:
count += 1
current = current.next
return count
def print_list(self):
if not self.head:
print("空链表")
return
current = self.head
while True:
print(current.data, end=" -> ")
current = current.next
if current == self.head:
break
print(f"(回到 {self.head.data})")
# 使用示例
clist = CircularLinkedList()
clist.append(1)
clist.append(2)
clist.append(3)
clist.prepend(0)
clist.print_list() # 0 -> 1 -> 2 -> 3 -> (回到 0)
clist.remove(2)
clist.print_list() # 0 -> 1 -> 3 -> (回到 0)
解决方案: - 在遍历时设置计数器或使用标志位 - 使用快慢指针法检测环的存在
解决方案(Floyd算法):
def detect_cycle_start(head):
if not head or not head.next:
return None
slow = fast = entry = head
while fast.next and fast.next.next:
slow = slow.next
fast = fast.next.next
if slow == fast: # 存在环
while entry != slow:
entry = entry.next
slow = slow.next
return entry
return None
解决方案:
def reverse_circular_list(head):
if not head:
return None
prev = None
current = head
next_node = None
while True:
next_node = current.next
current.next = prev
prev = current
current = next_node
if current == head:
break
head.next = prev
return prev
操作 | 时间复杂度 | 空间复杂度 |
---|---|---|
创建 | O(n) | O(n) |
插入 | O(n) | O(1) |
删除 | O(n) | O(1) |
查找 | O(n) | O(1) |
检测环 | O(n) | O(1) |
反转 | O(n) | O(1) |
环形链表是一种重要的数据结构,通过Python实现时需要注意: 1. 始终维护环形结构(尾节点指向头节点) 2. 遍历操作需要特殊终止条件 3. 插入/删除节点时要考虑头节点特殊情况 4. 快慢指针法是检测环的高效方法
掌握环形链表的实现有助于理解更复杂的数据结构,并在特定场景下提供高效的解决方案。 “`
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