单链表：从原理到实战应用

单链表的基本概念

单链表是一种线性数据结构，由一系列节点组成，每个节点包含数据域和指针域。数据域存储元素值，指针域存储下一个节点的地址。单链表的最后一个节点指向空（NULL），表示链表结束。

单链表的优势在于动态内存分配，插入和删除操作的时间复杂度为 $O(1)$（已知位置时），但随机访问需要 $O(n)$ 时间。

单链表的节点结构

单链表的节点通常用结构体或类实现。以下是C语言和Python的实现示例：

C语言实现

struct Node {
    int data;
    struct Node* next;
};

Python实现

class Node:
    def __init__(self, data):
        self.data = data
        self.next = None

单链表的基本操作

插入操作

头部插入
新建节点并使其指向原头节点，更新头指针指向新节点。

void insertAtHead(struct Node** head, int data) {
    struct Node* newNode = (struct Node*)malloc(sizeof(struct Node));
    newNode->data = data;
    newNode->next = *head;
    *head = newNode;
}

尾部插入
遍历链表至最后一个节点，将新节点链接到末尾。

def insert_at_tail(head, data):
    new_node = Node(data)
    if not head:
        head = new_node
        return
    current = head
    while current.next:
        current = current.next
    current.next = new_node

删除操作

删除指定值节点
找到目标节点的前驱节点，修改其指针以跳过目标节点。

void deleteNode(struct Node** head, int key) {
    struct Node* temp = *head, *prev = NULL;
    if (temp != NULL && temp->data == key) {
        *head = temp->next;
        free(temp);
        return;
    }
    while (temp != NULL && temp->data != key) {
        prev = temp;
        temp = temp->next;
    }
    if (temp == NULL) return;
    prev->next = temp->next;
    free(temp);
}

遍历操作

从头节点开始，依次访问每个节点直至末尾。

def traverse(head):
    current = head
    while current:
        print(current.data, end=" -> ")
        current = current.next
    print("NULL")

单链表的应用场景

动态内存管理：适合频繁插入和删除的场景，如内存池管理。
实现其他数据结构：栈、队列和图的邻接表均可基于单链表实现。
多项式运算：用链表存储多项式系数和指数，便于加减乘操作。

单链表的变体

带头节点的单链表：头节点不存储数据，简化插入/删除逻辑。
循环单链表：尾节点指向头节点，适合环形缓冲区等场景。

通过理解单链表的核心操作和实现，可以更好地掌握动态数据结构的灵活性与效率。

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