单链表操作全解析：从入门到精通

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。链表的优势在于动态内存分配和高效的插入/删除操作，但随机访问效率较低。

单链表的节点定义

单链表的节点通常通过结构体（C语言）或类（C++）实现。以下是C++的节点定义示例：

struct ListNode {
    int val;          // 数据域
    ListNode *next;   // 指针域
    ListNode(int x) : val(x), next(nullptr) {}
};

单链表的初始化

初始化链表时需要创建头节点（哨兵节点），简化边界条件处理。以下是初始化示例：

ListNode* initList() {
    ListNode *dummy = new ListNode(-1); // 头节点不存储实际数据
    return dummy;
}

单链表的插入操作

头插法：将新节点插入链表头部。时间复杂度为 $O(1)$。

void insertAtHead(ListNode* dummy, int val) {
    ListNode *newNode = new ListNode(val);
    newNode->next = dummy->next;
    dummy->next = newNode;
}

尾插法：将新节点插入链表尾部。需遍历链表，时间复杂度为 $O(n)$。

void insertAtTail(ListNode* dummy, int val) {
    ListNode *cur = dummy;
    while (cur->next != nullptr) {
        cur = cur->next;
    }
    cur->next = new ListNode(val);
}

单链表的删除操作

删除指定值的节点需遍历链表，时间复杂度为 $O(n)$。

void deleteNode(ListNode* dummy, int val) {
    ListNode *cur = dummy;
    while (cur->next != nullptr && cur->next->val != val) {
        cur = cur->next;
    }
    if (cur->next != nullptr) {
        ListNode *tmp = cur->next;
        cur->next = cur->next->next;
        delete tmp;
    }
}

单链表的查找操作

查找是否存在某个值，时间复杂度为 $O(n)$。

bool search(ListNode* dummy, int val) {
    ListNode *cur = dummy->next;
    while (cur != nullptr) {
        if (cur->val == val) return true;
        cur = cur->next;
    }
    return false;
}

单链表的遍历与打印

遍历链表并打印所有节点的值：

void printList(ListNode* dummy) {
    ListNode *cur = dummy->next;
    while (cur != nullptr) {
        cout << cur->val << " ";
        cur = cur->next;
    }
    cout << endl;
}

单链表的内存释放

动态分配的内存需手动释放，避免内存泄漏：

void freeList(ListNode* dummy) {
    ListNode *cur = dummy;
    while (cur != nullptr) {
        ListNode *tmp = cur;
        cur = cur->next;
        delete tmp;
    }
}

单链表的应用场景

动态内存管理：适合频繁插入/删除的场景，如实现队列或栈。
多项式表示：每个节点存储系数和指数，方便多项式运算。
哈希冲突解决：链地址法中，哈希表的每个槽位使用链表存储冲突元素。

常见问题与优化

边界条件：处理空链表或头尾节点时需谨慎。
虚拟头节点：简化插入/删除操作，避免特殊处理头节点。
双指针技巧：快慢指针可用于检测环或查找中间节点。

通过以上实现和优化，单链表可以高效支持动态数据操作，成为算法和工程中的基础工具。

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