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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怕被问穿