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数据结构第三篇
一、几个注意点
1、同时持有头尾结点的引用
双链表一般同时持有头尾结点的引用
因为在工程应用中，通常在容器尾插入元素，双链表持有尾部节点的引用，就可以在O（1）时间复杂度的情况下在尾部添加元素。
对于单链表，持有尾节点的引用也有优化效果，比如在单链表尾部添加元素；如果没有尾部节点的引用，就需要遍历整个链表找到尾部节点，时间复杂度O（n）；如果有尾部节点的引用，就可以在O（1）的时间复杂度内完成尾部添加元素的操作；如果删除一次单链表的尾节点，那么之前的尾节点的引用就会失效，还需要遍历一次才能找到尾节点？但是其实，可以更新尾结点的引用
2、虚拟头尾结点
在创建双链表时，创建一个虚拟的头尾结点，无论双链表是否为空，这两个结点都存在，这样就不会出现空指针的问题，避免边界处理的问题。
空的双链表：
dummyHead <-> dummyTail添加两个元素：
dummyHead <-> 1 <-> 2 <-> dummyTail之前需要在头部插入元素，需要分类讨论，现在有了虚拟头尾结点，无论是否为空，都不需要分类讨论。
注意：虚拟头尾结点是对外不可见的
3、内存泄漏
// 假设单链表头结点 head = 1 -> 2 -> 3 -> 4 -> 5
// 删除单链表头结点
head = head.next; // 此时 head = 2 -> 3 -> 4 -> 5删除结点，最好是把删除的结点都设为null
二、代码实现
1、双链表
#include <iostream>
#include <stdexcept>template<typename E>
class MyLinkedList {// 虚拟头尾节点struct Node {E val;Node* next;Node* prev;Node(E value) : val(value), next(nullptr), prev(nullptr) {}};Node* head;Node* tail;int size;public:// 构造函数初始化虚拟头尾节点MyLinkedList() {head = new Node(E());tail = new Node(E());head->next = tail;tail->prev = head;size = 0;}// ***** 增 *****void addLast(E e) {Node* x = new Node(e);Node* temp = tail->prev;// temp <-> xtemp->next = x;x->prev = temp;x->next = tail;tail->prev = x;// temp <-> x <-> tailsize++;}void addFirst(E e) {Node* x = new Node(e);Node* temp = head->next;// head <-> temptemp->prev = x;x->next = temp;head->next = x;x->prev = head;// head <-> x <-> tempsize++;}void add(int index, E element) {checkPositionIndex(index);if (index == size) {addLast(element);return;}// 找到 index 对应的 NodeNode* p = getNode(index);Node* temp = p->prev;// temp <-> p// 新要插入的 NodeNode* x = new Node(element);p->prev = x;temp->next = x;x->prev = temp;x->next = p;// temp <-> x <-> psize++;}// ***** 删 *****E removeFirst() {if (size < 1) {throw std::out_of_range("No elements to remove");}// 虚拟节点的存在是我们不用考虑空指针的问题Node* x = head->next;Node* temp = x->next;// head <-> x <-> temphead->next = temp;temp->prev = head;E val = x->val;delete x;// head <-> tempsize--;return val;}E removeLast() {if (size < 1) {throw std::out_of_range("No elements to remove");}Node* x = tail->prev;Node* temp = tail->prev->prev;// temp <-> x <-> tailtail->prev = temp;temp->next = tail;E val = x->val;x->prev = null;x->next = null;delete x;// temp <-> tailsize--;return val;}E remove(int index) {checkElementIndex(index);// 找到 index 对应的 NodeNode* x = getNode(index);Node* prev = x->prev;Node* next = x->next;// prev <-> x <-> nextprev->next = next;next->prev = prev;E val = x->val;x->prev = null;x->next = null;delete x;// prev <-> nextsize--;return val;}// ***** 查 *****E get(int index) {checkElementIndex(index);// 找到 index 对应的 NodeNode* p = getNode(index);return p->val;}E getFirst() {if (size < 1) {throw std::out_of_range("No elements in the list");}return head->next->val;}E getLast() {if (size < 1) {throw std::out_of_range("No elements in the list");}return tail->prev->val;}// ***** 改 *****E set(int index, E val) {checkElementIndex(index);// 找到 index 对应的 NodeNode* p = getNode(index);E oldVal = p->val;p->val = val;return oldVal;}// ***** 其他工具函数 *****int getSize() const {return size;}bool isEmpty() const {return size == 0;}void display() {std::cout << "size = " << size << std::endl;for (Node* p = head->next; p != tail; p = p->next) {std::cout << p->val << " <-> ";}std::cout << "null" << std::endl;std::cout << std::endl;}private:Node* getNode(int index) {checkElementIndex(index);Node* p = head->next;// TODO: 可以优化，通过 index 判断从 head 还是 tail 开始遍历for (int i = 0; i < index; i++) {p = p->next;}return p;}bool isElementIndex(int index) const {return index >= 0 && index < size;}bool isPositionIndex(int index) const {return index >= 0 && index <= size;}// 检查 index 索引位置是否可以存在元素void checkElementIndex(int index) const {if (!isElementIndex(index))throw std::out_of_range("Index: " + std::to_string(index) + ", Size: " + std::to_string(size));}// 检查 index 索引位置是否可以添加元素void checkPositionIndex(int index) const {if (!isPositionIndex(index))throw std::out_of_range("Index: " + std::to_string(index) + ", Size: " + std::to_string(size));}~MyLinkedList() {while (size > 0) {removeFirst();}delete head;delete tail;}
};int main() {MyLinkedList<int> list;list.addLast(1);list.addLast(2);list.addLast(3);list.addFirst(0);list.add(2, 100);list.display();// size = 5// 0 <-> 1 <-> 100 <-> 2 <-> 3 <-> nullreturn 0;
}2、单链表
#include <iostream>
#include <stdexcept>template <typename E>
class MyLinkedList2 {
private:// 节点结构struct Node {E val;Node* next;Node(E value) : val(value), next(nullptr) {}};Node* head;// 实际的尾部节点引用Node* tail;int size_;public:MyLinkedList2() {head = new Node(E());tail = head;size_ = 0;}void addFirst(E e) {Node* newNode = new Node(e);newNode->next = head->next;head->next = newNode;if (size_ == 0) {tail = newNode;}size_++;}void addLast(E e) {Node* newNode = new Node(e);tail->next = newNode;tail = newNode;size_++;}void add(int index, E element) {checkPositionIndex(index);if (index == size_) {addLast(element);return;}Node* prev = head;for (int i = 0; i < index; i++) {prev = prev->next;}Node* newNode = new Node(element);newNode->next = prev->next;prev->next = newNode;size_++;}E removeFirst() {if (isEmpty()) {throw std::out_of_range("No elements to remove");}Node* first = head->next;head->next = first->next;if (size_ == 1) {tail = head;}size_--;E val = first->val;delete first;return val;}E removeLast() {if (isEmpty()) {throw std::out_of_range("No elements to remove");}Node* prev = head;while (prev->next != tail) {prev = prev->next;}E val = tail->val;delete tail;prev->next = nullptr;tail = prev;size_--;return val;}E remove(int index) {checkElementIndex(index);Node* prev = head;for (int i = 0; i < index; i++) {prev = prev->next;}Node* nodeToRemove = prev->next;prev->next = nodeToRemove->next;// 删除的是最后一个元素if (index == size_ - 1) {tail = prev;}size_--;E val = nodeToRemove->val;delete nodeToRemove;return val;}// ***** 查 *****E getFirst() {if (isEmpty()) {throw std::out_of_range("No elements in the list");}return head->next->val;}E getLast() {if (isEmpty()) {throw std::out_of_range("No elements in the list");}return getNode(size_ - 1)->val;}E get(int index) {checkElementIndex(index);Node* p = getNode(index);return p->val;}// ***** 改 *****E set(int index, E element) {checkElementIndex(index);Node* p = getNode(index);E oldVal = p->val;p->val = element;return oldVal;}// ***** 其他工具函数 *****int size() {return size_;}bool isEmpty() {return size_ == 0;}~MyLinkedList2() {Node* current = head;while (current != nullptr) {Node* next = current->next;delete current;current = next;}}private:bool isElementIndex(int index) {return index >= 0 && index < size_;}bool isPositionIndex(int index) {return index >= 0 && index <= size_;}// 检查 index 索引位置是否可以存在元素void checkElementIndex(int index) {if (!isElementIndex(index)) {throw std::out_of_range("Index: " + std::to_string(index) + ", size_: " + std::to_string(size_));}}// 检查 index 索引位置是否可以添加元素void checkPositionIndex(int index) {if (!isPositionIndex(index)) {throw std::out_of_range("Index: " + std::to_string(index) + ", size_: " + std::to_string(size_));}}// 返回 index 对应的 Node// 注意：请保证传入的 index 是合法的Node* getNode(int index) {Node* p = head->next;for (int i = 0; i < index; i++) {p = p->next;}return p;}
};int main() {MyLinkedList2<int> list;list.addFirst(1);list.addFirst(2);list.addLast(3);list.addLast(4);list.add(2, 5);std::cout << list.removeFirst() << std::endl; // 2std::cout << list.removeLast() << std::endl; // 4std::cout << list.remove(1) << std::endl; // 5std::cout << list.getFirst() << std::endl; // 1std::cout << list.getLast() << std::endl; // 3std::cout << list.get(1) << std::endl; // 3return 0;
}