C++数据结构之实现邻接表

//文件名："GraphAdjList.h"
#pragma once
#ifndef GRAPHADJLISL_H_
#define GRAPHADJLISL_H_
 
#include <string>
#include "ObjArrayList.h"
using namespace std;
 
/*
. 图（邻接表实现） Graph Adjacency List
. 相关术语：
. 顶点 Vertex ； 边 Arc ；权 Weight ；
. 有向图 Digraph ；无向图 Undigraph ；
. 有向网 Directed Network ；无向网 Undirected Network ；
. 存储结构：
. 1.顶点表只能采用顺序结构。（因为若采用链式结构，顶点结点定义与边表结点定义就相互引用，无法定义）
. 2.边表采用链表结构。
*/
 
class GraphAdjList
{
 /*
 . 边表（链表）结点
 */
 struct ArcNode
 {
 int adjVex; //邻接顶点所在表中下标
 int weight; //边权重
 ArcNode * next; //下一条边
 };
 /*
 . 顶点表（顺序表）结点
 */
 struct VNode
 {
 string name; //顶点名
 ArcNode * first; //指向的第一个依附该顶点的顶点边结点
 };
public:
 /*
 . 图 种类
 */
 enum GraphType
 {
 DG, //有向图，默认 0
 UDG, //无向图，默认 1
 DN, //有向网，默认 2
 UDN //无向网，默认 3
 };
 /*
 . 边（弧）数据，注：供外部初始化边数据使用
 */
 struct ArcData
 {
 string Tail; //弧尾
 string Head; //弧头
 int Weight; //权重
 };
 
private:
 static const int _MAX_VERTEX_NUM = 10; //支持最大顶点数
 
 VNode vexs[_MAX_VERTEX_NUM]; //顶点表
 int vexs_visited[_MAX_VERTEX_NUM]; //顶点访问标记数组：0|未访问 1|已访问
 int vexNum; //顶点数
 int arcNum; //边数
 int type; //图种类
 
 void _CreateVexSet(ObjArrayList<string> * vexs); //创建顶点集合
 void _CreateDG(ObjArrayList<ArcData> * arcsList); //创建有向图
 void _CreateUDG(ObjArrayList<ArcData> * arcsList); //创建无向图
 void _CreateDN(ObjArrayList<ArcData> * arcsList); //创建有向网
 void _CreateUDN(ObjArrayList<ArcData> * arcsList); //创建无向网
 
 int _Locate(string vertex);   //定位顶点元素位置
 void _InsertArc(int tail, int head, int weight); //插入边（元操作，不分有向/无向）
 void _DeleteArc(int tail, int head);  //删除边（元操作，不分有向/无向）
 void _DFS_R(int index);   //深度优先遍历 递归
 void _DFS(int index);   //深度优先遍历 非递归
 
public:
 GraphAdjList(int type); //构造函数：初始化图种类
 ~GraphAdjList();  //析构函数
 void Init(ObjArrayList<string> * vexs, ObjArrayList<ArcData> * arcsList); //初始化顶点、边数据为 图|网
 void InsertArc(ArcData * arcData); //插入边（含有向/无向操作）
 void DeleteArc(ArcData * arcData); //删除边（含有向/无向操作）
 void Display();  //显示 图|网
 void Display_DFS_R(string *vertex); //从指定顶点开始，深度优先 递归 遍历
 void Display_DFS(string *vertex); //从指定顶点开始，深度优先 非递归 遍历
 void Display_BFS(string *vertex); //从指定顶点开始，广度优先遍历
 
};

//文件名："GraphAdjList.cpp"
#include "stdafx.h"
#include <string>
#include "ObjArrayList.h"
#include "LinkQueue.h"
#include "LinkStack.h"
#include "GraphAdjList.h"
using namespace std;
 
GraphAdjList::GraphAdjList(int type)
{
 /*
 . 构造函数：初始化图类型
 */
 this->type = type;
 this->vexNum = 0;
 this->arcNum = 0;
}
 
GraphAdjList::~GraphAdjList()
{
 /*
 . 析构函数：销毁图
 */
}
 
void GraphAdjList::Init(ObjArrayList<string> * vexs, ObjArrayList<ArcData> * arcsList)
{
 /*
 . 初始化顶点、边数据，并构建 图|网
 . 入参：
 . vexs: 顶点 列表
 . arcsList: 边数据 列表
 */
 //1.创建顶点集
 _CreateVexSet(vexs);
 //2.根据图类型，创建指定的图
 switch (this->type)
 {
 case DG:
 _CreateDG(arcsList); break;
 case UDG:
 _CreateUDG(arcsList); break;
 case DN:
 _CreateDN(arcsList); break;
 case UDN:
 _CreateUDN(arcsList); break;
 default:
 break;
 }
}
 
void GraphAdjList::_CreateVexSet(ObjArrayList<string> * vexs)
{
 /*
 . 创建顶点集合
 */
 string vertex = "";
 //顶点最大数校验
 if (vexs->Length() > this->_MAX_VERTEX_NUM)
 {
 return;
 }
 //遍历顶点表，无重复插入顶点，并计数顶点数
 for (int i = 0; i < vexs->Length(); i++)
 {
 vertex = *vexs->Get(i);
 if (_Locate(vertex) == -1)
 {
 this->vexs[this->vexNum].name = vertex;
 this->vexs[this->vexNum].first = NULL;
 this->vexNum++;
 }
 }
}
 
void GraphAdjList::_CreateDG(ObjArrayList<ArcData> * arcsList)
{
 /*
 . 创建有向图
 . 邻接矩阵为 非对称边
 */
 //初始化临时 边对象
 ArcData * arcData = NULL;
 //初始化 Tail Head 顶点下标索引
 int tail = 0, head = 0;
 //遍历边数据列表
 for (int i = 0; i < arcsList->Length(); i++)
 {
 //按序获取边（弧）
 arcData = arcsList->Get(i);
 //定位（或设置）边的两端顶点位置
 tail = _Locate(arcData->Tail);
 head = _Locate(arcData->Head);
 //插入边
 _InsertArc(tail, head, 0);
 }
}
 
void GraphAdjList::_CreateUDG(ObjArrayList<ArcData> * arcsList)
{
 /*
 . 创建无向图
 . 邻接矩阵为 对称边
 */
 //初始化临时 边对象
 ArcData * arcData = NULL;
 //初始化 Tail Head 顶点下标索引
 int tail = 0, head = 0;
 //遍历边数据列表
 for (int i = 0; i < arcsList->Length(); i++)
 {
 //按序获取边（弧）
 arcData = arcsList->Get(i);
 //定位（或设置）边的两端顶点位置
 tail = _Locate(arcData->Tail);
 head = _Locate(arcData->Head);
 //插入对称边
 _InsertArc(tail, head, 0);
 _InsertArc(head, tail, 0);
 }
}
 
void GraphAdjList::_CreateDN(ObjArrayList<ArcData> * arcsList)
{
 /*
 . 创建有向网
 . 邻接矩阵为 非对称矩阵
 */
 //初始化临时 边对象
 ArcData * arcData = NULL;
 //初始化 Tail Head 顶点下标索引
 int tail = 0, head = 0;
 //遍历边数据列表
 for (int i = 0; i < arcsList->Length(); i++)
 {
 //按序获取边（弧）
 arcData = arcsList->Get(i);
 //定位（或设置）边的两端顶点位置
 tail = _Locate(arcData->Tail);
 head = _Locate(arcData->Head);
 //插入边
 _InsertArc(tail, head, arcData->Weight);
 }
}
 
void GraphAdjList::_CreateUDN(ObjArrayList<ArcData> * arcsList)
{
 /*
 . 创建无向网
 . 邻接矩阵为 对称矩阵
 */
 //初始化临时 边对象
 ArcData * arcData = NULL;
 //初始化 Tail Head 顶点下标索引
 int tail = 0, head = 0;
 //遍历边数据列表
 for (int i = 0; i < arcsList->Length(); i++)
 {
 //按序获取边（弧）
 arcData = arcsList->Get(i);
 //定位（或设置）边的两端顶点位置
 tail = _Locate(arcData->Tail);
 head = _Locate(arcData->Head);
 //插入对称边
 _InsertArc(tail, head, arcData->Weight);
 _InsertArc(head, tail, arcData->Weight);
 }
}
 
int GraphAdjList::_Locate(string vertex)
{
 /*
 . 定位顶点元素位置
 . 后期可改成【字典树】，顶点数超过100个后定位顶点位置可更快
 */
 //遍历定位顶点位置
 for (int i = 0; i < this->_MAX_VERTEX_NUM; i++)
 {
 if (vertex == this->vexs[i].name)
 {
 return i;
 }
 }
 //cout << endl << "顶点[" << vertex << "]不存在。" << endl;
 return -1;
}
 
void GraphAdjList::_InsertArc(int tail, int head, int weight)
{
 /*
 . 插入边（元操作，不分有向/无向）
 */
 //边结点指针：初始化为 弧尾 指向的第一个边
 ArcNode * p = this->vexs[tail].first;
 //初始化 前一边结点的指针
 ArcNode * q = NULL;
 //重复边布尔值
 bool exist = false;
 //1.边的重复性校验
 while (p != NULL)
 {
 //若已存在该边，则标记为 存在 true
 if (p->adjVex == head)
 {
 exist = true;
 break;
 }
 //若不是该边，继续下一个边校验
 q = p;
 p = p->next;
 }
 //2.1.如果边存在，则跳过，不做插入
 if (exist)
 return;
 //2.2.边不存在时，创建边
 ArcNode * newArc = new ArcNode();
 newArc->adjVex = head;
 newArc->weight = weight;
 newArc->next = NULL;
 //3.1.插入第一条边
 if (q == NULL)
 {
 this->vexs[tail].first = newArc;
 }
 //3.2.插入后序边
 else
 {
 q->next = newArc;
 }
 //4.边 计数
 this->arcNum++;
}
 
void GraphAdjList::InsertArc(ArcData * arcData)
{
 /*
 . 插入边（含有向/无向操作）
 */
 //初始化 Tail Head 顶点下标索引
 int tail = 0, head = 0;
 tail = _Locate(arcData->Tail);
 head = _Locate(arcData->Head);
 //根据图类型，插入边
 switch (this->type)
 {
 case DG:
 _InsertArc(tail, head, 0);
 break;
 case UDG:
 _InsertArc(tail, head, 0);
 _InsertArc(head, tail, 0);
 break;
 case DN:
 _InsertArc(tail, head, arcData->Weight);
 break;
 case UDN:
 _InsertArc(tail, head, arcData->Weight);
 _InsertArc(head, tail, arcData->Weight);
 break;
 default:
 break;
 }
}
 
void GraphAdjList::_DeleteArc(int tail, int head)
{
 /*
 . 删除边（元操作，不分有向/无向）
 */
 //边结点指针：初始化为 弧尾 指向的第一个边
 ArcNode * p = this->vexs[tail].first;
 //初始化 前一边结点的指针
 ArcNode * q = NULL;
 //1.遍历查找边
 while (p != NULL)
 {
 //若存在该边，则结束循环
 if (p->adjVex == head)
 {
 break;
 }
 //若不是该边，继续下一个边
 q = p;
 p = p->next;
 }
 //2.1.边不存在
 if (p == NULL)
 {
 cout << endl << "边[" << this->vexs[head].name << "->" << this->vexs[head].name << "]不存在。" << endl;
 return;
 }
 //2.2.边存在，删除边
 //2.2.1.若为第一条边
 if (q == NULL)
 {
 this->vexs[tail].first = p->next;
 }
 //2.2.2.非第一条边
 else
 {
 q->next = p->next;
 }
 //3.释放 p
 delete p;
}
 
void GraphAdjList::DeleteArc(ArcData * arcData)
{
 /*
 . 删除边（含有向/无向操作）
 */
 //初始化 Tail Head 顶点下标索引
 int tail = 0, head = 0;
 tail = _Locate(arcData->Tail);
 head = _Locate(arcData->Head);
 //根据图类型，删除边
 switch (this->type)
 {
 case DG:
 _DeleteArc(tail, head);
 break;
 case UDG:
 _DeleteArc(tail, head);
 _DeleteArc(head, tail);
 break;
 case DN:
 _DeleteArc(tail, head);
 break;
 case UDN:
 _DeleteArc(tail, head);
 _DeleteArc(head, tail);
 break;
 default:
 break;
 }
}
 
void GraphAdjList::Display()
{
 /*
 . 显示 图|网
 */
 //初始化边表结点指针
 ArcNode * p = NULL;
 cout << endl << "邻接表：" << endl;
 //遍历顶点表
 for (int i = 0; i < this->_MAX_VERTEX_NUM; i++)
 {
 //空顶点（在删除顶点的操作后会出现此类情况）
 if (this->vexs[i].name == "")
 {
 continue;
 }
 //输出顶点
 cout << "[" << i << "]" << this->vexs[i].name << " ";
 //遍历输出边顶点
 p = this->vexs[i].first;
 while (p != NULL)
 {
 cout << "[" << p->adjVex << "," << p->weight << "] ";
 p = p->next;
 }
 cout << endl;
 }
}
 
void GraphAdjList::_DFS_R(int index)
{
 /*
 . 深度优先遍历 递归
 */
 //1.访问顶点，并标记已访问
 cout << this->vexs[index].name << " ";
 this->vexs_visited[index] = 1;
 //2.遍历访问其相邻顶点
 ArcNode * p = this->vexs[index].first;
 int adjVex = 0;
 while (p != NULL)
 {
 adjVex = p->adjVex;
 //当顶点未被访问过时，可访问
 if (this->vexs_visited[adjVex] != 1)
 {
 _DFS_R(adjVex);
 }
 p = p->next;
 }
}
 
void GraphAdjList::Display_DFS_R(string *vertex)
{
 /*
 . 从指定顶点开始，深度优先 递归 遍历
 */
 //1.判断顶点是否存在
 int index = _Locate(*vertex);
 if (index == -1)
 return;
 //2.初始化顶点访问数组
 for (int i = 0; i < this->_MAX_VERTEX_NUM; i++)
 {
 this->vexs_visited[i] = 0;
 }
 //3.深度优先遍历 递归
 cout << "深度优先遍历（递归）：（从顶点" << *vertex << "开始）" << endl;
 _DFS_R(index);
}
 
void GraphAdjList::_DFS(int index)
{
 /*
 . 深度优先遍历 非递归
 */
 //1.访问第一个结点，并标记为 已访问
 cout << this->vexs[index].name << " ";
 vexs_visited[index] = 1;
 //初始化 边结点 栈
 LinkStack<ArcNode> * s = new LinkStack<ArcNode>();
 //初始化边结点 指针
 ArcNode * p = this->vexs[index].first;
 //2.寻找下一个（未访问的）邻接结点
 while (!s->Empty() || p != NULL)
 {
 //2.1.未访问过，则访问 （纵向遍历）
 if (vexs_visited[p->adjVex] != 1)
 {
 //访问结点，标记为访问，并将其入栈
 cout << this->vexs[p->adjVex].name << " ";
 vexs_visited[p->adjVex] = 1;
 s->Push(p);
 //指针 p 移向 此结点的第一个邻接结点
 p = this->vexs[p->adjVex].first;
 }
 //2.2.已访问过，移向下一个边结点 （横向遍历）
 else
 p = p->next;
 //3.若无邻接点，则返回上一结点层，并出栈边结点
 if (p == NULL)
 {
 p = s->Pop();
 }
 }
 //释放 栈
 delete s;
}
 
void GraphAdjList::Display_DFS(string *vertex)
{
 /*
 . 从指定顶点开始，深度优先 非递归 遍历
 */
 //1.判断顶点是否存在
 int index = _Locate(*vertex);
 if (index == -1)
 return;
 //2.初始化顶点访问数组
 for (int i = 0; i < this->_MAX_VERTEX_NUM; i++)
 {
 this->vexs_visited[i] = 0;
 }
 //3.深度优先遍历 递归
 cout << "深度优先遍历（非递归）：（从顶点" << *vertex << "开始）" << endl;
 _DFS(index);
}
 
void GraphAdjList::Display_BFS(string *vertex)
{
 /*
 . 从指定顶点开始，广度优先遍历
 */
 //1.判断顶点是否存在
 int index = _Locate(*vertex);
 if (index == -1)
 return;
 //2.初始化顶点访问数组
 for (int i = 0; i < this->_MAX_VERTEX_NUM; i++)
 {
 this->vexs_visited[i] = 0;
 }
 //3.广度优先遍历
 cout << "广度优先遍历：（从顶点" << *vertex << "开始）" << endl;
 //3.1.初始化队列
 LinkQueue<int> * vexQ = new LinkQueue<int>();
 //3.2.访问开始顶点，并标记访问、入队
 cout << this->vexs[index].name << " ";
 this->vexs_visited[index] = 1;
 vexQ->EnQueue(new int(index));
 //3.3.出队，并遍历邻接顶点（下一层次），访问后入队
 ArcNode * p = NULL;
 int adjVex = 0;
 while (vexQ->GetHead() != NULL)
 {
 index = *vexQ->DeQueue();
 p = this->vexs[index].first;
 //遍历邻接顶点
 while (p != NULL)
 {
 adjVex = p->adjVex;
 //未访问过的邻接顶点
 if (this->vexs_visited[adjVex] != 1)
 {
 //访问顶点，并标记访问、入队
 cout << this->vexs[adjVex].name << " ";
 this->vexs_visited[adjVex] = 1;
 vexQ->EnQueue(new int(adjVex));
 }
 p = p->next;
 }
 }
 
 //4.释放队列
 int * e;
 while (vexQ->GetHead() != NULL)
 {
 e = vexQ->DeQueue();
 delete e;
 }
 delete vexQ;
}

//文件名："GraphAdjList_Test.cpp"
#include "stdafx.h"
#include <iostream>
#include "GraphAdjList.h"
#include "ObjArrayList.h"
using namespace std;
 
int main()
{
 //初始化顶点数据
 string * v1 = new string("v1");
 string * v2 = new string("v2");
 string * v3 = new string("v3");
 string * v4 = new string("v4");
 string * v5 = new string("v5");
 string * v6 = new string("v6");
 string * v7 = new string("v7");
 ObjArrayList<string> * vexs = new ObjArrayList<string>();
 vexs->Add(v1);
 vexs->Add(v2);
 vexs->Add(v3);
 vexs->Add(v4);
 vexs->Add(v5);
 vexs->Add(v6);
 vexs->Add(v7);
 
 //初始化边（弧）数据
 GraphAdjList::ArcData * arc1 = new GraphAdjList::ArcData{ "v1", "v2", 2 };
 GraphAdjList::ArcData * arc2 = new GraphAdjList::ArcData{ "v1", "v3", 3 };
 GraphAdjList::ArcData * arc3 = new GraphAdjList::ArcData{ "v1", "v4", 4 };
 GraphAdjList::ArcData * arc4 = new GraphAdjList::ArcData{ "v3", "v1", 5 };
 GraphAdjList::ArcData * arc5 = new GraphAdjList::ArcData{ "v3", "v2", 6 };
 GraphAdjList::ArcData * arc6 = new GraphAdjList::ArcData{ "v3", "v5", 7 };
 GraphAdjList::ArcData * arc7 = new GraphAdjList::ArcData{ "v2", "v5", 8 };
 GraphAdjList::ArcData * arc8 = new GraphAdjList::ArcData{ "v4", "v6", 9 };
 GraphAdjList::ArcData * arc9 = new GraphAdjList::ArcData{ "v4", "v7", 9 };
 GraphAdjList::ArcData * arc10 = new GraphAdjList::ArcData{ "v6", "v7", 9 };
 ObjArrayList<GraphAdjList::ArcData> * arcsList = new ObjArrayList<GraphAdjList::ArcData>();
 arcsList->Add(arc1);
 arcsList->Add(arc2);
 arcsList->Add(arc3);
 arcsList->Add(arc4);
 arcsList->Add(arc5);
 arcsList->Add(arc6);
 arcsList->Add(arc7);
 arcsList->Add(arc8);
 arcsList->Add(arc9);
 arcsList->Add(arc10);
 
 //测试1：无向图
 cout << endl << "无向图初始化：" << endl;
 GraphAdjList * udg = new GraphAdjList(GraphAdjList::UDG);
 udg->Init(vexs, arcsList);
 udg->Display();
 //1.1.深度优先遍历
 cout << endl << "无向图深度优先遍历序列：（递归）" << endl;
 udg->Display_DFS_R(v1);
 cout << endl << "无向图深度优先遍历序列：（非递归）" << endl;
 udg->Display_DFS(v1);
 //1.2.广度优先遍历
 cout << endl << "无向图广度优先遍历序列：" << endl;
 udg->Display_BFS(v2);
 //1.3.插入新边
 cout << endl << "无向图新边：" << endl;
 udg->InsertArc(new GraphAdjList::ArcData{ "v7", "v1", 8 });
 udg->Display();
 //1.4.删除边
 cout << endl << "无向图删除边arc9：" << endl;
 udg->DeleteArc(arc9);
 udg->Display();
 
 //测试2：有向图
 cout << endl << "有向图：" << endl;
 GraphAdjList * dg = new GraphAdjList(GraphAdjList::DG);
 dg->Init(vexs, arcsList);
 dg->Display();
 //2.1.深度优先遍历
 cout << endl << "有向图深度优先遍历序列：（递归）" << endl;
 dg->Display_DFS_R(v1);
 cout << endl << "有向图深度优先遍历序列：（非递归）" << endl;
 dg->Display_DFS(v1);
 //2.2.广度优先遍历
 cout << endl << "有向图广度优先遍历序列：" << endl;
 dg->Display_BFS(v2);
 
 //测试：无向网
 cout << endl << "无向网：" << endl;
 GraphAdjList * udn = new GraphAdjList(GraphAdjList::UDN);
 udn->Init(vexs, arcsList);
 udn->Display();
 
 //测试：有向网
 cout << endl << "有向网：" << endl;
 GraphAdjList * dn = new GraphAdjList(GraphAdjList::DN);
 dn->Init(vexs, arcsList);
 dn->Display();
 
 return 0;
}