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C++邻接表 C++数据结构之实现邻接表

碣石观海 人气:3

一、图的邻接表实现

1.实现了以顶点顺序表、边链表为存储结构的邻接表;

2.实现了图的创建(有向/无向/图/网)、边的增删操作、深度优先递归/非递归遍历、广度优先遍历的算法;

3.采用顶点对象列表、边(弧)对象列表的方式,对图的创建进行初始化;引用 "ObjArrayList.h"头文件,头文件可参看之前博文“数据结构之顺序列表(支持对象元素)”代码;

4.深度优先遍历分别采用递归/非递归算法;非递归中用到的栈,引用"LinkStack.h"头文件,头文件可参看之前博文“数据结构之栈”代码;

5.广度优先遍历采用队列方式实现;用到的队列,引用 "LinkQueue.h"头文件,头文件可参看之前博文“数据结构之队列”代码;

6.测试代码中以有向网的所有带权边作为边的初始化数据,选择图类型(DG, UDG, DN, UDN)可创建成不同类型的图。

7.优劣分析:

7.1.(优势)邻接表存储结构,相比邻接矩阵,消除了无邻接关系顶点的边存储空间;

7.2.(优势)邻接表比邻接矩阵更容易访问某顶点的邻接顶点;

7.3.(优势)邻接表比邻接矩阵更易于统计边总数,无需逐行逐列遍历;

7.4.(劣势)在确定两顶点间是否有边的搜索过程中,邻接表不如邻接矩阵可直接寻址快,反而需要顶点到边链的遍历;

7.5.(劣势)邻接矩阵在删除顶点时,只需清除对应行列数据即可;而邻接表在清除顶点指向的边链后,还需遍历整个边表,清除所有邻接于此顶点的边结点;

7.6.(不足)邻接表在统计有向图出度时容易,只需遍历依附此顶点的边链;却在统计其入度时,需要遍历整个边表,比较麻烦;可采用十字链表(邻接表与逆邻接表的结合)解决这个问题;

7.7.(不足)邻接表在无向图的存储中,属于行列对称矩阵形式,因此会有一半重复的边数据,故可采用邻接多重表,只存储一半边,来优化存储。

二、测试代码中的图结构

深度优先遍历序列(从 v1 顶点开始):

1.无向图/网:v1-v2-v3-v5-v4-v6-v7

2.有向图/网:v1-v2-v5-v3-v4-v6-v7

广度优先遍历序列(从 v2 顶点开始):

1.无向图/网:v2-v1-v3-v5-v4-v6-v7

2.有向图/网:v2-v5 后序无法遍历

注:有向图的遍历 是遵循出度方向遍历的,若无出度方向,则遍历终止。

三、代码

//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;
}

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