关于数据结构的一个整理：
1、邻接多重表
1、顶点头文件：VertexNode.h
#pragma once
#include"ArcNode.h"
template<class T>
class VertexNode
{
private:
T data;
ArcNode<T>* firstedge;
public:
VertexNode() :firstedge(nullptr) {}
void set_data(T ata) {
this->data = ata;
}
T get_data() {
return data;
}
void set_firstedge(ArcNode<T>* ik) {
this->firstedge = ik;
}
ArcNode<T>* get_firstedge() {
return firstedge;
}
};
2、弧结点头文件：ArcNode.h
#pragma once
template<class T>
class ArcNode
{
private:
int mark; //访问标记 0 代表未访问
int ivex, jvex; //该边依附两个顶点的的位置
ArcNode<T>* ilink, * jlink; //分别指向依附这2个顶点的下一条边
public:
ArcNode() :ivex(0), jvex(0), ilink(nullptr), jlink(nullptr), mark(0) {}
void set_mark(int i) {
this->mark = i;
}
int get_mark() {
return mark;
}
void set_ivex(int i1) {
this->ivex = i1;
}
int get_ivex() {
return ivex;
}
void set_jvex(int i2) {
this->jvex = i2;
}
int get_jvex() {
return jvex;
}
void set_ilink(ArcNode<T>* it) {
this->ilink = it;
}
ArcNode<T>* get_ilink() {
return ilink;
}
void set_jlink(ArcNode<T>* ik) {
this->jlink = ik;
}
ArcNode<T>* get_jlink() {
return jlink;
}
};
3、cpp文件：UNGraphList.cpp
#include<iostream>
#include"ArcNode.h"
#include"VertexNode.h"
#include<Windows.h>
#include<string>
#include<queue>
using namespace std;
const int MAXNUM = 20;//常量表示数组的空间及顶点数组的空间
bool visited[MAXNUM] = { 0 };//初值设为0
typedef string type;//初始类型设为string
template<class T>
class ListGraph
{
private:
int vernum, arcnum;//顶点数，弧数
VertexNode<type>* vertex_arr[MAXNUM];//顶点指针数组
public:
ListGraph();//构造函数
~ListGraph();//析构函数
void run();
int GetIndexByVertexVal(T data);//得到顶点下标
bool DestoryGraph();//销毁图
bool DeleteArc(int i, int j);//删除弧
void DeleteVex(T data);//删除顶点
void CreateGraphs();//创建图
void Display();//输出图
int ComputeDegree(int i);//计算度
};
template<class T>
ListGraph<T>::ListGraph()
{
vernum = 0;//顶点个数
arcnum = 0;//弧个数
for (int i = 0; i < MAXNUM; i++) {
vertex_arr[i] = nullptr;//顶点指针数组置空
}
}
template<class T>
ListGraph<T>::~ListGraph()
{
DestoryGraph();//调用销毁函数
}
template<class T>
int ListGraph<T>::GetIndexByVertexVal(T data)//获得数据data的下标
{
for (int i = 0; i < vernum; ++i)
{
if (data == vertex_arr[i]->get_data())
return i;
}
return -1;
}
template<class T>
bool ListGraph<T>::DestoryGraph()//销毁函数
{
for (int i = vernum - 1; i >= 0; i--) {
DeleteVex(vertex_arr[i]->get_data());
}
return true;
}
template<class T>
bool ListGraph<T>::DeleteArc(int i, int j)//删除边
{
//i和j是要两个顶点的下标
ArcNode<T>* p = nullptr, * q = nullptr;
//以i下标为起点的顶点开始遍历
p = vertex_arr[i]->get_firstedge();//p指向顶点i的第1条边
if (p && p->get_jvex() == j) {//i的临边要是j，因为邻接表有两个下标都要进行判断所以比较i和j
vertex_arr[i]->set_firstedge(p->get_ilink());
}//如果是第一条边则直接连接顶点
else if (p && p->get_ivex() == j) {
vertex_arr[i]->set_firstedge(p->get_jlink());
}
else//第1条边不是待删除边
{
while (p)//向后查找弧<i，j>
{//ivex确保是此顶点下标，jvex找待删除边
if (p->get_ivex() == i && p->get_jvex() != j)//不是待删除边
{
q = p;
p = p->get_ilink();//找下一个邻接顶点
}
else if (p->get_jvex() == i && p->get_ivex() != j)//不是待删除边
{
q = p;
p = p->get_jlink();//找下一个邻接顶点
}
else
{
break;//是邻接顶点w
}
}
if (!p) { return 1; }//p为空则表示没有此边，直接退出
if (p->get_ivex() == i && p->get_jvex() == j)//找到弧<i,j>(判断是否按ilink遍历的)
{//q是p的前驱
if (q->get_ivex() == i)
{//p的前驱连接q的下一个
q->set_ilink(p->get_ilink());
}
else
{
q->set_jlink(p->get_ilink());
}
}
else if (p->get_ivex() == j && p->get_jvex() == i)//找到弧<i,j>(按jlink遍历)
{
if (q->get_ivex() == i)
{
q->set_ilink(p->get_jlink());
}
else
{
q->set_jlink(p->get_jlink());
}
}
}
//以j下标为起点的顶点开始遍历
p = vertex_arr[j]->get_firstedge();//p指向顶点w的第1条边
if (p->get_jvex() == i) {// 第1条边即为待删除边(情况1)
vertex_arr[j]->set_firstedge(p->get_ilink());
}
else if (p->get_ivex() == i) {// 第1条边即为待删除边(情况2)
vertex_arr[j]->set_firstedge(p->get_jlink());
}
else // 第1条边不是待删除边
{
while (p)//向后查找弧<i，j>
{
if (p->get_ivex() == j && p->get_jvex() != i)//不是待删除边
{
q = p;
p = p->get_ilink();//找下一个邻接顶点
}
else if (p->get_jvex() == j && p->get_ivex() != i)//不是待删除边
{
q = p;
p = p->get_jlink();//找下一个邻接顶点
}
else
{
break;//是邻接顶点w
}
}
if (!p) { return 1; }
if (p->get_ivex() == i && p->get_jvex() == j)//找到弧<i,j>(情况1)
{
if (q->get_ivex() == j)
{
q->set_ilink(p->get_jlink());
}
else
{
q->set_jlink(p->get_jlink());
}
}
else if (p->get_ivex() == j && p->get_jvex() == i)//找到弧<i,j>(情况2)
{
if (q->get_ivex() == j)
{
q->set_ilink(p->get_ilink());
}
else
{
q->set_jlink(p->get_ilink());
}
}
}
delete p;//释放结点
p = nullptr;
arcnum--;//边数-1
return 0;
}
template<class T>
void ListGraph<T>::DeleteVex(T data)
{
int i = GetIndexByVertexVal(data);// i为待删除顶点的序号
if (i == -1) {
cout << "未找到此数据。" << endl;
return;
}
for (int j = 0; j < vernum; j++)//删除与顶点i相连的边(如果有的话)
{
if (i != j) {
DeleteArc(i, j);//如果存在此弧，则删除
}
}
for (int j = i + 1; j < vernum; j++)//排在顶点v后面的顶点的序号减1
{
vertex_arr[j - 1] = vertex_arr[j];
}
vernum--; // 顶点数减1
ArcNode<T>* p = nullptr, * q = nullptr;
for (int j = i; j < vernum; j++) // 修改序号大于i的顶点在表结点中的序号
{
p = vertex_arr[j]->get_firstedge();
if (p)
if (p->get_ivex() == j + 1)//ivxe是此顶点的下标与j+1进行判断
{
p->set_ivex(p->get_ivex() - 1);
p = p->get_ilink();
}
else
{
p->set_jvex(p->get_jvex() - 1);
p = p->get_jlink();
}
}
}
template<class T>
void ListGraph<T>::CreateGraphs()//创造无向图
{
int ding = 0, hu = 0;
cout << "输入顶点个数和边数：";
cin >> ding >> hu;
if (hu == 0 && ding == 0)return;
//判断越界
int sss = vernum;//避免改动vernum
if (sss + ding > MAXNUM) {
cout << "StackOverflow！" << endl;
return;
}
//无向图顶点与弧的最多个数是Cn2：n(n-1)/2
if (!(arcnum + hu <= (sss + ding) * (sss + ding - 1) / 2)) {//判断弧的数
cout << "你输入的弧的数量达到上限，强制退出，下次再输入。" << endl; system("pause");
return;
}
//顶点数据输入
for (int i = vernum; i < vernum + ding; i++) {
vertex_arr[i] = new VertexNode<T>;//先开辟空间，不然无法使用get_data()
}
cout << "请输入" << ding << "个顶点" << endl;
for (int i = vernum; i < vernum + ding; ++i)
{
cout << i + 1 << " :";
T val;
while (1) {
bool f = false;
cin >> val;
for (int j = 0; j < vernum + ding; j++) {
if (val == vertex_arr[j]->get_data()) {
cout << "数据重复。重新输入：";
f = true;
break;
}
}
if (!f)break;
}
vertex_arr[i]->set_data(val);
vertex_arr[i]->set_firstedge(nullptr);
}
vernum += ding;//更新顶点个数
//弧节点选择
cout << "请输入由两个顶点构成的边" << arcnum + hu << "条" << endl;
for (int i = arcnum; i < arcnum + hu; ++i)
{
int m = 0, n = 0;
while (1) {
bool f = false;
T one, two;
cout << "顶点one：";
cin >> one;
cout << "顶点two：";
cin >> two;
m = GetIndexByVertexVal(one);//查找顶点one和two的下标
n = GetIndexByVertexVal(two);
if (m == -1 || n == -1) {
cout << "访问越界，不存在此弧，请再次输入" << endl;
f = true;
}
else {//判断两个节点之间是否存在相同的边
ArcNode<T>* p, * q;
int max = 0, min = 0;
if (m > n) {//确保顶点下标位置不反过来
max = m;
min = n;
}
else {
max = n;
min = m;
}
//过一遍ilink这个链表
p = vertex_arr[min]->get_firstedge();//min就是自己的位置，max就是临边的下标
while (p) {
if (p->get_jvex() == max) {
cout << "弧重复。重新输入*" << endl;
f = true;
}
p = p->get_ilink();
}
//过一遍jlink这个链表
q = vertex_arr[min]->get_firstedge();
while (q) {
if (q->get_ivex() == max) {
cout << "弧重复。重新输入*" << endl;
f = true;
}
q = q->get_jlink();
}
}
if (!f)break;
}
//顶点下标，弧节点连接
ArcNode<T>* arc = new ArcNode<T>;
arc->set_ivex(m);
arc->set_jvex(n);
//表头连接m
arc->set_ilink(vertex_arr[m]->get_firstedge());//表头插入法
vertex_arr[m]->set_firstedge(arc);
//表头连接n
arc->set_jlink(vertex_arr[n]->get_firstedge());//表头插入法
vertex_arr[n]->set_firstedge(arc);
cout << "-----------------" << endl;
}
arcnum += hu;//更新弧的个数
system("pause");
}
template<class T>
void ListGraph<T>::Display()
{ //输出无向图的邻接多重表
//置边的访问标记为未被访问
if (vernum > 0) {
int i;
ArcNode<T>* p = nullptr;
for (i = 0; i < vernum; i++)
{//从所有的顶点处开始遍历，将所有mark设为0
p = vertex_arr[i]->get_firstedge();
while (p)
{
p->set_mark(0);//0 未访问，1 已访问
if (p->get_ivex() == i) {
p = p->get_ilink();//若ivex不再是下标i是则表明在别的顶点中亦含有这条边，故跳到jlink中
}
else {
p = p->get_jlink();
}
}
}
cout << vernum << "个顶点:" << endl;
for (i = 0; i < vernum; ++i) { cout << vertex_arr[i]->get_data() << " "; }
cout << endl << arcnum << "条边:" << endl;
for (i = 0; i < vernum; i++)
{
p = vertex_arr[i]->get_firstedge();
while (p)
if (p->get_ivex() == i)//边的i端与该顶点有关
{
if (!p->get_mark())//只输出一次
{
cout << vertex_arr[i]->get_data() << "—" << vertex_arr[p->get_jvex()]->get_data() << endl;
p->set_mark(1);
}
p = p->get_ilink();
}
else // 边的j端与该顶点有关
{
if (!p->get_mark())//只输出一次
{
cout << vertex_arr[p->get_ivex()]->get_data() << "—" << vertex_arr[i]->get_data() << endl;
p->set_mark(1);
}
p = p->get_jlink();
}
}
}
else {
cout << "图中无数据。" << endl;
}
cout << endl;
system("pause");
}
template<class T>
int ListGraph<T>::ComputeDegree(int i)//计算下标为i的顶点的度
{
int degree = 0;
ArcNode<T>* p = vertex_arr[i]->get_firstedge();
while (p) {
if (p->get_ivex() == i || p->get_jvex() == i) {
degree++;//度
}
if (p->get_ivex() == i) {//如果在自己这层则ilink遍历，否则指向jlink
p = p->get_ilink();
}
else {
p = p->get_jlink();
}
}
return degree;
}
void menu()
{
cout << "**********" << endl;
cout << "-1.增加" << endl;
cout << "-2.打印" << endl;
cout << "-3.顶点的度" << endl;
cout << "-4.销毁" << endl;
cout << "-5.删除弧" << endl;
cout << "-6.删除顶点" << endl;
cout << "-0.退出 请选择：";
}
template<class T>
void ListGraph<T>::run()
{
while (1)
{
system("cls");
menu();
string f1 = "";
cin >> f1;
cout << endl;
if (f1 == "1") {
CreateGraphs();
}
else if (f1 == "2") {
Display();
}
else if (f1 == "3") {
cout << "请输入顶点：";
T data;
cin >> data;
int index = GetIndexByVertexVal(data);
if (index == -1)
{
cout << "查找失败。" << endl;
}
else
{
cout << "该顶点的度是：" << ComputeDegree(index) << endl;
}
system("pause");
}
else if (f1 == "4") {
if (vernum > 0) {
cout << "销毁 " << vernum << " 个顶点。" << endl;
DestoryGraph();
cout << "销毁完成。" << endl;
}
else {
cout << "图中没数据。" << endl;
}
system("pause");
}
else if (f1 == "5") {
if (vernum > 0) {
cout << "请输入两个顶点,删除它们的连线。" << endl;
int i = 0, j = 0;
while (1) {
T one, two;
cout << "顶点one：";
cin >> one;
cout << "顶点two：";
cin >> two;
i = GetIndexByVertexVal(one);
j = GetIndexByVertexVal(two);
if (i == -1 || j == -1) {
cout << "访问越界，不存在此弧，请再次输入" << endl;
}
else if (i == j) {
cout << "输入格式错误" << endl;
}
else {
if (DeleteArc(i, j)) {
cout << "不存在此弧。" << endl;
}
else {
cout << "删除成功。" << endl;
}
break;
}
}
}
else {
cout << "图中无数据。" << endl;
}
system("pause");
}
else if (f1 == "6") {
if (vernum > 0) {
cout << "请输入顶点,并删除它。" << endl;
T data;
cin >> data;
DeleteVex(data);
cout << "删除成功。" << endl;
}
else {
cout << "图中无数据。" << endl;
}
system("pause");
}
else if (f1 == "0") {
system("cls");
cout << "\n\t\t期待您的再次使用！" << endl;
break;
}
}
}
int main()
{
ListGraph<type> graph;
graph.run();
return 0;
}
2、十字链表泛型
1、顶点节点文件：VertexNode.h
#pragma once
// 定义顶点结点
#include"ArcNode.h"
template<class T>
class VertexNode
{
private:
T data; //存储有关顶点的信息
ArcNode<T>* firstInarc; //链接到以该顶点为终点的第一条弧
ArcNode<T>* firstOutarc;//链接到以该顶点为起点的第一条弧
public:
// 构造函数
VertexNode() : firstInarc(nullptr), firstOutarc(nullptr) {}
public:
T get_data() {
return data;
}
void set_data(T data) {
this->data = data;
}
ArcNode<T>* get_firstInarc() {
return firstInarc;
}
ArcNode<T>* get_firstOutarc() {
return firstOutarc;
}
void set_firstInarc(ArcNode<T>* f) {
this->firstInarc = f;
}
void set_firstOutarc(ArcNode<T>* t) {
this->firstOutarc = t;
}
};
2、弧结点文件：ArcNode.h
#pragma once
//定义弧结点
template<class T>
class ArcNode
{
private:
int tailvex; //弧尾
int headvex; //弧头
//int weight; //弧的权值
ArcNode<T>* tailnextarc;//出弧
ArcNode<T>* headnextarc;//入弧
int tag = 0; //标记域，标记该弧是否被处理或被搜索过 1表示删除
public:
// 构造函数
ArcNode(int tv, int hv) :tailvex(tv), headvex(hv),
tailnextarc(nullptr), headnextarc(nullptr) {}
public:
int get_tailvex() {
return tailvex;
}
int get_headvex() {
return headvex;
}
void set_tailvex(int t) {
this->tailvex = t;
}
void set_headvex(int h) {
this->headvex = h;
}
int get_tag() {
return tag;
}
void set_tag(int flag) {
this->tag = flag;
}
ArcNode<T>* get_tailnextarc() {
return tailnextarc;
}
ArcNode<T>* get_headnextarc() {
return headnextarc;
}
void set_tailnextarc(ArcNode<T>* f) {
this->tailnextarc = f;
}
void set_headnextarc(ArcNode<T>* t) {
this->headnextarc = t;
}
};
3、GraphList.cpp：程序启动文件
#include <iostream>
#include<Windows.h>
#include"ArcNode.h"
#include"VertexNode.h"
using namespace std;
const int MAXNUM = 20;//顶点最大容量
typedef string type;
template<class T>
class ListGraph
{
private:
int vernum, arcnum;//顶点数，弧数
VertexNode<type>* vertex_arr[MAXNUM];//顶点指针数组
public:
ListGraph();
~ListGraph();
bool DestoryGraph();//销毁图
void use_InsertNode();//调用增加顶点的函数
void InsertNode(T value);//增加顶点
void use_DeleteNode();//调用删除顶点的函数
void DeleteNode(int pos_index);
void use_InsertEdge();//调用增加弧的函数
bool InsertEdge(int tail, int head);//添加弧
void use_DeleteEdge();//调用删除弧的函数
void DeleteEdge(int tail_index, int head_index);//删除弧
void Print();//图的遍历
void ComputeDegree();//计算度
};
template<class T>
ListGraph<T>::ListGraph()//构造函数
{
vernum = 0;//顶点个数
arcnum = 0;//弧个数
for (int i = 0; i < MAXNUM; i++) {
vertex_arr[i] = nullptr;
}
}
template<class T>
ListGraph<T>::~ListGraph()//析构函数
{
DestoryGraph();
}
template<class T>
bool ListGraph<T>::DestoryGraph()//销毁函数
{
if (vernum <= 0)return false;
for (int i = 0; i < vernum; i++) { // 释放所有顶点的内存空间
ArcNode<T>* p = vertex_arr[i]->get_firstOutarc(), * q = NULL;
while (p != NULL) { // 释放所有出弧节点的内存空间
q = p;
p = p->get_tailnextarc();
delete q;
q = nullptr;
}
}
vernum = 0;
arcnum = 0;
return true;
}
template<class T>
void ListGraph<T>::use_InsertNode()//调用增加节点的函数
{
if (vernum >= MAXNUM) {//顶点空间不够的话
cout << "空间不够。" << endl; Sleep(3500); return;
}
int n;
cout << "添加顶点个数：";
cin >> n;
for (int i = 1; i <= n; i++) {
cout << "第" << i << "个：";
T data;
while (1) {
cin >> data;
bool f = false;//为true则表明数据重复
for (int i = 0; i < vernum; i++) {
if (vertex_arr[i]->get_data() == data) {
cout << "输入的顶点数据重复。重新输入：";
f = true;
break;
}
}
if (!f)break;
}
InsertNode(data);//插入数据
}
cout << "添加顶点数据过程结束。" << endl;
Sleep(350);
}
template<class T>
void ListGraph<T>::InsertNode(T value)//顶点数据的插入
{
if (vernum >= MAXNUM) {
cout << "顶点已经达到上限，不可添加了。" << endl;
return;
}
cout << "将数据 " << value << " 存放到顶点为 " << vernum + 1 << " 的位置。" << endl;
//添加新顶点到顶点数组
vertex_arr[vernum] = new VertexNode<T>;
vertex_arr[vernum]->set_data(value);
vertex_arr[vernum]->set_firstInarc(NULL);
vertex_arr[vernum]->set_firstOutarc(NULL);
++vernum;//顶点自增
cout << "Insert successful!" << endl;
}
template<class T>
void ListGraph<T>::use_DeleteNode()
{
if (vernum > 0) {
cout << "共有顶点数量：" << vernum << endl;
cout << "请输入要删除的顶点结点数据：";
T data;
cin >> data;
bool f = false;
for (int i = 0; i < vernum; i++) {
if (vertex_arr[i]->get_data() == data) {
DeleteNode(i);
f = true;
break;
}
}
if (f) {
cout << "成功删除此节点的所有相关信息。" << endl;
}
else {
cout << "未找到此数据的信息。" << endl;
}
}
else {
cout << "没有顶点数据。" << endl;
}
system("pause");
}
template<class T>
void ListGraph<T>::DeleteNode(int pos_index)
{
//删除顶点的所有出度
for (int j = 0; j < vernum; j++)
{
if (pos_index != j) {
DeleteEdge(pos_index, j);//删除每个顶点与pos_index相关的边
}
}
//删除所有顶点的入度
for (int j = 0; j < vernum; j++)
{
if (pos_index != j) {
DeleteEdge(j, pos_index);//删除每个顶点与pos_index相关的边
}
}
for (int j = pos_index + 1; j < vernum; j++)//排在顶点v后面的顶点的序号减1
{
vertex_arr[j - 1] = vertex_arr[j];
}
vernum--; // 顶点数减1
//标志
ArcNode<T>* pq = nullptr;
for (int i = 0; i < vernum; i++) {
pq = vertex_arr[i]->get_firstOutarc();
while (pq != NULL)
{
pq->set_tag(0);
pq = pq->get_tailnextarc();
}
}
//修改下标
ArcNode<T>* p = nullptr;
for (int j = 0; j < vernum; j++)//修改序号大于i的顶点在表结点中的序号
{
p = vertex_arr[j]->get_firstOutarc();//出度开始遍历
while (p != NULL)
{
if (!p->get_tag()) {
if (p->get_tailvex() > pos_index) {
p->set_tailvex(p->get_tailvex() - 1);
}
if (p->get_headvex() > pos_index) {
p->set_headvex(p->get_headvex() - 1);
}
p->set_tag(1);
}
p = p->get_tailnextarc();
}
}
}
template<class T>
void ListGraph<T>::use_InsertEdge()//调用增加边的函数
{
cout << "共有顶点数量：" << vernum << endl;
if (vernum < 2) {
cout << "顶点不够，不能添加弧。" << endl; system("pause"); return;
}
int n = 0, max = 0;
cout << "请输入添加边的数量：";
cin >> n;
max = vernum * (vernum - 1);//最多边数
if (max < arcnum + n) {
cout << "边数已经满了" << endl;
system("pause");
return;
}
while (n--) {
int vh, vt;
cout << "****" << endl;
while (1)
{
cout << "出发点：";
cin >> vt;
cout << "终点：";
cin >> vh;
if (vt == vh) {
cout << "输入错误。重新输入：" << endl;
}
else if (vt - 1 < vernum && vh - 1 < vernum) {
InsertEdge(vt - 1, vh - 1);//数组下标从0开始
break;
}
else {
cout << "弧的位置越界。重新添加：" << endl;
}
}
}
Sleep(350);
}
template<class T>
bool ListGraph<T>::InsertEdge(int tail, int head)//添加边<tail,head>
{
//添加新的弧 arc，这需要两部分连接出弧和入弧
ArcNode<T>* arc = new ArcNode<T>(tail, head);
//先检查是否已经存在该弧
ArcNode<T>* arc1 = vertex_arr[tail]->get_firstOutarc();//出弧顶点
while (arc1 != nullptr) {
if (arc1->get_headvex() == head) {
cout << "不可重复添加相同的弧。" << endl;
return 0;
}
arc1 = arc1->get_tailnextarc();//出弧那么每个节点都是尾部
}
bool flag = false;
//在起点的出弧中添加该弧
if (vertex_arr[tail]->get_firstOutarc() == nullptr)
{//顶点的下个为空的话，让出弧指向它
vertex_arr[tail]->set_firstOutarc(arc);
flag = true;
}
else {//尾插
ArcNode<T>* next_arc = vertex_arr[tail]->get_firstOutarc();
while (next_arc->get_tailnextarc() != nullptr) {//同一个起点的下一条弧
next_arc = next_arc->get_tailnextarc();//找到一个空的弧头
}
next_arc->set_tailnextarc(arc);
flag = true;
}
// 在终点的入弧中添加该弧
if (vertex_arr[head]->get_firstInarc() == nullptr)
{//被指向的顶点，也是入弧
vertex_arr[head]->set_firstInarc(arc);
flag = true;
}
else {
ArcNode<T>* in_arc = vertex_arr[head]->get_firstInarc();
while (in_arc->get_headnextarc() != nullptr) {//对到达同一终点的入弧遍历找空
in_arc = in_arc->get_headnextarc();
}
in_arc->set_headnextarc(arc);
flag = true;
}
if (flag) {
arcnum++;//弧个数增加
cout << "Arc insertion successful!" << endl;
return 1;
}
else {
cout << "Arc insertion failed!" << endl;
return 0;
}
}
template<class T>
void ListGraph<T>::use_DeleteEdge()//调用删除边的操作
{
if (vernum < 2) {
cout << "没有弧。" << endl; system("pause"); return;
}
int vh, vt;
cout << "*每次只能删除一条弧。" << endl;
while (1)
{
cout << "起点：";
cin >> vt;
cout << "终点：";
cin >> vh;
if (vt == vh) {
cout << "输入错误。重新输入：" << endl;
}
else if (vt - 1 < vernum && vh - 1 < vernum) {
//检查此弧是否存在
bool f = false;
ArcNode<T>* arc = vertex_arr[vt-1]->get_firstOutarc();//出弧顶点
while (arc != nullptr) {
if (arc->get_headvex() == vh-1) {
f = true;
DeleteEdge(vt-1, vh-1);
break;
}
arc = arc->get_tailnextarc();//出弧那么每个节点都是尾部
}
if (f) {
cout << "您已经成功删除了一条弧。" << endl;
}
else {
cout << "该弧删除失败。" << endl;
}
break;
}
else {
cout << "弧的位置越界。重新输入：" << endl;
}
}
Sleep(350);
}
template<class T>
void ListGraph<T>::DeleteEdge(int tail_index, int head_index)//删除边<tail,head>
{
ArcNode<T>* p = vertex_arr[tail_index]->get_firstOutarc(), * q = NULL;
while (p != NULL && p->get_headvex() != head_index) { // 寻找待删除的弧节点
q = p;
p = p->get_tailnextarc();//找到待删除节点p
}
//未找到待删除的弧节点则返回
if (p == NULL) {
//cout << "未找到此弧节点。" << endl;
return;
}
//出弧
//待删除的是第一个出弧，则更新firstout指针
if (q == NULL) {
vertex_arr[tail_index]->set_firstOutarc(p->get_tailnextarc());
}
else
{//待删除的不是第一个出弧，则修改前驱弧节点的next指针
q->set_tailnextarc(p->get_tailnextarc());
}
//入弧
//待删除的是第一个入弧，则更新firstin指针
if (vertex_arr[head_index]->get_firstInarc() == p) {
vertex_arr[head_index]->set_firstInarc(p->get_headnextarc());
}
else
{//待删除的不是第一个入弧，则修改前驱弧节点的hlink指针
q = vertex_arr[head_index]->get_firstInarc();
while (q->get_headnextarc() != p) {
q = q->get_headnextarc();//从入弧开始找节点p
}
q->set_headnextarc(p->get_headnextarc());//入弧的跳跃
}
delete p;//释放待删除的弧节点的内存空间
p = nullptr;
}
template<class T>
void ListGraph<T>::Print()//打印我的图
{
for (int i = 0; i < vernum; i++)
{
cout << "----------------------------------------" << endl;
VertexNode<T>* ver = vertex_arr[i];//起初表示方法
cout << "顶点位置：" << i + 1 << " 顶点数据:" << ver->get_data() << endl;//第一个顶点的数据
ArcNode<T>* out_arc = ver->get_firstOutarc();//顶点出弧指针
if (out_arc == nullptr)cout << "没有出弧。";//为空
else {//各个顶点的出弧情况
cout << "出:";
while (out_arc != nullptr) {
cout << out_arc->get_tailvex() + 1 << "->" << out_arc->get_headvex() + 1 << " ";
out_arc = out_arc->get_tailnextarc();
}
}
cout << endl;
ArcNode<T>* in_arc = ver->get_firstInarc();
if (in_arc == nullptr)cout << "没有入弧。";
else {//各个顶点的入弧情况
cout << "入:";
while (in_arc != nullptr) {
cout << in_arc->get_tailvex() + 1 << "->" << in_arc->get_headvex() + 1 << " ";
in_arc = in_arc->get_headnextarc();
}
}
cout << endl;
}
if (vernum == 0) { cout << "无数据。" << endl; }
system("pause");
}
template<class T>
void ListGraph<T>::ComputeDegree()//计算出入度
{
if (vernum > 0) {
cout << "共有顶点数量：" << vernum << endl;
cout << "请输入要看的顶点结点的出度和入度：";
T data;
cin >> data;
bool f = false;
for (int i = 0; i < vernum; i++) {
if (vertex_arr[i]->get_data() == data)
{
f = true;
ArcNode<T>* q = NULL;
int outDegree = 0, inDegree = 0;
//计算顶点Vertex[i]的出度
q = vertex_arr[i]->get_firstOutarc();
while (q != NULL)
{
outDegree++;
q = q->get_tailnextarc();
}
//计算顶点Vertex[i]的入度
q = vertex_arr[i]->get_firstInarc();
while (q != NULL)
{
inDegree++;
q = q->get_headnextarc();
}
cout << "顶点" << vertex_arr[i]->get_data() << "的出度为" << outDegree << endl;
cout << "顶点" << vertex_arr[i]->get_data() << "的入度为" << inDegree << endl;
break;
}
}
if (!f) { cout << "未查到此顶点数据。" << endl; }
}
else {
cout << "没有顶点数据。" << endl;
}
system("pause");
}
void menu()
{
cout << "**********" << endl;
cout << "-1.增加顶点" << endl;
cout << "-2.删除顶点" << endl;
cout << "-3.增加弧" << endl;
cout << "-4.删除弧" << endl;
cout << "-5.打印" << endl;
cout << "-6.顶点的度" << endl;
cout << "-7.销毁" << endl;
cout << "-0.退出 请选择：";
}
void run()
{
ListGraph<type> graph;
while (1)
{
system("cls");
menu();
string f1 = "";
cin >> f1;
cout << endl;
if (f1 == "1") {
graph.use_InsertNode();
}
else if (f1 == "2") {
graph.use_DeleteNode();
}
else if (f1 == "3") {
graph.use_InsertEdge();
}
else if (f1 == "4") {
graph.use_DeleteEdge();
}
else if (f1 == "5") {
graph.Print();
}
else if (f1 == "6") {
graph.ComputeDegree();
}
else if (f1 == "7") {
bool f = graph.DestoryGraph();
if (f) {
cout << "销毁完成。" << endl;
}else{
cout << "无顶点数据。" << endl;
}
system("pause");
}
else if (f1 == "0") {
system("cls");
cout << "\n\t\t期待您的再次使用！" << endl;
break;
}
}
}
int main()
{
run();
return 0;
}
3、边集数组
头文件
EdgeNode.h
#pragma once
template<class T>
class EdgeNode
{
private:
int begin;
int end;
public:
bool operator==(const EdgeNode& obj) const {
if (begin == obj.begin && end == obj.end)return true;
return false;
}
EdgeNode& operator=(const EdgeNode& obj) {
this->begin = obj.begin;
this->end = obj.end;
return *this;
}
EdgeNode() {
begin = 0;
end = 0;
}
int get_begin() {
return begin;
}
int get_end() {
return end;
}
void set_begin(int b) {
this->begin = b;
}
void set_end(int e) {
this->end = e;
}
};
cpp文件
Array.cpp
#include<iostream>
#include"EdgeNode.h"
#include<string>
#include<vector>
using namespace std;
template<class T>
class Arrary//边集数组类
{
private:
vector<EdgeNode<T>> arr;//动态数组
public:
~Arrary();
void run();
void CreateEdges();//添加边
void Display();//打印
void DeleteArc();//删除边
void Destroy();//销毁
bool IsConnected();//是否连通
void ChangeDirecton();//改变连通方向
};
template<class T>
void Arrary<T>::CreateEdges()//添加边
{
int hu = 0;
cout << "请输入边的数量：";
cin >> hu;
if (hu <= 0)return;//如果数量小于0则输入错误
//弧节点选择
cout << "请输入由两个顶点构成的边" << hu << "条" << endl;
while (hu)
{
int one = 0, two = 0;
while (1) {
cout << "起点：";
cin >> one;
cout << "终点：";
cin >> two;
if (one > 0 && two > 0 && one != two)break;//起点和终点不能相同
else {
cout << "格式错误。重新输入" << endl;
}
}
EdgeNode<T> a;//定义边的对象
a.set_begin(one);
a.set_end(two);
//查重函数,重载==运算符
if (find(arr.begin(), arr.end(), a) == arr.end()) {//find函数从头迭代，如果没有返回最后的对象
arr.push_back(a);//如果不重复，则插入在数组最后
hu--;
}
else {
cout << "已经存在此弧了，请再次输入" << endl;
}
cout << "-----------------" << endl;
}
system("pause");
}
template<class T>
void Arrary<T>::Display()//遍历打印
{
cout << "共有" << arr.size() << "条边" << endl;
for (int i = 0; i < arr.size(); i++) {//外层循环表示边的数量
EdgeNode<T> a1 = arr[i];//a1对象暂时指代arr[i]
cout << a1.get_begin() << "->" << a1.get_end() << endl;
}
system("pause");
}
template<class T>
void Arrary<T>::DeleteArc()//删除边
{
if (arr.size() == 0) {
cout << "没有边" << endl;
system("pause");
return;
}
int sa, sb;
cout << "请输入你要删除边的起点和终点" << endl;
while (1) {
cout << "起点：";
cin >> sa;
cout << "终点：";
cin >> sb;
if (sa > 0 && sb > 0 && sa != sb)break;//不能相同
else {
cout << "格式错误。重新输入" << endl;
}
}
bool f = false;//用来判断是否被删除
for (int i = 0; i < arr.size(); i++) {
EdgeNode<T> aa = arr[i];
if (aa.get_begin() == sa && aa.get_end() == sb) {
//arr.begin() + i为指定被删除元素位置的迭代器
arr.erase(arr.begin() + i);//删除元素，个数减1，capicity不变
f = true;
break;
}
}
if (f) {
cout << "删除成功" << endl;
}
else {
cout << "未查到此数据" << endl;
}
system("pause");
}
template<class T>
void Arrary<T>::Destroy()//销毁
{
int num = arr.size();//数据个数
if (num <= 0) {
cout << "未查找到边" << endl;
}
else {
cout << "销毁" << num << "个数据" << endl;
for (int i = 0; i < num; i++) {
arr.pop_back();//删除最后一个元素，并且释放空间
}
arr.shrink_to_fit();//清除多于空间
cout << "销毁完成" << endl;
}
system("pause");
}
template<class T>
bool Arrary<T>::IsConnected()//判断是否连通
{
int sa, sb;
cout << "请输入你要查找边的起点和终点" << endl;
while (1) {
cout << "起点：";
cin >> sa;
cout << "终点：";
cin >> sb;
if (sa > 0 && sb > 0 && sa != sb)break;
else {
cout << "格式错误。重新输入" << endl;
}
}
bool f = false;
for (int i = 0; i < arr.size(); i++) {
EdgeNode<T> aa = arr[i];
if (aa.get_begin() == sa && aa.get_end() == sb) {
return true;
}
}
return false;
}
template<class T>
void Arrary<T>::ChangeDirecton()//改变起点或终点
{
if (arr.size() <= 0) {
cout << "没有数据" << endl;
system("pause");
return;
}
int sa, sb;
cout << "请输入要改变的边的起点和终点" << endl;
while (1) {
cout << "起点：";
cin >> sa;
cout << "终点：";
cin >> sb;
if (sa > 0 && sb > 0 && sa != sb)break;
else {
cout << "格式错误。重新输入" << endl;
}
}
//找到位置
int index = -1;
for (int i = 0; i < arr.size(); i++) {
EdgeNode<T> aa = arr[i];
if (aa.get_begin() == sa && aa.get_end() == sb) {
index = i;
break;
}
}
int ch = 0, one = 0, two = 0;
cout << "选择1.更换起点2.更换终点\n选择：" << endl;
cin >> ch;
if (ch == 1) {
EdgeNode<T> ac;//临时对象存放新数据
while (1) {
cout << "新起点：";
cin >> one;
ac.set_begin(one);
ac.set_end(sb);
if (one != sa) {
//查重函数,重载==运算符
if (!(find(arr.begin(), arr.end(), ac) == arr.end())) {
cout << "已经存在此弧了，请再次输入" << endl;
continue;
}
}
bool f = false;
for (int i = 0; i < arr.size(); i++) {//检查是否存在one的值
EdgeNode<T> abcd = arr[i];
if (abcd.get_begin() == one) {
f = true;
break;
}
}
if (f && one != sb)break;
else {
cout << "数据不存在或格式错误,退出。" << endl;
system("pause");
return;
}
}
arr[index] = ac;//修改数值
cout << "更改成功" << endl;
system("pause");
}
if (ch == 2) {
EdgeNode<T> aw;
while (1) {
cout << "新终点：";
cin >> two;
aw.set_begin(sa);
aw.set_end(two);
if (two != sb) {
//查重函数,重载==运算符
if (!(find(arr.begin(), arr.end(), aw) == arr.end())) {
cout << "已经存在此弧了，请再次输入" << endl;
continue;
}
}
bool f = false;
for (int i = 0; i < arr.size(); i++) {
EdgeNode<T> abcd = arr[i];
if (abcd.get_end() == two) {
f = true; break;
}
}
if (f && two != sa)break;
else {
cout << "数据不存在或格式错误,退出。" << endl;
system("pause");
return;
}
}
arr[index] = aw;//修改数值
cout << "更改成功" << endl;
system("pause");
}
}
void menu()
{
cout << "**********" << endl;
cout << "-1.添加边" << endl;
cout << "-2.打印" << endl;
cout << "-3.销毁" << endl;
cout << "-4.删除边" << endl;
cout << "-5.检查是否连通" << endl;
cout << "-6.改变连接方向" << endl;
cout << "-0.退出 请选择：";
}
template<class T>
Arrary<T>::~Arrary()
{
int num = arr.size();
for (int i = 0; i < num; i++) {
arr.pop_back();//删除最后一个元素，并且释放空间
}
arr.shrink_to_fit();//清除多于空间
}
template<class T>
void Arrary<T>::run()
{
while (1)
{
system("cls");
menu();
string f1 = "";
cin >> f1;
cout << endl;
if (f1 == "1") {
CreateEdges();
}
else if (f1 == "2") {
Display();
}
else if (f1 == "3") {
Destroy();
}
else if (f1 == "4") {
DeleteArc();
}
else if (f1 == "5") {
if (arr.size() == 0) {
cout << "没有边" << endl;
}
else {
bool f = IsConnected();
if (f) {
cout << "此边已经连通" << endl;
}
else {
cout << "没连通" << endl;
}
}
system("pause");
}
else if (f1 == "6") {
ChangeDirecton();
}
else if (f1 == "0") {
system("cls");
cout << "\n\t\t期待您的再次使用！" << endl;
break;
}
}
}
int main()
{
Arrary<string> graph;
graph.run();
return 0;
}