1、图的父类
是一个抽象类，不能实类化对象，应具有的是抽象方法，提供一个接口，在由子类继承，实现自己的方法，
应提供的共有抽象方法和保护的数据：
public: virtual bool insertVertex(const Type &v) = 0; //插入顶点 virtual bool insertEdge(const Type &v1, const Type &v2) = 0; //插入边 virtual bool removeVertex(const Type &v) = 0; //删除顶点 virtual bool removeEdge(const Type &v1, const Type &v2) = 0; //删除边 virtual int getFirstNeighbor(const Type &v) = 0; //得到第一个相邻顶点 virtual int getNextNeighbor(const Type &v, const Type &w) = 0; //得到下一个相邻顶点 public: virtual int getVertexIndex(const Type &v)const = 0; //得到顶点下标 virtual void showGraph()const = 0; //显示图 protected: int maxVertices; //最大顶点数 int curVertices; //当前顶点数 int curEdges; //当前边数
2、子类继承、实现自己的方法
C++实现，继承的体现，是为了实现多态
(1)Graph.h
#ifndef _GRAPH_H_
#define _GRAPH_H_
#include<iostream>
using namespace std;
#define VERTEX_DEFAULT_SIZE 10
template<typename Type>
class Graph{
public:
bool isEmpty()const{
return curVertices == 0;
}
bool isFull()const{
if(curVertices >= maxVertices || curEdges >= curVertices*(curVertices-1)/2)
return true; //图满有2种情况：(1)、当前顶点数超过了最大顶点数，存放顶点的空间已满
return false; //(2)、当前顶点数并没有满，但是当前顶点所能达到的边数已满
}
int getCurVertex()const{
return curVertices;
}
int getCurEdge()const{
return curEdges;
}
public:
virtual bool insertVertex(const Type &v) = 0; //插入顶点
virtual bool insertEdge(const Type &v1, const Type &v2) = 0; //插入边
virtual bool removeVertex(const Type &v) = 0; //删除顶点
virtual bool removeEdge(const Type &v1, const Type &v2) = 0; //删除边
virtual int getFirstNeighbor(const Type &v) = 0; //得到第一个相邻顶点
virtual int getNextNeighbor(const Type &v, const Type &w) = 0; //得到下一个相邻顶点
public:
virtual int getVertexIndex(const Type &v)const = 0; //得到顶点下标
virtual void showGraph()const = 0; //显示图
protected:
int maxVertices; //最大顶点数
int curVertices; //当前顶点数
int curEdges; //当前边数
};
///////////////////////////////////////////////////下面先是邻接矩阵
template<typename Type>
class GraphMtx : public Graph<Type>{ //邻接矩阵继承父类矩阵
#define maxVertices Graph<Type>::maxVertices //因为是模板，所以用父类的数据或方法都得加上作用域限定符
#define curVertices Graph<Type>::curVertices
#define curEdges Graph<Type>::curEdges
public:
GraphMtx(int vertexSize = VERTEX_DEFAULT_SIZE){ //初始化邻接矩阵
maxVertices = vertexSize > VERTEX_DEFAULT_SIZE ? vertexSize : VERTEX_DEFAULT_SIZE;
vertexList = new Type[maxVertices]; //申请顶点空间
for(int i = 0; i < maxVertices; i++){ //都初始化为0
vertexList[i] = 0;
}
edge = new int*[maxVertices]; //申请边的行
for(i = 0; i < maxVertices; i++){ //申请列空间
edge[i] = new int[maxVertices];
}
for(i = 0; i < maxVertices; i++){ //赋初值为0
for(int j = 0; j < maxVertices; j++){
edge[i][j] = 0;
}
}
curVertices = curEdges = 0; //当前顶点和当前边数
}
GraphMtx(Type (*mt)[4], int sz){ //通过已有矩阵的初始化
int e = 0; //统计边数
maxVertices = sz > VERTEX_DEFAULT_SIZE ? sz : VERTEX_DEFAULT_SIZE;
vertexList = new Type[maxVertices]; //申请顶点空间
for(int i = 0; i < maxVertices; i++){ //都初始化为0
vertexList[i] = 0;
}
edge = new int*[maxVertices]; //申请边的行
for(i = 0; i < maxVertices; i++){ //申请列空间
edge[i] = new Type[maxVertices];
}
for(i = 0; i < maxVertices; i++){ //赋初值为矩阵当中的值
for(int j = 0; j < maxVertices; j++){
edge[i][j] = mt[i][j];
if(edge[i][j] != 0){
e++; //统计列的边数
}
}
}
curVertices = sz;
curEdges = e/2;
}
~GraphMtx(){}
public:
bool insertVertex(const Type &v){
if(curVertices >= maxVertices){
return false;
}
vertexList[curVertices++] = v;
return true;
}
bool insertEdge(const Type &v1, const Type &v2){
int maxEdges = curVertices*(curVertices-1)/2;
if(curEdges >= maxEdges){
return false;
}
int v = getVertexIndex(v1);
int w = getVertexIndex(v2);
if(v==-1 || w==-1){
cout<<"edge no exit"<<endl; //要插入的顶点不存在，无法插入
return false;
}
if(edge[v][w] != 0){ //当前边已经存在，不能进行插入
return false;
}
edge[v][w] = edge[w][v] = 1; //因为是无向图，对称的，存在边赋为1；
return true;
} //删除顶点的高效方法
bool removeVertex(const Type &v){
int i = getVertexIndex(v);
if(i == -1){
return false;
}
vertexList[i] = vertexList[curVertices-1];
int edgeCount = 0;
for(int k = 0; k < curVertices; k++){
if(edge[i][k] != 0){ //统计删除该行的边数
edgeCount++;
}
}
//删除行
for(int j = 0; j < curVertices; j++){
edge[i][j] = edge[curVertices-1][j];
}
//删除列
for(j = 0; j < curVertices; j++){
edge[j][i] = edge[j][curVertices-1];
}
curVertices--;
curEdges -= edgeCount;
return true;
}
/* //删除顶点用的是数组一个一个移动的方法，效率太低。
bool removeVertex(const Type &v){
int i = getVertexIndex(v);
if(i == -1){
return false;
}
for(int k = i; k < curVertices-1; ++k){
vertexList[k] = vertexList[k+1];
}
int edgeCount = 0;
for(int j = 0; j < curVertices; ++j){
if(edge[i][j] != 0)
edgeCount++;
}
for(int k = i; k < curVertices-1; ++k)
{
for(int j = 0; j < curVertices; ++j)
{
edge[k][j] = edge[k+1][j];
}
}
for(int k = i; k < curVertices-1; ++k)
{
for(int j = 0; j < curVertices; ++j)
{
edge[j][k] = edge[j][k+1];
}
}
curVertices--;
curEdges -= edgeCount;
return true;
}
*/
bool removeEdge(const Type &v1, const Type &v2){
int v = getVertexIndex(v1);
int w = getVertexIndex(v2);
if(v==-1 || w==-1){ //判断要删除的边是否在当前顶点内
return false; //顶点不存在
}
if(edge[v][w] == 0){ //这个边根本不存在，没有必要删
return false;
}
edge[v][w] = edge[w][v] = 0; //删除这个边赋值为0，代表不存在；
curEdges--;
return true;
}
int getFirstNeighbor(const Type &v){
int i = getVertexIndex(v);
if(i == -1){
return -1;
}
for(int col = 0; col < curVertices; col++){
if(edge[i][col] != 0){
return col;
}
}
return -1;
}
int getNextNeighbor(const Type &v, const Type &w){
int i = getVertexIndex(v);
int j = getVertexIndex(w);
if(i==-1 || j==-1){
return -1;
}
for(int col = j+1; col < curVertices; col++){
if(edge[i][col] != 0){
return col;
}
}
return -1;
}
public:
void showGraph()const{
if(curVertices == 0){
cout<<"Nul Graph"<<endl;
return;
}
for(int i = 0; i < curVertices; i++){
cout<<vertexList[i]<<" ";
}
cout<<endl;
for(i = 0; i < curVertices; i++){
for(int j = 0; j < curVertices; j++){
cout<<edge[i][j]<<" ";
}
cout<<vertexList[i]<<endl;
}
}
int getVertexIndex(const Type &v)const{
for(int i = 0; i < curVertices; i++){
if(vertexList[i] == v){
return i;
}
}
return -1;
}
private:
Type *vertexList; //存放顶点的数组
int **edge; //存放顶点关系的矩阵用边表示
};
///////////////////////////////////////////////////////////////下面是邻接表
template<typename Type>
class Edge{ //边的存储结构
public:
Edge(int num) : dest(num), link(NULL){}
public:
int dest;
Edge *link;
};
template<typename Type>
class Vertex{ //顶点的存储结构
public:
Type data;
Edge<Type> *adj;
};
template<typename Type>
class GraphLnk : public Graph<Type>{
#define maxVertices Graph<Type>::maxVertices //因为是模板，所以用父类的数据或方法都得加上作用域限定符
#define curVertices Graph<Type>::curVertices
#define curEdges Graph<Type>::curEdges
public:
GraphLnk(int sz = VERTEX_DEFAULT_SIZE){
maxVertices = sz > VERTEX_DEFAULT_SIZE ? sz : VERTEX_DEFAULT_SIZE;
vertexTable = new Vertex<Type>[maxVertices];
for(int i = 0; i < maxVertices; i++){
vertexTable[i].data = 0;
vertexTable[i].adj = NULL;
}
curVertices = curEdges = 0;
}
public:
bool insertVertex(const Type &v){
if(curVertices >= maxVertices){
return false;
}
vertexTable[curVertices++].data = v;
return true;
}
bool insertEdge(const Type &v1, const Type &v2){
int v = getVertexIndex(v1);
int w = getVertexIndex(v2);
if(v==-1 || w==-1){
return false;
}
Edge<Type> *p = vertexTable[v].adj;
while(p != NULL){ //这里主要判断边是否已经存在
if(p->dest == w){ //无向图，判断一边即可;
return false;
}
p = p->link;
}
//v1-->v2 //采用头插
Edge<Type> *s = new Edge<Type>(w);
s->link = vertexTable[v].adj;
vertexTable[v].adj = s;
//v2-->v1 //采用头插
Edge<Type> *q = new Edge<Type>(v);
q->link = vertexTable[w].adj;
vertexTable[w].adj = q;
curEdges++;
return true;
}
bool removeVertex(const Type &v){
int i = getVertexIndex(v);
if(i == -1){
return false;
}
Edge<Type> *p = vertexTable[i].adj;
while(p != NULL){
vertexTable[i].adj = p->link;
int k = p->dest;
Edge<Type> *q = vertexTable[k].adj;
if(q->dest == i){
vertexTable[k].adj = q->link;
delete q;
}else{
while(q->link != NULL && q->link->dest != i){
q = q->link;
}
Edge<Type> *t = q->link;
q->link = t->link;
delete t;
}
delete p;
p = vertexTable[i].adj;
curEdges--;
}
curVertices--; //下面实行覆盖
vertexTable[i].data = vertexTable[curVertices].data;
vertexTable[i].adj = vertexTable[curVertices].adj;
vertexTable[curVertices].adj = NULL;
int k = curVertices;
p = vertexTable[i].adj;
while(p != NULL){
Edge<Type> *s = vertexTable[p->dest].adj;
while(s != NULL){
if(s->dest == k){
s->dest = i;
break;
}
s = s->link;
}
p = p->link;
}
return true;
}
bool removeEdge(const Type &v1, const Type &v2){
int i = getVertexIndex(v1);
int j = getVertexIndex(v2);
if(i==-1 || j==-1){ //保证顶点的保存在
return false;
}
//v1-->v2
Edge<Type> *p = vertexTable[i].adj;
if(p == NULL){ //判断有没有边
return false;
}
if(p->link == NULL && p->dest == j){ //删除的是第一个边，其后没有边了；
vertexTable[i].adj = NULL;
delete p;
}else if(p->dest == j){ //删除的是第一个边,并且其后还有边
vertexTable[i].adj = p->link;
delete p;
}else{
while(p->link != NULL){
if(p->link->dest == j){
Edge<Type> *q = p->link;
p->link = q->link;
delete q;
}
p = p->link;
}
}
//v2-->v1
Edge<Type> *s = vertexTable[j].adj;
if(s == NULL){ //判断有没有边
return false;
}
if(s->link == NULL && s->dest == i){ //删除的是第一个边，其后没有边了；
vertexTable[j].adj = NULL;
delete s;
curEdges--;
return false;
}else if(s->dest == i){ //删除的是第一个边,并且其后还有边
vertexTable[j].adj = s->link;
delete s;
curEdges--;
return true;
}else{
while(s->link != NULL){
if(s->link->dest == i){
Edge<Type> *q = s->link;
s->link = q->link;
delete q;
curEdges--;
return true;
}
s = s->link;
}
}
return true;
}
int getFirstNeighbor(const Type &v){
int i = getVertexIndex(v);
if(i != -1){
Edge<Type> *p = vertexTable[i].adj;
if(p != NULL){
return p->dest;
}
}
return -1;
}
int getNextNeighbor(const Type &v, const Type &w){
int i = getVertexIndex(v);
int j = getVertexIndex(w);
if(i==-1 || j==-1){
return -1;
}
Edge<Type> *p = vertexTable[i].adj;
while(p != NULL){
if(p->dest == j && p->link != NULL){
return p->link->dest;
}
p = p->link;
}
return -1;
}
public:
int getVertexIndex(const Type &v)const{
for(int i = 0; i < curVertices; i++){
if(vertexTable[i].data == v){
return i;
}
}
return -1;
}
void showGraph()const{
for(int i = 0; i < curVertices; i++){
cout<<vertexTable[i].data<<":-->";
Edge<Type> *p = vertexTable[i].adj;
while(p != NULL){
cout<<p->dest<<"-->";
p = p->link;
}
cout<<"Nul. "<<endl;
}
}
private:
Vertex<Type> *vertexTable; //指向顶点的指针，是申请数组用的
};
#endif(2)、Graph.cpp
#include"Graph.h"
int main(void){
GraphMtx<char> gm; //邻接矩阵
gm.insertVertex('A'); //插入顶点
gm.insertVertex('B');
gm.insertVertex('C');
gm.insertVertex('D');
gm.insertEdge('A','B'); //插入边
gm.insertEdge('A','D');
gm.insertEdge('B','C');
gm.insertEdge('C','D');
cout<<gm.getFirstNeighbor('A')<<endl; //B
cout<<gm.getNextNeighbor('A','B')<<endl;//D
gm.showGraph();
gm.removeEdge('A','B');
gm.removeVertex('B');
cout<<"-----------------------------------------------------------------"<<endl;
gm.showGraph();
///////////////////////////////////////////////////////////////////////////////////////////
GraphLnk<char> gl; //邻接表
gl.insertVertex('A');
gl.insertVertex('B');
gl.insertVertex('C');
gl.insertVertex('D');
gl.insertEdge('A','B');
gl.insertEdge('A','D');
gl.insertEdge('B','C');
gl.insertEdge('C','D');
gl.showGraph();
cout<<gl.getFirstNeighbor('A')<<endl;
cout<<gl.getNextNeighbor('A','B')<<endl;
gl.removeEdge('B','C');
cout<<"---------------------"<<endl;
gl.removeVertex('B');
gl.showGraph();
return 0;
}3、邻接多重表
是一个十字交叉链的形式；在很大程度上节省了空间，还是要对链表的操作很熟悉；
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