1·图的建立
邻接法表示法：
对于图中的每个节点Vi,建立一个单链表,把与Vi相邻的节点放入这个链表中；
该表有三部分组成:
(1): point结构体,由节点的位置,边的信息(例如边的权值),下个节点的地址构成；
(2): firstpoint结构体,即单链表的首节点,主要由节点的数据,与首节点连接的第一个节点的地址构成;
(3): graphy结构体,主要由所有节点构成的数组,图的节点总数和边的总数构成;
代码:
#include <iostream>
using namespace std;
typedef struct point{
int position; //首节点的位置
int otherimfor; //与边相关的信息,例如边的权值;
struct point *nextnode;
}point;
typedef struct firstpoint{
int data;
point *next;
}firstpoint,manypoints[100];
typedef struct graph{
manypoints p;
int pointnum,sidenum;
}graph;
void createWuXianggraph(graph &g,int v,int e){ //无向图
g.pointnum=v; g.sidenum=e;
for(int i=1;i<=v;i++)
{
cin>>g.p[i].data;
g.p[i].next=NULL;
} int v1,v2;
for(int i=0;i<e;i++)
{
cin>>v1>>v2;
int po1=v1,po2=v2;
point *p=new point;
p->position=po2;
p->nextnode=g.p[po1].next; g.p[po1].next=p;
point *pp=new point;
pp->position=po1;
pp->nextnode=g.p[po2].next; g.p[po2].next=pp;
}
}
void createYouXianggraph(graph &g,int v,int e){ //有向图
g.pointnum=v; g.sidenum=e;
for(int i=1;i<=v;i++)
{
cin>>g.p[i].data;
g.p[i].next=NULL;
} int v1,v2;
for(int i=0;i<e;i++)
{
cin>>v1>>v2;
int po1=v1,po2=v2;
point *p=new point;
p->position=po2;
p->nextnode=g.p[po1].next; g.p[po1].next=p;
}
}
void showgraph(graph g){
for(int i=0;i<g.pointnum;i++)
{
cout<<"V"<<g.p[i].data;
point *p=new point;
p=g.p[i].next;
if(p) cout<<"->";
while(p)
{
cout<<p->position;
if(p->nextnode) cout<<"->";
p=p->nextnode;
} cout<<endl;
}
}
int main(){
graph g;
int v,e;
while(cin>>v>>e)
{
creategraph(g,v,e);
showgraph(g);
}
}2·图的遍历:
深度优先搜索,类似与树的先序遍历:
数组visited用来记录每个点是否被访问
函数 firstvisitpoint(g,v)用于查找在链表中与每个顶点相邻的第一个点,并返回其位置;
函数 nextvistpoint（g,v)用于查找在链表中每个顶点相邻的且没被访问的点,并返回其位置;
int visited[100];
int firstvisitpoint(graph g,int v){
return g.p[v].next->position;
}
int nextvistpoint(graph g,int v){
point *tmp=g.p[v].next;
while(tmp){
if(!visited[tmp->position])
return tmp->position;
tmp=tmp->nextnode;
} return -1;}
void dfs(graph g,int v,int visited[100]){
cout<<g.p[v].data<<" ";
visited[v]=1;
point *p=g.p[v].next;
while(p){
int vv=p->position;
if(!visited[vv])
dfs(g,vv,visited);
p=p->nextnode;
}
}
int main(){
graph g;
int v,e; //图的点和边的总数;
while(cin>>v>>e)
{
for(int i=1;i<=v;i++)
visited[i]=0;
createYouXianggraph(g,v,e);
showgraph(g);
dfs(g,1,visited); cout<<endl;
}
}
广度优先搜素:
从某顶点v开始访问,依此访问v的未被访问的邻接点,并在访问的过程中将这些点存进队列.
将队列里的元素vi依此弹出,访问vi的未被访问的邻接点,并在访问的过程中将这些点存进队列.
重复上一行的操作,直至队列元素为空
typedef struct List{
int num;
struct List *next;
}List,*PList;
typedef struct{
List *head,*tail;
}Queue;
void InitQueue(Queue &q){
q.head=q.tail=new List;
q.head->next=NULL;
}
void Push(Queue &q,int x){
PList tmp=new List;
tmp->num=x; tmp->next=NULL;
q.tail->next=tmp; q.tail=tmp;
}
void Pop(Queue &q,int &x){
PList tmp=q.head->next;
x=tmp->num;
q.head->next=tmp->next;
if(tmp==q.tail) q.tail=q.head;
delete tmp;
}
int firstvisitpoint(graph g,int v){
return g.p[v].next->position;
}
int nextvistpoint(graph g,int v){
point *tmp=g.p[v].next;
while(tmp)
{
if(!visited[tmp->position])
return tmp->position;
tmp=tmp->nextnode;
}
return -1;
}
void bfs(graph g,int v,int visited[100]){
Queue q; InitQueue(q); Push(q,v); visited[v]=1;
cout<<g.p[v].data<<" ";
while(!IsEmpty(q))
{
int x; Pop(q,x);
for(int i=firstvisitpoint(g,x);i>=1;i=nextvistpoint(g,x))
{
if(!visited[i])
{
cout<<g.p[i].data<<" ";
Push(q,i);
visited[i]=1;
}
}
}
}
int main(){
graph g;
int v,e;
while(cin>>v>>e)
{
for(int i=1;i<=v;i++)
visited[i]=0;
createYouXianggraph(g,v,e);
showgraph(g);
bfs(g,1,visited); cout<<endl;
}
}
