图的遍历和生成树求解实现|图遍历,生成树,实现,邻接矩阵,邻接表,深度广度遍历,最小生成树

#include <iostream>
#include <malloc.h>
using namespace std;
#define int_max 10000
#define inf 9999
#define max 20
//…………………………………………邻接矩阵定义……………………
typedef struct ArcCell
{
int adj;
char *info;
}ArcCell,AdjMatrix[20][20];
typedef struct
{
char vexs[20];
AdjMatrix arcs;
int vexnum,arcnum;
}MGraph_L;
//^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
int localvex(MGraph_L G,char v)//返回V的位置
{
int i=0;
while(G.vexs[i]!=v)
{
++i;
}
return i;
}

int creatMGraph_L(MGraph_L &G)//创建图用邻接矩阵表示
{
char v1,v2;
int i,j,w;
cout<<"…………创建无向图…………"<<endl<<"请输入图G顶点和弧的个数:(4 6)不包括“()”"<<endl;
cin>>G.vexnum>>G.arcnum;
for(i=0;i!=G.vexnum;++i)
{
cout<<"输入顶点"<<i<<endl;
cin>>G.vexs[i];
}
for(i=0;i!=G.vexnum;++i)
for(j=0;j!=G.vexnum;++j)
{
G.arcs[i][j].adj=int_max;
G.arcs[i][j].info=NULL;
}
for(int k=0;k!=G.arcnum;++k)
{
cout<<"输入一条边依附的顶点和权:(a b 3)不包括“()”"<<endl;
cin>>v1>>v2>>w;//输入一条边依附的两点及权值
i=localvex(G,v1);//确定顶点V1和V2在图中的位置
j=localvex(G,v2);
G.arcs[i][j].adj=w;
G.arcs[j][i].adj=w;
}
cout<<"图G邻接矩阵创建成功！"<<endl;
return G.vexnum;
}
void ljjzprint(MGraph_L G)
{
int i,j;
for(i=0;i!=G.vexnum;++i)
{
for(j=0;j!=G.vexnum;++j)
cout<<G.arcs[i][j].adj<<" ";
cout<<endl;
}
}
int visited[max];//访问标记
int we;
typedef struct arcnode//弧结点
{
int adjvex;//该弧指向的顶点的位置
struct arcnode *nextarc;//弧尾相同的下一条弧
char *info;//该弧信息
}arcnode;
typedef struct vnode//邻接链表顶点头接点
{
char data;//结点信息
arcnode *firstarc;//指向第一条依附该结点的弧的指针
}vnode,adjlist;
typedef struct//图的定义
{
adjlist vertices[max];
int vexnum,arcnum;
int kind;
}algraph;
//…………………………………………队列定义……………………
typedef struct qnode
{
int data;
struct qnode *next;

}qnode,*queueptr;

typedef struct
{
queueptr front;
queueptr rear;

}linkqueue;
//………………………………………………………………………
typedef struct acr
{
int pre;//弧的一结点
int bak;//弧另一结点
int weight;//弧的权
}edg;

int creatadj(algraph &gra,MGraph_L G)//用邻接表存储图
{

int i=0,j=0;
arcnode *arc,*tem,*p;
for(i=0;i!=G.vexnum;++i)
{
gra.vertices[i].data=G.vexs[i];
gra.vertices[i].firstarc=NULL;
}
for(i=0;i!=G.vexnum;++i)
{
for(j=0;j!=G.vexnum;++j)
{
if(gra.vertices[i].firstarc==NULL)
{
if(G.arcs[i][j].adj!=int_max&&j!=G.vexnum)
{
arc=(arcnode *)malloc(sizeof(arcnode));
arc->adjvex=j;
gra.vertices[i].firstarc=arc;
arc->nextarc=NULL;
p=arc;
++j;
while(G.arcs[i][j].adj!=int_max&&j!=G.vexnum)
{
tem=(arcnode *)malloc(sizeof(arcnode));
tem->adjvex=j;
gra.vertices[i].firstarc=tem;
tem->nextarc=arc;
arc=tem;
++j;
}
--j;
}
}
else
{
if(G.arcs[i][j].adj!=int_max&&j!=G.vexnum)
{
arc=(arcnode *)malloc(sizeof(arcnode));
arc->adjvex=j;
p->nextarc=arc;
arc->nextarc=NULL;
p=arc;
}

}

}
}
gra.vexnum=G.vexnum;
gra.arcnum=G.arcnum;

/*for(i=0;i!=gra.vexnum;++i)
{
arcnode *p;
cout<<i<<" ";
p=gra.vertices[i].firstarc;
while(p!=NULL)
{
cout<<p->adjvex;
p=p->nextarc;
}
cout<<endl;

}*/
cout<<"图G邻接表创建成功！"<<endl;
return 1;
}
void adjprint(algraph gra)
{
int i;
for(i=0;i!=gra.vexnum;++i)
{
arcnode *p;
cout<<i<<" ";
p=gra.vertices[i].firstarc;
while(p!=NULL)
{
cout<<p->adjvex;
p=p->nextarc;
}
cout<<endl;
}
}

int firstadjvex(algraph gra,vnode v)//返回依附顶点V的第一个点
//即以V为尾的第一个结点
{
if(v.firstarc!=NULL)
return v.firstarc->adjvex;

}
int nextadjvex(algraph gra,vnode v,int w)//返回依附顶点V的相对于W的下一个顶点
{
arcnode *p;
p=v.firstarc;
while(p!=NULL&&p->adjvex!=w)
{
p=p->nextarc;
}
if(p->adjvex==w&&p->nextarc!=NULL)
{
p=p->nextarc;
return p->adjvex;
}
if(p->adjvex==w&&p->nextarc==NULL)
return -10;

}
int initqueue(linkqueue &q)//初始化队列
{
q.rear=(queueptr)malloc(sizeof(qnode));
q.front=q.rear;
if(!q.front)
return 0;
q.front->next=NULL;
return 1;
}
int enqueue(linkqueue &q,int e)//入队
{
queueptr p;
p=(queueptr)malloc(sizeof(qnode));
if(!p)
return 0;
p->data=e;
p->next=NULL;
q.rear->next=p;
q.rear=p;
return 1;

}
int dequeue(linkqueue &q,int &e)//出队
{
queueptr p;
if(q.front==q.rear)
return 0;
p=q.front->next;
e=p->data;
q.front->next=p->next;
if(q.rear==p)
q.rear=q.front;
free(p);
return 1;

}
int queueempty(linkqueue q)//判断队为空
{
if(q.front==q.rear)
return 1;
return 0;
}
void bfstra(algraph gra)//广度优先遍历
{
int i,e;
linkqueue q;
for(i=0;i!=gra.vexnum;++i)
visited[i]=0;
initqueue(q);
for(i=0;i!=gra.vexnum;++i)

if(!visited[i])
{ visited[i]=1;
cout<<gra.vertices[i].data;
enqueue(q,i);
while(!queueempty(q))
{
dequeue(q,e);
// cout<<" "<<e<<" ";
for(we=firstadjvex(gra,gra.vertices[e]);we>=0;we=nextadjvex(gra,gra.vertices[e],we))
{
if(!visited[we])
{
visited[we]=1;
cout<<gra.vertices[we].data;
enqueue(q,we);
}
}
}
}
}

int dfs(algraph gra,int i);//声明DFS

int dfstra(algraph gra)
{
int i,j;
for(i=0;i!=gra.vexnum;++i)
{
visited[i]=0;
}
for(j=0;j!=gra.vexnum;++j)
{
if(visited[j]==0)
dfs(gra,j);
}
return 0;
}
int dfs(algraph gra,int i)
{
visited[i]=1;
int we1;
// cout<<i<<visited[i]<<endl;
cout<<gra.vertices[i].data;
// cout<<endl;
for(we=firstadjvex(gra,gra.vertices[i]);we>=0;we=nextadjvex(gra,gra.vertices[i],we))
{
// cout<<we<<visited[we]<<endl;
we1=we;
// cout<<nextadjvex(gra,gra.vertices[i],we)<<endl;
if(visited[we]==0)
// cout<<
dfs(gra,we);//<<endl;
// cout<<i<<we1<<endl;
we=we1;
// cout<<nextadjvex(gra,gra.vertices[i],we)<<endl;
}
return 12;
}
int bfstra_fen(algraph gra)//求连通分量
{
int i,j;
for(i=0;i!=gra.vexnum;++i)
{
visited[i]=0;
}
for(j=0;j!=gra.vexnum;++j)
{
if(visited[j]==0)
{
dfs(gra,j);
cout<<endl;
}
}
return 0;
}

typedef struct
{
int adjvex;
int lowcost;
}closedge;
/*int minimum(closedge *p);
int minispantree(MGraph_L G,char u)
{

int k,j,i;
closedge closedge_a[20];
k=localvex(G,u);
// cout<<k<<endl;
for(j=0;j!=G.vexnum;++j)
{
if(j!=k)
{
closedge_a[j].adjvex=u;
closedge_a[j].lowcost=G.arcs[k][j].adj;
}
for(i=1;i!=G.vexnum;++i)
{
k=minimum(closedge_a);
cout<<k;
cout<<closedge_a[k].adjvex<<" "<<G.vexs[k]<<endl;
closedge_a[k].lowcost=0;
for(j=0;j!=G.vexnum;++j)
if(G.arcs[k][j].adj<closedge_a[j].lowcost)
{
closedge_a[j].adjvex=G.vexs[k];
closedge_a[j].lowcost=G.arcs[k][j].adj;
}

}
}
return 0;
}
int minimum(closedge *p)
{
int s=10000;
for(;p!=NULL;++p)
{
if(s>p->lowcost)
s=p->lowcost;
}
return s;

}*/
int prim(int g[][max],int n) //最小生成树PRIM算法
{
int lowcost[max],prevex[max]; //LOWCOST[]存储当前集合U分别到剩余结点的最短路径
//prevex[]存储最短路径在U中的结点
int i,j,k,min;
for(i=2;i<=n;i++) //n个顶点，n-1条边
{
lowcost[i]=g[1][i]; //初始化
prevex[i]=1; //顶点未加入到最小生成树中
}
lowcost[1]=0; //标志顶点1加入U集合
for(i=2;i<=n;i++) //形成n-1条边的生成树
{
min=inf;
k=0;
for(j=2;j<=n;j++) //寻找满足边的一个顶点在U,另一个顶点在V的最小边
if((lowcost[j]<min)&&(lowcost[j]!=0))
{
min=lowcost[j];
k=j;
}
printf("(%d,%d)%d/t",prevex[k]-1,k-1,min);
lowcost[k]=0; //顶点k加入U
for(j=2;j<=n;j++) //修改由顶点k到其他顶点边的权值
if(g[k][j]<lowcost[j])
{
lowcost[j]=g[k][j];
prevex[j]=k;
}
printf("/n");
}
return 0;
}
int acrvisited[100];//kruscal弧标记数组
int find(int acrvisited[],int f)
{
while(acrvisited[f]>0)
f=acrvisited[f];
return f;
}
void kruscal_arc(MGraph_L G,algraph gra)
{

edg edgs[20];
int i,j,k=0;
for(i=0;i!=G.vexnum;++i)
for(j=i;j!=G.vexnum;++j)
{
if(G.arcs[i][j].adj!=10000)
{
edgs[k].pre=i;
edgs[k].bak=j;
edgs[k].weight=G.arcs[i][j].adj;
++k;
}
}
int x,y,m,n;
int buf,edf;
for(i=0;i!=gra.arcnum;++i)
acrvisited[i]=0;
for(j=0;j!=G.arcnum;++j)
{
m=10000;
for(i=0;i!=G.arcnum;++i)
{
if(edgs[i].weight<m)
{
m=edgs[i].weight;
x=edgs[i].pre;
y=edgs[i].bak;
n=i;
}

}
// cout<<x<<y<<m;
// cout<<endl;
buf=find(acrvisited,x);
edf=find(acrvisited,y);
// cout<<buf<<" "<<edf<<endl;
edgs
.weight=10000;
if(buf!=edf)
{
acrvisited[buf]=edf;

cout<<"("<<x<<","<<y<<")"<<m;
cout<<endl;
}
}

}

void main()
{
algraph gra;
MGraph_L G;
int i,d,g[20][20];
char a='a';
d=creatMGraph_L(G);
creatadj(gra,G);
vnode v;
cout<<endl<<"……####注意：若该图为非强连通图(含有多个连通分量)时"<<endl
<<" 最小生成树不存在,则显示为非法值。"<<endl<<endl;
cout<<"…………………菜单……………………"<<endl<<endl;
cout<<"0、显示该图的邻接矩阵……………………"<<endl;
cout<<"1、显示该图的邻接表……………………"<<endl;
cout<<"2、深度优先遍历…………………………"<<endl;
cout<<"3、广度优先遍历…………………………"<<endl;
cout<<"4、最小生成树PRIM算法…………………"<<endl;
cout<<"5、最小生成树KRUSCAL算法………………"<<endl;
cout<<"6、该图的连通分量………………………"<<endl<<endl;
int s;
char y='y';
while(y='y')
{
cout<<"请选择菜单："<<endl;
cin>>s;
switch(s)
{
case 0:
cout<<"邻接矩阵显示如下："<<endl;
ljjzprint(G);
break;
case 1:
cout<<"邻接表显示如下："<<endl;
adjprint(gra);
break;
case 2:
cout<<"广度优先遍历：";
bfstra(gra);
cout<<endl;
break;
case 3:
for(i=0;i!=gra.vexnum;++i)
{
visited[i]=0;
}
cout<<"深度优先遍历：";
dfstra(gra);
cout<<endl;
break;
case 4:
for(i=0;i!=G.vexnum;++i)
for(int j=0;j!=G.vexnum;++j)
g[i+1][j+1]=G.arcs[i][j].adj;
cout<<"prim:"<<endl;
prim(g,d);
break;
case 5:
cout<<"kruscal:"<<endl;
kruscal_arc(G,gra);
break;
case 6:
cout<<"连通分量:";
bfstra_fen(gra);
break;

}
cout<<endl<<"是否继续？y/n:";
cin>>y;
if(y=='n')
break;
}

}