对于图的遍历的四种问题

2023年11月7日 337次阅读来源: 数据结构之图

图建立，输入示例：
input the number for vexnum and arcnum:8 9

input8char for vexs(use -enter- to change):a
b
c
d
e
f
g
h

input9arc(char -enter- char -enter- weigh):
0:a
b
11

1:a
c
11

2:b
d
11

3:b
e
11

4:d
h
23

5:e
h
11

6:c
f
11

7:c
g
11

8:f
g
11

遍历建立的矩阵：
88 11 11 88 88 88 88 88
11 88 88 11 11 88 88 88
11 88 88 88 88 11 11 88
88 11 88 88 88 88 88 23
88 11 88 88 88 88 88 11
88 88 11 88 88 88 11 88
88 88 11 88 88 11 88 88
88 88 88 23 11 88 88 88
遍历的结果：
a
b
d
h
e
c
f
g
(邻接矩阵图深度遍历结果)

实际图形示例：

b c

d e f——g

h
(其他是上下连起)
代码：

邻接表图的广度遍历

#include <stdio.h>
#include <stdlib.h>
#include <iostream.h>

#define INFINITY INT_MAX
#define MAX_VERTEX_NUM 20

#defineMAXQSIZE 10//最大队列长度
#define FALSE 0
#define TRUE 1

typedef int VRType;
typedef char VertexType;
typedef int Status;
typedef int QElemType;

typedef struct
{
QElemType*base;
intfront;
intrear;
} SqQueue;

typedef struct ArcNode
{
int adjvex;
struct ArcNode *nextarc;
}ArcNode;

typedef struct VNode
{
VertexType data;
ArcNode *firstarc;
}VNode, AdjList[MAX_VERTEX_NUM];

typedef struct
{
AdjList vertices;
int vexnum, arcnum;
}ALGraph;

bool visited[MAX_VERTEX_NUM];
Status (*VisitFunc)(int v);
int w;

void CreateGraph(ALGraph &G);
void BFSTraverse(ALGraph G, Status (*Visit)(int v));
Status printGraph(int v);
int FirstAdjVex(ALGraph G, int v);
int NextAdjVex(ALGraph G, int v, int w);

StatusInitQueue(SqQueue &);
StatusEnQueue(SqQueue &, QElemType);
StatusDeQueue(SqQueue &, QElemType &);
Status QueueEmpty(SqQueue);

void main( void )
{

int i;
ALGraph G;
ArcNode *p;

CreateGraph(G);

for(i= 0; i < G.vexnum; i++)
{
cout<<i<<” “<<G.vertices[i].data;
p = G.vertices[i].firstarc;
while(p != NULL)
{
cout<<“—>”;
cout<<(G.vertices[p->adjvex].data);
p = p->nextarc;
}
cout<<endl;
}
BFSTraverse(G, printGraph);
}
void CreateGraph(ALGraph &G)
{
int i, j = 0, k = 0;
char hand, tide;
ArcNode *p;

cout<<“input the number for vexnum and arcnum:”;
cin>>G.vexnum>>G.arcnum;
cout<<endl;
cout<<“input”<<G.vexnum<<“char for vexs:”;
for(i=0; i < G.vexnum; i++)
cin>>G.vertices[i].data;
cout<<endl;
for(i=0;i<G.vexnum;++i)
G.vertices[i].firstarc=NULL;
cout<<“input”<<G.arcnum<<“arc(char-enter-char):”<<endl;
j = 0;
k = 0;
for(i=0; i < G.arcnum; i++)
{
cout<<i<<“:”;
cin>>hand;
cin>>tide;
while (hand != G.vertices[j].data)
j++;
while (tide != G.vertices[k].data)
k++;
p=new ArcNode;
p->adjvex=j;
p->nextarc=G.vertices[j].firstarc;
G.vertices[k].firstarc=p;
p=new ArcNode;
p->adjvex=k;
p->nextarc=G.vertices[j].firstarc;
G.vertices[j].firstarc=p;

j = 0;
k = 0;
cout<<endl;
}
}

void BFSTraverse(ALGraph G, Status (*Visit)(int v))
{
SqQueueQ;
QElemType u;

InitQueue(Q);

for(int v=0; v < G.vexnum;++v)
visited[v]=FALSE;
for(v=0; v<G.vexnum;++v)
if(!visited[v])
{
visited[v]=TRUE;
EnQueue(Q, v);
Visit(v);
while(QueueEmpty(Q))
{
DeQueue(Q, u);
for(w = FirstAdjVex(G, u); w; w = NextAdjVex(G, u, w))
if(! visited[w])
{
visited[w]=TRUE;
Visit(w);
EnQueue(Q, w);
}
}
}
}

int FirstAdjVex(ALGraph G, int v)
{
ArcNode *p;
p = G.vertices[v].firstarc;
while(p != NULL)
{
if(visited[p->adjvex] != 1)
return p->adjvex;
p = p->nextarc;
}
return 0;
}

int NextAdjVex(ALGraph G, int v, int w)
{
ArcNode *p;
p = G.vertices[v].firstarc;
while(p != NULL)
{
if(visited[p->adjvex] != 1 && p->adjvex != w)
return p->adjvex;
p = p->nextarc;
}
return 0;
}

Status printGraph(int v)
{
printf(“%c”, v + ‘a’);
cout<<endl;
return 1;
}

Status InitQueue(SqQueue & queue)
{
queue.base = (QElemType *) malloc(MAXQSIZE * sizeof(QElemType));

if (!queue.base)
return FALSE;
queue.front = queue.rear = 0;

return TRUE;
}

///////////////////////////////////////////////////////////////////////
//
// 函数名 : EnQueue
// 功能描述 : 插入元素到队列
// 参数 : SqQueue &queue
// 参数 : QElemType element
// 返回值 : Status
//
///////////////////////////////////////////////////////////////////////
StatusEnQueue(SqQueue &queue, QElemType element)
{
//先判断是不是没满的队列
if ((queue.rear + 1) % MAXQSIZE == queue.front)
return FALSE;
queue.base[queue.rear] = element;

queue.rear = (queue.rear + 1) % MAXQSIZE;

return TRUE;
}

///////////////////////////////////////////////////////////////////////
//
// 函数名 : DeQueue
// 功能描述 : 删除队列的头结点
// 参数 : SqQueue &queue
// 参数 : QElemType &element
// 返回值 : Status
//
///////////////////////////////////////////////////////////////////////
Status DeQueue(SqQueue &queue, QElemType &element)
{
//判断队列是不是空的
if (queue.front == queue.rear)
return FALSE;
element = queue.base[queue.front];
queue.front = (queue.front + 1) % MAXQSIZE;

return TRUE;
}

Status QueueEmpty(SqQueue queue)
{
if (queue.front == queue.rear)
return FALSE;
else
return TRUE;

}

邻接表图的深度遍历

#include <stdio.h>
#include <stdlib.h>
#include <iostream.h>

#define INFINITY INT_MAX
#define MAX_VERTEX_NUM 20

typedef int VRType;
typedef char VertexType;
typedef int Status;

typedef struct ArcNode
{
int adjvex;
struct ArcNode *nextarc;
}ArcNode;

typedef struct VNode
{
VertexType data;
ArcNode *firstarc;
}VNode, AdjList[MAX_VERTEX_NUM];

typedef struct
{
AdjList vertices;
int vexnum, arcnum;
}ALGraph;

bool visited[MAX_VERTEX_NUM];
Status (*VisitFunc)(int v);
int w;

void CreateGraph(ALGraph &G);
void DFSTraverse(ALGraph G, Status (*Visit)(int v));
Status printGraph(int v);
int FirstAdjVex(ALGraph G, int v);
int NextAdjVex(ALGraph G, int v, int w);
void DFS(ALGraph G, int v);

void main( void )
{

int i;
ALGraph G;
ArcNode *p;

CreateGraph(G);

for(i= 0; i < G.vexnum; i++)
{
cout<<i<<” “<<G.vertices[i].data;
p = G.vertices[i].firstarc;
while(p != NULL)
{
cout<<“—>”;
cout<<(G.vertices[p->adjvex].data);
p = p->nextarc;
}
cout<<endl;
}
DFSTraverse(G, printGraph);
}
void CreateGraph(ALGraph &G)
{
int i, j = 0, k = 0;
char hand, tide;
ArcNode *p;

j = 0;
k = 0;
cout<<endl;
}
}

void DFSTraverse(ALGraph G, Status (*Visit)(int v))
{
int j;
VisitFunc = Visit;
for( j=0; j<G.vexnum; j++)
visited[j] = 0;
for(j=0; j<G.vexnum; j++)
if(!visited[j])
DFS(G, j);
}

void DFS(ALGraph G, int v)
{

visited[v]=1;
VisitFunc(v);
for(w=FirstAdjVex(G, v); w; w=NextAdjVex(G, v, w))
if(!visited[w])
DFS(G, w);
}

int FirstAdjVex(ALGraph G, int v)
{
ArcNode *p;
p = G.vertices[v].firstarc;
while(p != NULL)
{
if(visited[p->adjvex] != 1)
return p->adjvex;
p = p->nextarc;
}
return 0;
}

int NextAdjVex(ALGraph G, int v, int w)
{
ArcNode *p;
p = G.vertices[v].firstarc;
while(p != NULL)
{
if(visited[p->adjvex] != 1 && p->adjvex != w)
return p->adjvex;
p = p->nextarc;
}
return 0;
}

Status printGraph(int v)
{
printf(“%c”, v + ‘a’);
cout<<endl;
return 1;
}

邻接矩阵的广度遍历

#include <stdio.h>
#include <stdlib.h>
#include <iostream.h>

#define INFINITY INT_MAX
#define MAX_VERTEX_NUM 20

#defineMAXQSIZE 10//最大队列长度
#define FALSE 0
#define TRUE 1

typedef int VRType;
typedef int InfoType;
typedef char VertexType;
typedef int Status;
typedef int QElemType;

typedef struct
{
QElemType*base;
intfront;
intrear;
} SqQueue;

typedef struct ArcCell
{
VRType adj;
InfoType *info;
}ArcCell, AdjMatrix[MAX_VERTEX_NUM][MAX_VERTEX_NUM];

typedef struct
{
VertexType vexs[MAX_VERTEX_NUM];
AdjMatrix arcs;
int vexnum, arcnum;
}MGraph;

bool visited[MAX_VERTEX_NUM];
Status (*VisitFunc)(int v);
int w;

void CreateGraph(MGraph &G);
void BFSTraverse(MGraph G, Status (*Visit)(int v));
Status printGraph(int v);
int FirstAdjVex(MGraph G, int v);
int NextAdjVex(MGraph G, int v, int w);

StatusInitQueue(SqQueue &);
StatusEnQueue(SqQueue &, QElemType);
StatusDeQueue(SqQueue &, QElemType &);
Status QueueEmpty(SqQueue);

void main( void )
{
int i, j;
MGraph G;

CreateGraph(G);
for(i = 0; i < G.vexnum; i++)
{
for(j = 0; j < G.vexnum; j++)
{
cout<<G.arcs[i][j].adj;
cout<<” “;
}
cout<<endl;
}
BFSTraverse(G, printGraph);
}
void CreateGraph(MGraph &G)
{
int weigh;
int i, j = 0, k = 0;
char hand, tide;

cout<<“input the number for vexnum and arcnum:”;
cin>>G.vexnum>>G.arcnum;

for(i = 0; i < G.vexnum; i++)
{
for(j = 0; j < G.vexnum; j++)
G.arcs[i][j].adj = 88;
}

cout<<endl;
cout<<“input”<<G.vexnum<<“char for vexs(use -enter- to change):”;
for(i=0; i < G.vexnum; i++)
cin>>G.vexs[i];
cout<<endl;
cout<<“input”<<G.arcnum<<“arc(char -enter- char -enter- weigh):”<<endl;
j = 0;
k = 0;
for(i=0; i < G.arcnum; i++)
{
cout<<i<<“:”;
cin>>hand;
cin>>tide;
cin>>weigh;
while (hand != G.vexs[j])
j++;
while (tide != G.vexs[k])
k++;
G.arcs[j][k].adj = weigh;
G.arcs[k][j].adj = weigh;
j = 0;
k = 0;
cout<<endl;
}
}

void BFSTraverse(MGraph G, Status (*Visit)(int v))
{

SqQueueQ;
QElemType u;

InitQueue(Q);

for(int v=0; v < G.vexnum;++v)
visited[v]=FALSE;
for(v=0; v<G.vexnum;++v)
if(!visited[v])
{
visited[v]=TRUE;
Visit(v);
EnQueue(Q, v);
while(QueueEmpty(Q))
{
DeQueue(Q, u);
for(w = FirstAdjVex(G, u); w; w = NextAdjVex(G, u, w))
if(! visited[w])
{
visited[w]=TRUE;
Visit(w);
EnQueue(Q, w);
}
}
}
}

int FirstAdjVex(MGraph G, int v)
{
int j;
for(j = 0; j < G.vexnum; j++)
{
if(G.arcs[v][j].adj != 88 && visited[j] != 1)
return j;
}
return 0;
}

int NextAdjVex(MGraph G, int v, int w)
{
int j;
for(j = 0; j < G.vexnum; j++)
{
if(G.arcs[v][j].adj != 88 && j != w && visited[j] != 1)
return j;
}
return 0;
}

Status printGraph(int v)
{
printf(“%c”, v + ‘a’);
cout<<endl;
return 1;
}

Status InitQueue(SqQueue & queue)
{
queue.base = (QElemType *) malloc(MAXQSIZE * sizeof(QElemType));

if (!queue.base)
return FALSE;
queue.front = queue.rear = 0;

return TRUE;
}

queue.rear = (queue.rear + 1) % MAXQSIZE;

return TRUE;
}

Status QueueEmpty(SqQueue queue)
{
if (queue.front == queue.rear)
return FALSE;
else
return TRUE;

}

邻接矩阵的深度遍历

#include <stdio.h>
#include <stdlib.h>
#include <iostream.h>

#define INFINITY INT_MAX
#define MAX_VERTEX_NUM 20

typedef int VRType;
typedef int InfoType;
typedef char VertexType;
typedef int Status;

typedef struct ArcCell
{
VRType adj;
InfoType *info;
}ArcCell, AdjMatrix[MAX_VERTEX_NUM][MAX_VERTEX_NUM];

typedef struct
{
VertexType vexs[MAX_VERTEX_NUM];
AdjMatrix arcs;
int vexnum, arcnum;
}MGraph;

bool visited[MAX_VERTEX_NUM];
Status (*VisitFunc)(int v);
int w;

void CreateGraph(MGraph &G);
void DFSTraverse(MGraph G, Status (*Visit)(int v));
Status printGraph(int v);
int FirstAdjVex(MGraph G, int v);
int NextAdjVex(MGraph G, int v, int w);
void DFS(MGraph G, int v);

void main( void )
{
int i, j;
MGraph G;

CreateGraph(G);
for(i = 0; i < G.vexnum; i++)
{
for(j = 0; j < G.vexnum; j++)
{
cout<<G.arcs[i][j].adj;
cout<<” “;
}
cout<<endl;
}
DFSTraverse(G, printGraph);
}
void CreateGraph(MGraph &G)
{
int weigh;
int i, j = 0, k = 0;
char hand, tide;

cout<<“input the number for vexnum and arcnum:”;
cin>>G.vexnum>>G.arcnum;

for(i = 0; i < G.vexnum; i++)
{
for(j = 0; j < G.vexnum; j++)
G.arcs[i][j].adj = 88;
}

void DFSTraverse(MGraph G, Status (*Visit)(int v))
{
int j;
VisitFunc = Visit;
for( j=0; j<G.vexnum; j++)
visited[j] = 0;
for(j=0; j<G.vexnum; j++)
if(!visited[j])
DFS(G, j);
}

void DFS(MGraph G, int v)
{

visited[v]=1;
VisitFunc(v);
for(w=FirstAdjVex(G, v); w; w=NextAdjVex(G, v, w))
if(!visited[w])
DFS(G, w);
}

int FirstAdjVex(MGraph G, int v)
{
int j;
for(j = 0; j < G.vexnum; j++)
{
if(G.arcs[v][j].adj != 88 && visited[j] != 1)
return j;
}
return 0;
}

int NextAdjVex(MGraph G, int v, int w)
{
int j;
for(j = 0; j < G.vexnum; j++)
{
if(G.arcs[v][j].adj != 88 && j != w && visited[j] != 1)
return j;
}
return 0;
}

Status printGraph(int v)
{
printf(“%c”, v + ‘a’);
cout<<endl;
return 1;
}

    原文作者：数据结构之图
    原文地址: https://blog.csdn.net/iteye_20954/article/details/81312534
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