图之邻接表

最新推荐文章于 2023-02-05 18:34:04 发布

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本文介绍了一种使用邻接表表示有向图的方法，并实现了有向图的基本操作，包括创建有向图、计算顶点的入度和出度、深度优先遍历等。通过这些操作可以更好地理解和应用图论算法。

#ifndef _GRAPH_H_
#define _GRAPH_H

#define OK 1
#define ERROR 0
#define INFINTY -1
#define MAX_VERTEX_NUM 20

typedef int VertexType;
typedef int Status;
//邻接表表示
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;
int kind;
}ALGraph;

void CreateDG(ALGraph &G);
Status InDegree(ALGraph G, VertexType v);
Status OutDegree(ALGraph G, VertexType v);
void DFS(ALGraph G, VertexType v1);
void DFSTraverse(ALGraph G);
Status FirstAdjVex(ALGraph G, VertexType v1);
Status NextAdjVex(ALGraph G, VertexType v1, VertexType w);

#endif

#include"graph.h"
#include<iostream>
using namespace std;
//邻接表创建有向图
void CreateDG(ALGraph &G)
{
ArcNode *p;
int num, i, v1, v2;
cout << "请输入顶点数:" << endl;
cin >> G.vexnum;
cout << "请输入弧数:" << endl;
cin >> G.arcnum;
for (i = 0; i < G.vexnum; i++)
{
  G.vertices[i].firstarc = NULL;
  G.vertices[i].data = i;
}
for (i = 0; i < G.arcnum; i++)
{
  cout << "请输入第" << i << "边" << endl;
  cin >> v1 >> v2;
  p = (ArcNode*)malloc(sizeof(ArcNode));
  p->adjvex = v2;
  p->nextarc = G.vertices[v1].firstarc;
  G.vertices[v1].firstarc = p;
}
}

//有向图的出度
Status OutDegree(ALGraph G, VertexType v)
{
ArcNode *p;
int OutDegree=0;
if (v >= G.vexnum)
{
  return ERROR;
}
else
{
  p = G.vertices[v].firstarc;
  while (p)
  {
   OutDegree++;
   p = p->nextarc;
  }
  return OutDegree;
}
}

//有向图的入度
Status InDegree(ALGraph G, VertexType v)
{
ArcNode *p;
int i,j,InDegree=0;
if (v >= G.vexnum)
{
  return ERROR;
}
else
{
  for (j = 0; j < G.vexnum; j++)
  {
   p = G.vertices[j].firstarc;
   while (p)
   {
    if (p->adjvex == v)
    {
     InDegree++;
    }
    p = p->nextarc;
   }
  }
return InDegree;
}
}

//返回邻接表的第一个邻接点
Status FirstAdjVex(ALGraph G, VertexType v)
{
ArcNode *p;
p = G.vertices[v].firstarc;
if (p)
{
return p->adjvex;
}
else
{
return ERROR;
}
}

//邻接表返回v相对于w的下一个邻接顶点的第一个邻接点
Status NextAdjVex(ALGraph G, VertexType v, VertexType w)
{
ArcNode *p;
p = G.vertices[w].firstarc;
if (p)
{
return p->adjvex;
}
else
{
return ERROR;
}
}

//邻接表深度优先遍历
bool visit[20];
void DFS(ALGraph G, VertexType v)
{
int w;
visit[v] = 1;
cout << v<< " ";
for (w = FirstAdjVex(G, v); w >= 0; w = NextAdjVex(G, v, w))
{
  if (w != ERROR)
  {
   if (!visit[w])
   {
    DFS(G, w);
   }
  }
}
}

void DFSTraverse(ALGraph G)
{
int v;
for (v = 0; v < G.vexnum; v++)
{
  visit[v] = 0;
}
for (v = 0; v < G.vexnum; v++)
{
  if (!visit[v])
  {
   DFS(G, v);
  }
}
}

#include"graph.h"
#include<iostream>
using namespace std;

int main()
{
int select, v;
ALGraph G;
do
{
  cout << "1.创建有向图!" << endl;
  cout << "2.有向图的出度(邻接表)!" << endl;
  cout << "3.有向图的入度(邻接表)!" << endl;
  cout << "4.邻接表深度优先遍历!" << endl;
  cout << "0.结束!" << endl;
  cout << "请选择:" << endl;
  cin >> select;
  switch (select)
  {
  case 1:
   CreateDG(G);
   break;
  case 2:
   cout << "请输入顶点:" << endl;
   cin >> v;
   if (OutDegree(G, v) == ERROR)
   {
    cout << "出度为0或没有该顶点!" << endl;
   }
   else
   {
    cout << v << "的出度为:" << OutDegree(G, v) << endl;
   }
   break;
  case 3:
   cout << "请输入顶点:" << endl;
   cin >> v;
   if (InDegree(G, v) == ERROR)
   {
    cout << "入度为0或没有该顶点!" << endl;
   }
   else
   {
    cout << v << "的入度为:" << InDegree(G, v) << endl;
   }
   break;
  case 4:
   DFSTraverse(G);
   break;
  case 0:
   cout << "操作结束!" << endl;
   break;
  default:
   cout << "输入错误!" << endl;
  }
} while (select != 0);
}