【数据结构】图的邻接矩阵存储实现

图的邻接表存储实现：http://blog.csdn.net/wenqian1991/article/details/24667287

图的邻接表DFS和BFS算法：http://blog.csdn.net/wenqian1991/article/details/24812393

这里则介绍图的另外一种存储方式：邻接矩阵。参考资料《大话数据结构》《C算法：卷二》

一、图的数据结构

图的邻接矩阵存储方式是用两个数据来表示。一个一维数组存储图中顶点信息，一个二维数组（称为邻接矩阵）存储图中的边的信息。

见下图：（图片来源于《大话数据结构》）

                  

/*图的邻接矩阵存储*/
typedef int VertexType;
typedef int EdgeType;
#define MAXVEX 100
#define INFI 65535

typedef struct
{
VertexType vexs[MAXVEX];           /*顶点表*/
EdgeType matrix[MAXVEX][MAXVEX];   /*邻接矩阵*/
unsigned int numVertexes;          /*顶点数*/
unsigned int numEdges;             /*边数*/
}Graph;

二、创建一个图

/*创建一个邻接矩阵无向图*/
Graph* CreateGraph()
{
Graph *pGragh = new Graph;
if (NULL == pGragh)
return NULL;

cout << "输入顶点数和边数：" << endl;
cin >> pGragh->numVertexes >> pGragh->numEdges;

for (int i = 0; i < pGragh->numVertexes; ++i)/*建立顶点表*/
(pGragh->vexs)[i] = i;
for (int i = 0; i < pGragh->numVertexes; ++i)/*邻接矩阵初始化*/
{
for (int j = 0; j < pGragh->numVertexes; ++j)
{
(pGragh->matrix)[i][j] = INFI;
if (i == j)
(pGragh->matrix)[i][j] = 0;
}
}
for (int k = 0; k < pGragh->numEdges; ++k)
{
int i, j, w;
cout << "输入边(vi,vj)上的下标i，下标j和权重w：" << endl;
cin >> i >> j >> w;
(pGragh->matrix)[i][j] = w;
(pGragh->matrix)[j][i] = (pGragh->matrix)[i][j];//无向图是对称矩阵
}
return pGragh;
}

/*创建一个邻接矩阵有向图*/
Graph* CreateDiGraph()
{
Graph *pGragh = new Graph;
if (NULL == pGragh)
return NULL;

cout << "输入顶点数和边数：" << endl;
cin >> pGragh->numVertexes >> pGragh->numEdges;

for (int i = 0; i < pGragh->numVertexes; ++i)/*建立顶点表*/
(pGragh->vexs)[i] = i;
for (int i = 0; i < pGragh->numVertexes; ++i)/*邻接矩阵初始化*/
{
for (int j = 0; j < pGragh->numVertexes; ++j)
{
(pGragh->matrix)[i][j] = INFI;
if (i == j)
(pGragh->matrix)[i][j] = 0;
}
}
for (int k = 0; k < pGragh->numEdges; ++k)
{
int i, j, w;
cout << "输入边<vi,vj>上的下标i，下标j和权重w：" << endl;
cin >> i >> j >> w;
(pGragh->matrix)[i][j] = w;//清楚上面输入的顺序，有向边的开始点和终点
}
return pGragh;
}

三、检查图中两个顶点间是否有边

/*检查两个顶点之间是否有边
对于邻接矩阵存储图，这比较简单。其中有向图对输入顶点顺序有要求*/
bool GraphHasEdge(Graph *pGraph, unsigned int begin, unsigned int end)
{
if (NULL == pGraph || begin >= pGraph->numVertexes || end >= pGraph->numVertexes)
return false;
if (begin == end)
return false;

return ((pGraph->matrix)[begin][end] != INFI) ? true : false;
}

四、DFS

关于DFS与BFS的介绍见开篇链接

/*DFS*/
/*邻接矩阵的深度优先递归算法*/
void DFSUtil(Graph *pGraph, int start, bool visited[])
{
visited[start] = true;
cout << start << endl;

for (int j = 0; j < pGraph->numVertexes; ++j)
{
if ((pGraph->matrix)[start][j] != 0 && (pGraph->matrix)[start][j] != INFI && !visited[j])
DFSUtil(pGraph, j, visited);
}
}
/*邻接矩阵的深度优先搜索*/
void DFS(Graph *pGraph)
{
if (NULL == pGraph)
return;
bool *visited = new bool[pGraph->numVertexes];
memset(visited, false, pGraph->numVertexes);

for (int i = 0; i < pGraph->numVertexes; ++i)
{
if (!visited[i])
DFSUtil(pGraph, i, visited);
}
delete[] visited;
}

五、BFS

/*BFS*/
void BFS(Graph *pGraph)
{
if (NULL == pGraph)
return;

bool *visited = new bool[pGraph->numVertexes];
memset(visited, false, pGraph->numVertexes);

list<int> queue;//利用链表构造一个队列
for (int i = 0; i < pGraph->numVertexes; ++i)
{
if (!visited[i])
{
visited[i] = true;
cout << pGraph->vexs[i] << endl;
queue.push_back(i);
while (!queue.empty())
{
i = *queue.begin();
queue.pop_front();
for (int j = 0; j < pGraph->numVertexes; ++j)
{
if ((pGraph->matrix)[i][j] != 0 && (pGraph->matrix)[i][j] != INFI && !visited[j])
{
visited[j] = true;
cout << pGraph->vexs[j] << endl;
queue.push_back(j);
}
}
}
}
}
}

这里只提供相关代码实现，代码已测试，理论部分请参考相关资料。