主要讲解图的最常用的两种创建方式，邻接矩阵和邻接表，代码实现0x01. Adjacency matrix
Meaning: two arrays diagram showing information stored in a one-dimensional array of vertices, a two-dimensional array (the adjacency matrix) storing information or arc edge.
For normal view (refer to FIG no weights):
If you or
then
.
On the contrary, .
Seeking a degree vertex , in fact, this vertex in the matrix of the
elements of the line and.
For undirected graphs, such as:
For the FIG., Such as:
FIG net, weighted values are diagrams.
If you or
then
. (W refers to weight)
If , then
.
If the edge points does not exist, it was generally considered impossible to achieve by conventional values, expressed as 32727,65535. Such as:
structure:
#define MAXSIZE 100
#define INTMAX 32767//通常认为无法到达的int值，short型的边界值
typedef struct
{
char ver[MAXSIZE];//顶点信息域
int edge[MAXSIZE][MAXSIZE];
int numv;//顶点数
int nume;//边数
}Graph;set up:
void CreateGraph(Graph *G)
{
int i, j, k, w;
printf("请输入图的顶点数和边数：\n");
scanf("%d %d", &G->numv, &G->nume);
while (getchar() != '\n');
printf("请输入节点信息：");
for (i = 0; i < G->numv; i++)//读入顶点信息
{
scanf("%c", &G->ver[i]);
}
for (i = 0; i < G->numv; i++)//初始化邻接矩阵
{
for (j = 0; j < G->numv; j++)
{
G->edge[i][j] = INTMAX;
}
}
for (k = 0; k < G->nume; k++)//读入边信息，最好加上i-i权值为0，不然其它都会是INTMAX
{
printf("请输入第 %d 条边（Vi,Vj）的下标i，j，和权值w：\n", k + 1);
while (getchar() != '\n');//必须清空缓冲区
scanf("%d %d %d",&i, &j, &w);
G->edge[i][j] = w;
G->edge[j][i] = G->edge[i][j];//无向图则矩阵对称，有向图不需要
}
}Time complexity: n e vertices edges create 
, initialize 
0x02. Adjacency list
Meaning: For a small number of edges in the graph adjacency matrix is wasteful, then consider using a chain memory structure stored side information, one-dimensional array to store the vertices, the array also stores a pointer pointing to the first edge, the edge list single chain stores, such vertices and edges will connect up.
Defect: adjacency table is stored is a default of the vertex, i.e., the vertex points, it is difficult to determine the level information.
Inverse adjacency table: solving the adjacency list of the defect information can not be determined, but in order to establish a first arc vertex adjacent table, but can not determine the degree information.
Icon:
structure:
#define MAXSIZE 100
//边表结构
typedef struct EdgeNode
{
int adjvex;//存储该顶点对应的数组下标
int weight;//存储权值
struct EdgeNode* next;//指针域，指向下一个邻接点
}EdgeNode;
//顶点结构
typedef struct VertexNode
{
char data;//存储顶点的信息
EdgeNode* firstedge;//代表边表的头指针
}VertexNode,AdjList[MAXSIZE];//同时创建了一个大小为MAXSIZE的顶点数组
//整个图结构
typedef struct
{
AdjList adjList;//此时的AdjList代表顶点表的指针类型，adjList就是创建的顶点表数组
int numv;//顶点数
int nume;//边数
}GraphAdjList;set up:
void CreateALGraph(GraphAdjList* G)
{
int i, j,k,w;
EdgeNode* e;//建立边表的头结点
printf("请输入顶点数目和边数目，以空格隔开\n");
scanf("%d %d", &G->numv, &G->nume);
while (getchar() != '\n');//必须清空缓冲区
for (i = 0; i < G->numv; i++)//开始建立顶点表
{
scanf("%c", &G->adjList[i].data);//读取数据域
G->adjList[i].firstedge = NULL;//初始化边表头指针
}
for (k = 0; k < G->nume; k++)//开始建立边表
{
printf("请输入边左端下标 i ,右端下标 j，和权值 :\n");
while (getchar() != '\n');//必须清空缓冲区
scanf("%d %d %d", &i,&j,&w);
e = (EdgeNode*)malloc(sizeof(EdgeNode));//边表头结点申请内存
e->adjvex = j;//存储 i 指向的顶点的下标
e->weight = w;//存储该边的权值
e->next = G->adjList[i].firstedge;//将 e 指向顶点表中的边表头结点
G->adjList[i].firstedge = e;//将当前顶点表的头节点指向e，单链表的头插法
//以下代码对于无向图而言,对称的
e = (EdgeNode*)malloc(sizeof(EdgeNode));//e重新申请一块内存
e->adjvex = i;
e->weight = w;
e->next = G->adjList[j].firstedge;
G->adjList[j].firstedge = e;
}
}Adjacency list of common traversal:
void PrintfGraphAdjList(GraphAdjList G)//只传结构，不传指针，以防遍历时改变原来结构
{
for (int i = 0; i < G.numv; i++)
{
EdgeNode* p = G.adjList[i].firstedge;
printf("顶点 %c 的边有：\n", G.adjList[i].data);
while (p)//遍历链表
{
printf("顶点 %c 到顶点 %c ，权值为 %d \n", G.adjList[i].data, G.adjList[p->adjvex].data, p->weight);
p = p->next;
}
printf("\n");
}
}Time complexity: n vertices edges e O (n + e)
The main function test:
int main()
{
GraphAdjList G;
CreateALGraph(&G);
PrintfGraphAdjList(G);
return 0;
}
This chapter ends.
