1、用邻接矩阵表示图
typedef struct GNode *PtrToGNode;
struct GNode
{
int Nv; //顶点数
int Ne; //边数
DataType Data[MaxVertexNum]; //存顶点的数据
};
typedef PtrToGNode MGraph; //以邻接矩阵存储的图类型
MGraph初始化
- 初始化一个有VertexNum个顶点但没有边的图
typedef int Vertex; //用顶点下标表示顶点,为整型
MGraph CreateGraph(int VertexNum)
{
Vertex V, W;
MGraph Graph;
Graph = (MGraph)malloc(sizeof(struct GNode));
Graph->Nv = VertexNum;
Graph->Ne = 0;
/* 注意:这里默认顶点编号从0开始,到(Graph->Nv - 1) */
for (V = 0; V<Graph->Nv; V++)
for (W = 0; W<Graph->Nv; W++)
Graph->G[V][W] = 0; //或INFINITY
return Graph;
}
向MGraph中插入边
typedef struct ENode *PtrToENode;
struct ENode
{
Vertex V1, V2; //有向边<V1, V2>
WeightType Weight; //权重
};
typedef PtrToENode Edge;
void InsertEdge(MGraph Graph, Edge E)
{
Graph->G[E->V1][E->V2] = E->Weight;//插入边<V1, V2>
Graph->G[E->V2][E->V1] = E->Weight;//若是无向图,还要插入边<V2, V1>
}
完整地建立一个MGraph
- 输入格式
Nv Ne
V1 V2 Weight
……
MGraph BuildGraph()
{
MGraph Graph;
Edge E;
Vertex V;
int Nv, i;
scanf("%d", &Nv);
Graph = CreateGraph(Nv);
scanf("%d", &(Graph->Ne));
if (Graph->Ne != 0)
{
E = (Edge)malloc(sizeof(struct ENode));
for (i = 0; i<Graph->Ne; i++)
{
scanf("%d %d %d",&E->V1, &E->V2, &E->Weight);
InsertEdge(Graph, E);
}
}
//如果顶点有数据的话,读入数据
for (V = 0; V<Graph->Nv; V++)
scanf(" %c", &(Graph->Data[V]));
return Graph;
}
简单方法实现用邻接矩阵表示图的建立
int G[MAXN][MAXN], Nv, Ne;
void BuildGraph()
{
int i, j, v1, v2, w;
scanf("%d", &Nv);
//CreateGraph
for (i = 0; i<Nv; i++)
for (j = 0; j<Nv; j++)
G[i][j] = 0; //或INFINITY
scanf("%d", &Ne);
for (i = 0; i<Ne; i++)
{
scanf("%d %d %d", &v1, &v2, &w);
//InsertEdge
G[v1][v2] = w;
G[v2][v1] = w;
}
}
此种方法的缺点,这种建立方法只适用于用邻接矩阵表示图,若换一种表示方法,就不适用了,不推荐
2、用邻接表表示图
- 邻接表:G[N]为指针数组,对应矩阵每行一个链表,只存非0元素
typedef struct Vnode
{
PtrToAdjVNode FirstEdge;
DataType Data; //存顶点的数据
} AdjList[MaxVertexNum];
//AdjList是邻接表类型,
//有几个顶点就有几个链表,每一个链表开始于一个结点和一个指针
typedef struct GNode *PtrToGNode;
struct GNode
{
int Nv; //顶点数
int Ne; //边数
AdjList G; //邻接表
};
typedef PtrToGNode LGraph;
//以邻接表方式存储的图类型,包括有顶点,边和邻接表
typedef struct AdjVNode *PtrToAdjVNode;
struct AdjVNode {
Vertex AdjV; //邻接点下标
WeightType Weight; //边权重
PtrToAdjVNode Next;
};
LGraph初始化
- 初始化一个有VertexNum个顶点但没有边的图
typedef int Vertex; //用顶点下标表示顶点,为整型
LGraph CreateGraph(int VertexNum)
{
Vertex V, W;
LGraph Graph;
Graph = (LGraph)malloc(sizeof(struct GNode));
Graph->Nv = VertexNum;
Graph->Ne = 0;
//注意:这里默认顶点编号从0开始,到(Graph->Nv - 1)
for (V = 0; V<Graph->Nv; V++)
Graph->G[V].FirstEdge = NULL;
return Graph;
}
向LGraph中插入边
void InsertEdge(LGraph Graph, Edge E)
{
PtrToAdjVNode NewNode;
/************* 插入边<V1, V2> ************/
//为V2建立新的邻接点
NewNode = (PtrToAdjVNode)malloc(sizeof(struct AdjVNode));
NewNode->AdjV = E->V2;
NewNode->Weight = E->Weight;
//将V2插入V1的表头
NewNode->Next = Graph->G[E->V1].FirstEdge;
Graph->G[E->V1].FirstEdge = NewNode;
/****** 若是无向图,还要插入边<V2, V1> ******/
//为V1建立新的邻接点
NewNode = (PtrToAdjVNode)malloc(sizeof(struct AdjVNode));
NewNode->AdjV = E->V1;
NewNode->Weight = E->Weight;
//将V1插入V2的表头
NewNode->Next = Graph->G[E->V2].FirstEdge;
Graph->G[E->V2].FirstEdge = NewNode;
}
完整地建立一个LGraph
同完整地建立一个MGraph相同