【图(上)】小白专场：如何建立图

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