07-图6 旅游规划

#include<stdio.h>
#include<stdlib.h>
#define MaxVertexNum 500	/*最大定点数设为500*/
#define INFINITY 65535		/*∞设为双字节无符号整数的最大值65535*/
#define bool int
#define true 1
#define false -1
#define ERROR -1

typedef int Vertex;			/*用顶点下标表示顶点，为整型*/
typedef int WeightType;		/*边的权值设为整型*/
typedef char DataType;		/*顶点存储的数据类型设为字符型*/

/*边的定义*/
typedef struct ENode *PtrToENode;
struct ENode {
	Vertex V1,V2;		/*有向边<V1,V2>*/
	WeightType Weight;	/*权重*/
	WeightType Money;	/*路费*/
};
typedef PtrToENode Edge;

/*图结点的定义*/
typedef struct GNode *PtrToGNode;
struct GNode {
	int Nv;		/*顶点数*/
	int Ne;		/*边数*/
	WeightType G[MaxVertexNum][MaxVertexNum];	/*邻接矩阵*/
	WeightType M[MaxVertexNum][MaxVertexNum];	/*城市之间的路费*/
	//DataType Data[MaxVertexNum];				/*存顶点的数据*/
	/*注意：很多情况下，顶点无数据，此时Data[]可以不出现*/
};
typedef PtrToGNode MGraph;/*以邻接矩阵存储的图类型*/

MGraph CreateGraph(int VertexNum);
void InsertEdge(MGraph Graph,Edge E);
MGraph BuildGraph();
Vertex FindMinDist(MGraph Graph,int dist[],int collected[]);
bool Dijkstra(MGraph Graph,int dist[],int path[],int cost[],Vertex S);
void FindThePathOut(MGraph Graph,Vertex S,Vertex D);

int main(int argc,const char *argv[]) {
	MGraph Graph;
	Vertex S;/*S是出发地的城市编号*/
	Vertex D;/*D是目的地的城市编号*/
	Graph=BuildGraph(&S,&D);
	FindThePathOut(Graph,S,D);

	return 0;
}

MGraph CreateGraph(int VertexNum) {
	/*初始化一个有个VertexNum个顶点但没有边的图*/
	Vertex V,W;
	MGraph Graph;

	Graph=(MGraph)malloc(sizeof(struct GNode));/*建立图*/
	Graph->Nv=VertexNum;
	Graph->Ne=0;
	/*初始化邻接矩阵*/
	/*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]=INFINITY;
			Graph->M[V][W]=INFINITY;
		}
	}
	return Graph;
}

void InsertEdge(MGraph Graph,Edge E) {
	/*插入边<V1,V2>*/
	Graph->G[E->V1][E->V2]=E->Weight;
	Graph->M[E->V1][E->V2]=E->Money;
	/*若是无向图，还要插入边<V2,V1>*/
	Graph->G[E->V2][E->V1]=E->Weight;
	Graph->M[E->V2][E->V1]=E->Money;
}

MGraph BuildGraph(int *S,int *D) {
	MGraph Graph;
	Edge E;
	Vertex V;
	int Nv,i;

	scanf("%d",&Nv);	/*读入顶点个数*/
	Graph=CreateGraph(Nv);/*初始化有Nv个顶点但没有边的图*/

	scanf("%d",&(Graph->Ne));/*读入边数*/
	scanf("%d",S);/*读入起始城市编号*/
	scanf("%d",D);/*读入目的城市编号*/
	if(Graph->Ne!=0) { /*如果有边*/
		E=(Edge)malloc(sizeof(struct ENode));/*建立边结点*/
		/*读入边，格式为“起点 终点 权重”，插入邻接矩阵*/
		for(i=0; i<Graph->Ne; i++) {
			scanf("%d %d %d %d",&E->V1,&E->V2,&E->Weight,&E->Money);
			/*注意：如果权重不是整形，Weight的读入格式要改*/
			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;
}

Vertex FindMinDist(MGraph Graph,int dist[],int collected[]) {
	/*返回未被收录顶点dist最小者*/
	Vertex MinV,V;
	int MinDist=INFINITY;

	for(V=0; V<Graph->Nv; V++) {
		if(collected[V]==false&&dist[V]<MinDist) {
			/*若V未被收录，且dist[V]更小*/
			MinDist=dist[V];/*更新最小距离*/
			MinV=V;/*更新对应顶点*/
		}
	}
	if(MinDist<INFINITY)/*若找到最小dist*/
		return MinV;/*返回对应的顶点下标*/
	else return ERROR;/*若这样的顶点不存在，返回错误标记*/
}

bool Dijkstra(MGraph Graph,int dist[],int path[],int cost[],Vertex S) {
	int collected[Graph->Nv];
	Vertex V,W;

	/*初始化：此处默认邻接矩阵中不存在的边用INFINITY表示*/
	for(V=0; V<Graph->Nv; V++) {
		dist[V]=Graph->G[S][V];
		cost[V]=Graph->M[S][V];
		path[V]=-1;
		collected[V]=false;
	}
	/*先将起点收入集合*/
	dist[S]=0;
	cost[S]=0;
	collected[S]=true;

	while(1) {
		/*V=未被收录顶点中dist最小者*/
		V=FindMinDist(Graph,dist,collected);
		if(V==ERROR)/*若这样的V不存在*/
			break;/*算法结束*/
		collected[V]=true;/*收录V*/
		for(W=0; W<Graph->Nv; W++) /*对图中的每个顶点W*/
			/*若W是V的邻接点并且未被收录*/
			if(collected[W]==false&&Graph->G[V][W]<INFINITY) {
				if(Graph->G[V][W]<0)/*若有负边*/
					return false;/*不能正确解决，返回错误标记*/
				/*若收录V使得dist[W]变小*/
				if(dist[V]+Graph->G[V][W]<dist[W]) {
					dist[W]=dist[V]+Graph->G[V][W];/*更新dist[W]*/
					path[W]=V;/*更新S到W的路径*/
					cost[W]=cost[V]+Graph->M[V][W];
				} else if((dist[V]+Graph->G[V][W]==dist[W])&&(cost[V]+Graph->M[V][W]<cost[W])) {
					cost[W]=cost[V]+Graph->M[V][W];
				}
			}
	}/*while结束*/
	return true;/*算法执行完毕，返回正确标记*/
}

void FindThePathOut(MGraph Graph,Vertex S,Vertex D) {
	int dist[Graph->Nv];
	int path[Graph->Nv];
	int cost[Graph->Nv];
	Dijkstra(Graph,dist,path,cost,S);
	printf("%d %d\n",dist[D],cost[D]);
}