07-图6 旅游规划（25 分）

有了一张自驾旅游路线图，你会知道城市间的高速公路长度、以及该公路要收取的过路费。现在需要你写一个程序，帮助前来咨询的游客找一条出发地和目的地之间的最短路径。如果有若干条路径都是最短的，那么需要输出最便宜的一条路径。

输入格式:

输入说明：输入数据的第1行给出4个正整数N、M、S、D，其中N（2≤N≤500）是城市的个数，顺便假设城市的编号为0~(N−1)；M是高速公路的条数；S是出发地的城市编号；D是目的地的城市编号。随后的M行中，每行给出一条高速公路的信息，分别是：城市1、城市2、高速公路长度、收费额，中间用空格分开，数字均为整数且不超过500。输入保证解的存在。

输出格式:

在一行里输出路径的长度和收费总额，数字间以空格分隔，输出结尾不能有多余空格。

输入样例:

4 5 0 3
0 1 1 20
1 3 2 30
0 3 4 10
0 2 2 20
2 3 1 20

输出样例:

3 40


我的答案

#include <stdio.h>
#include <unistd.h>
#include <stdlib.h>

#define ERROR -1
#define false 0
#define true  1
#define MaxVertexNum 100
#define INFINITY     65535
typedef int Vertex;
typedef int WeightType;
typedef char DataType;
typedef int bool;


typedef struct ENode *PtrToENode;
struct ENode {
    Vertex V1, V2;
    WeightType Weight;
    WeightType Cost;
};
typedef PtrToENode Edge;

typedef struct GNode *PtrToGNode;
struct GNode {
    int Nv;
    int Ne;
    WeightType G[MaxVertexNum][MaxVertexNum];
    WeightType C[MaxVertexNum][MaxVertexNum];
};
typedef PtrToGNode MGraph;

MGraph CreateGraph(int VertexNum);
void InsertEdge(MGraph Graph, Edge E);
MGraph BuildGraph(int Nv, int Ne);
void PrintGraph(MGraph Graph);
Vertex FindMinDist(MGraph Graph, int dist[], int collected[]);
bool Dijkstra(MGraph Graph, int dist[], int path[], int cost[], Vertex S);
void PrintDist(MGraph Graph, int dist[]);
void PrintPath(int path[], int N);

MGraph CreateGraph(int VertexNum)
{
    Vertex V, W;
    MGraph Graph;

    Graph = (MGraph)malloc(sizeof(struct GNode));
    Graph->Nv = VertexNum;
    Graph->Ne = 0;

    for(V=0;V<Graph->Nv;V++)
        for(W=0;W<Graph->Nv;W++) {
            Graph->G[V][W] = INFINITY;
            Graph->C[V][W] = INFINITY;
        }

    return Graph;
}

void InsertEdge(MGraph Graph, Edge E)
{
    Graph->G[E->V1][E->V2] = E->Weight;
    Graph->G[E->V2][E->V1] = E->Weight;
    Graph->C[E->V1][E->V2] = E->Cost;
    Graph->C[E->V2][E->V1] = E->Cost;
}

MGraph BuildGraph(int Nv, int Ne)
{
    MGraph Graph;
    Edge E;
    int i;

    // scanf("%d", &Nv);
    Graph = CreateGraph(Nv);

    Graph->Ne = Ne;
    // 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 %d
", &E->V1, &E->V2, &E->Weight, &E->Cost);
            InsertEdge(Graph, E);
        }
    }

    return Graph;
}

void PrintGraph(MGraph Graph)
{
    Vertex V, W;
    printf("Graph:
");
    for(V=0;V<Graph->Nv;V++) {
        for(W=0;W<Graph->Nv;W++) 
            printf("[%5d %5d]	" , Graph->G[V][W], Graph->C[V][W]);
        printf("
");
    }
    printf("-----------------------
");
}

Vertex FindMinDist(MGraph Graph, int dist[], int collected[])
{
    Vertex MinV, V;
    int MinDist = INFINITY;

    for(V=0;V<Graph->Nv;V++) {
        if(collected[V] == false && dist[V]<MinDist) {      //未被访问并且距离最小
            MinDist = dist[V];
            MinV = V;
        }
    }
    if(MinDist < INFINITY)
        return MinV;
    else return ERROR;
}

bool Dijkstra(MGraph Graph, int dist[], int path[], int cost[], Vertex S)
{
    int collected[MaxVertexNum];
    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->C[S][V];
        if(dist[V]<INFINITY)
            path[V] = S;
        else
            path[V] = -1;
        collected[V] = false;
    }
// PrintPath(path, Graph->Nv);
    /* 先将起点收入集合 */
    dist[S] = 0;
    collected[S] = true;

    while(1) {
        /* V = 未被收录顶点中dist最小者 */
        V = FindMinDist(Graph, dist, collected);
// printf("[FindMinDist] V:%d
", V);
        if(V == ERROR)      /* 若这样的V不存在 */
            break;          /* 算法结束 */
        collected[V] = true;    /* 收录 */
        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（两点距离比一点距离短） */
                if(dist[V]+Graph->G[V][W]<dist[W]) {
                    dist[W] = dist[V] + Graph->G[V][W];     /* 更新dist[W] */
// printf("[FindMinDist] dist[W(%d)]=%d
", W, dist[W]);
                    path[W] = V;        /* 更新S到W的路径 */
                    cost[W] = cost[V] + Graph->C[V][W];
                } else if((dist[V]+Graph->G[V][W] == dist[W]) 
                            && (cost[V] + Graph->C[V][W] < cost[W])) {
                    cost[W] = cost[V] + Graph->C[V][W];
                }
            }
        }
    }

    return true;    /* 算法执行完毕，返回正确标记 */
}

void PrintDist(MGraph Graph, int dist[])
{
    Vertex V;
    for(V=0;V<Graph->Nv;V++) {
        printf("%d ", dist[V]);
    }
    printf("
");
}

void PrintPath(int path[], int N)
{
    int i;
    printf("[Path] ");
    for(i=0;i<N;i++)
        printf("%d ",path[i]);
    printf("
");
}

int main()
{
    int N, M;
    Vertex S, D;
    int *dist, *path, *cost;
    MGraph Graph;
    scanf("%d %d %d %d
", &N, &M, &S, &D);
    dist = (int *)malloc(sizeof(int)*N);
    path = (int *)malloc(sizeof(int)*N);
    cost = (int *)malloc(sizeof(int)*N);
    Graph = BuildGraph(N, M);
    // PrintGraph(Graph);
    Dijkstra(Graph, dist, path, cost, S);
    // PrintPath(path, N);
    printf("%d %d
", dist[D], cost[D]);
    return 0;
}