浙大数据结构第七周之07-图6 旅游规划

题目详情：

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

主要思路：

就是Dijkstra的变形

代码实现：

#include 
#include 
#define MAX_NODE_NUMS 505
#define NONE -1
#define INF 100000
#define TRUE 1
#define FALSE 0
typedef int bool;
typedef struct MatrixGraphNode MatrixGraphNode;
typedef MatrixGraphNode* MGraph;
struct MatrixGraphNode {
    int VertexNums, EdgeNums;
    int Distance[MAX_NODE_NUMS][MAX_NODE_NUMS];
    int Fare[MAX_NODE_NUMS][MAX_NODE_NUMS];
};
MGraph CreateEmptyGraph(int vertexNums, int edgeNums) {
    MGraph graph = (MGraph)malloc(sizeof(MatrixGraphNode));
    graph->VertexNums = vertexNums;
    graph->EdgeNums = edgeNums;
    for(int i = 0; i < vertexNums; i++) {
        for(int j = 0; j < vertexNums; j++) {
            if(i == j) {
                graph->Distance[i][i] = 0;
                graph->Fare[i][i] = 0;
            }
            else {
                graph->Distance[i][j] = INF;
                graph->Fare[i][j] = INF;
            }
        }
    }
    return graph;
}
void InsertEdge(int start, int end, int distance, int fare, MGraph graph) {
    graph->Distance[start][end] = distance; graph->Distance[end][start] = distance;
    graph->Fare[start][end] = fare; graph->Fare[end][start] = fare;
    return;
} 
MGraph BuildGraph(int vertexNums, int edgeNums) {
    MGraph graph = CreateEmptyGraph(vertexNums, edgeNums);
    int start, end, distance, fare;
    for(int i = 0; i < edgeNums; i++) {
        scanf("%d %d %d %d", &start, &end, &distance, &fare);
        InsertEdge(start, end, distance, fare, graph);
    }
    return graph;
}
int FindNearest(MGraph graph, int vis[], int start) {
    /*先找距离最近，距离同样近找最省钱*/
    int ret = NONE;
    int minDis = INF;
    int minFare = INF;
    for(int i = 0; i < graph->VertexNums; i++) {
        if(i != start && vis[i] == FALSE) {
            if(graph->Distance[start][i] < minDis) {
                ret = i;
                minDis = graph->Distance[start][i];
                minFare = graph->Fare[start][i];
            }
            else if(graph->Distance[start][i] == minDis) {
                if(graph->Fare[start][i] < graph->Fare[start][ret]) {
                    ret = i;
                    minDis = graph->Distance[start][i];
                    minFare = graph->Fare[start][i];
                }
            }
        }
    }
    return ret;
}
void Dijksta(MGraph graph, int start, int end) {
    int path[MAX_NODE_NUMS];
    int vis[MAX_NODE_NUMS];
    int dis[MAX_NODE_NUMS];
    int fare[MAX_NODE_NUMS];
    /*初始化*/
    for(int i = 0; i < graph->VertexNums; i++) {
        vis[i] = FALSE;
        if(i != start) {
            if(graph->Distance[start][i] < INF) {
                path[i] = start;
                dis[i] = graph->Distance[start][i];
                fare[i] = graph->Fare[start][i];
            }
            else {
                path[i] = NONE;
                dis[i] = INF;
                fare[i] = INF;
            }
        }
    }
    path[start] = NONE;
    dis[start] = 0;
    fare[start] = 0;

    while(TRUE) {
        int nearest = FindNearest(graph, vis, start);
        if(nearest == NONE) {
            break;
        }
        vis[nearest] = TRUE;
        for(int i = 0; i < graph->VertexNums; i++) {
            if(i != nearest && vis[i] == FALSE && graph->Distance[nearest][i] < INF) {
                if(graph->Distance[nearest][i] < 0) {
                    return;
                }
                else if(dis[nearest] + graph->Distance[nearest][i] < dis[i]) {
                    path[i] = nearest;
                    dis[i] = dis[nearest] + graph->Distance[nearest][i];
                    fare[i] = fare[nearest] + graph->Fare[nearest][i];
                }
                else if(dis[nearest] + graph->Distance[nearest][i] == dis[i]) {
                    if(fare[nearest] + graph->Fare[nearest][i] < fare[i]) {
                        path[i] = nearest;
                        fare[i] = fare[nearest] + graph->Fare[nearest][i];
                    }
                }
            }
        } 
    }
    
    printf("%d %d", dis[end], fare[end]);
} 
int main() {
    int vertexNums, edgeNums, startPoint, endPoint;
    scanf("%d %d %d %d", &vertexNums, &edgeNums, &startPoint, &endPoint);
    MGraph graph = BuildGraph(vertexNums, edgeNums);
    Dijksta(graph, startPoint, endPoint);
    free(graph);
    return 0;
}