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。
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。
4 5 0 3
0 1 1 20
1 3 2 30
0 3 4 10
0 2 2 20
2 3 1 20
3 40
就是Dijkstra的变形
#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;
}