数据结构作业——天梯地图

天梯地图
时间限制: 300 ms
内存限制: 64 MB

本题要求你实现一个天梯赛专属在线地图，队员输入自己学校所在地和赛场地点后，该地图应该推荐两条路线：一条是最快到达路线；一条是最短距离的路线。题目保证对任意的查询请求，地图上都至少存在一条可达路线。

输入格式：
输入在第一行给出两个正整数N（2 ≤ N ≤ 500）和M，分别为地图中所有标记地点的个数和连接地点的道路条数。随后M行，每行按如下格式给出一条道路的信息：

1	V1 V2 one-way length time

其中V1和V2是道路的两个端点的编号（从0到N-1）；如果该道路是从V1到V2的单行线，则one-way为1，否则为0；length是道路的长度；time是通过该路所需要的时间。最后给出一对起点和终点的编号。

输出格式：
首先按下列格式输出最快到达的时间T和用节点编号表示的路线：

1	Time = T: 起点 => 节点1 => ... => 终点

然后在下一行按下列格式输出最短距离D和用节点编号表示的路线：

1	Distance = D: 起点 => 节点1 => ... => 终点

如果最快到达路线不唯一，则输出几条最快路线中最短的那条，题目保证这条路线是唯一的。而如果最短距离的路线不唯一，则输出途径节点数最少的那条，题目保证这条路线是唯一的。

如果这两条路线是完全一样的，则按下列格式输出：

1	Time = T; Distance = D: 起点 => 节点1 => ... => 终点

输入样例1：

输出样例1：

1 2	Time = 6: 5 => 4 => 8 => 3 Distance = 3: 5 => 1 => 3

输入样例2：

输出样例2：

1	Time = 3; Distance = 4: 3 => 2 => 5

代码

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

struct Edge
{
    int Target;
    int Length;
    int Time;
    struct Edge *NextEdge;
};

struct Vertex
{
    struct Edge *Head;
    int Known;
    int Dist;
    int PathDist;
    int Time;
    int PathTime;
    int VertexNums;
};

void ReadGraph(struct Vertex *G, int n, int m)
{
    int begin, target, oneWay, length, time;
    struct Edge *p;
    for(int i = 0; i < n; ++i)
        G[i].Head = NULL;
    for(int i = 0; i < m; ++i)
    {
        scanf("%d %d %d %d %d", &begin, &target, &oneWay, &length, &time);
        p = G[begin].Head;
        G[begin].Head = (struct Edge *)malloc(sizeof(struct Edge));
        G[begin].Head->Target = target;
        G[begin].Head->Length = length;
        G[begin].Head->Time = time;
        G[begin].Head->NextEdge = p;
        if(!oneWay)
        {
            p = G[target].Head;
            G[target].Head = (struct Edge *)malloc(sizeof(struct Edge));
            G[target].Head->Target = begin;
            G[target].Head->Length = length;
            G[target].Head->Time = time;
            G[target].Head->NextEdge = p;
        }
    }
}

void Dijkstra(struct Vertex *G, int n, int begin)
{
    int v, vDist, vTime, vNums;

    for(int i = 0; i < n; ++i)
    {
        G[i].Known = 0;
        G[i].Dist = G[i].Time = G[i].PathDist = G[i].PathTime = G[i].VertexNums = -1;
    }
    G[begin].Dist = G[begin].Time = G[begin].VertexNums = 0;

    while(1)
    {
        v = vTime = -1;
        for(int i = 0; i < n; ++i)
            if(!G[i].Known && G[i].Time != -1)
            {
                if(v == -1 || G[i].Time < vTime)
                {
                    vTime = G[i].Time;
                    vDist = G[i].Dist;
                    v = i;
                }
                else if(G[i].Time == vTime && G[i].Dist < vDist)
                {
                    vDist = G[i].Dist;
                    v = i;
                }
            }
        if(v == -1)
            break;

        G[v].Known = 1;
        for(struct Edge *p = G[v].Head; p; p = p->NextEdge)
        {
            if(!G[p->Target].Known)
            {
                if(G[p->Target].Time == -1 || G[v].Time + p->Time < G[p->Target].Time)
                {
                    G[p->Target].Time = G[v].Time + p->Time;
                    G[p->Target].Dist = G[v].Dist + p->Length;
                    G[p->Target].PathTime = v;
                }
                else if((G[v].Time + p->Time == G[p->Target].Time) && (G[v].Dist + p->Length < G[p->Target].Dist))
                {
                    G[p->Target].Dist = G[v].Dist + p->Length;
                    G[p->Target].PathTime = v;
                }
            }
        }
    }

    for(int i = 0; i < n; ++i)
    {
        G[i].Known = 0;
        G[i].Dist = -1;
    }
    G[begin].Dist = 0;

    while(1)
    {
        v = vDist = -1;
        for(int i = 0; i < n; ++i)
            if(!G[i].Known && G[i].Dist != -1)
            {
                if(v == -1 || G[i].Dist < vDist)
                {
                    vDist = G[i].Dist;
                    vNums = G[i].VertexNums;
                    v = i;
                }
                else if(G[i].Dist == vDist && G[i].VertexNums < vNums)
                {
                    vNums = G[i].VertexNums;
                    v = i;
                }
            }
        if(v == -1)
            break;

        G[v].Known = 1;
        for(struct Edge *p = G[v].Head; p; p = p->NextEdge)
        {
            if(!G[p->Target].Known)
            {
                if(G[p->Target].Dist == -1 || G[v].Dist + p->Length < G[p->Target].Dist)
                {
                    G[p->Target].Dist = G[v].Dist + p->Length;
                    G[p->Target].VertexNums = G[v].VertexNums + 1;
                    G[p->Target].PathDist = v;
                }
                else if((G[v].Dist + p->Length == G[p->Target].Dist) && (G[v].VertexNums + 1 < G[p->Target].VertexNums))
                {
                    G[p->Target].VertexNums = G[v].VertexNums + 1;
                    G[p->Target].PathDist = v;
                }
            }
        }
    }
}

void PrintPath(struct Vertex *G, int end, int type)
{
    if(type)
    {
        if(G[end].PathDist != -1)
        {
            PrintPath(G, G[end].PathDist, 1);
            printf(" => %d", end);
        }
    }
    else
    {
        if(G[end].PathTime != -1)
        {
            PrintPath(G, G[end].PathTime, 0);
            printf(" => %d", end);
        }
    }
}

void Output(struct Vertex *G, int begin, int end)
{
    int i = end;
    while(i != begin)
    {
        if(G[i].PathDist != G[i].PathTime)
            break;
        i = G[i].PathDist;
    }
    if(i == begin)
    {
        printf("Time = %d; Distance = %d: %d", G[end].Time, G[end].Dist, begin);
        PrintPath(G, end, 0);
    }
    else
    {
        printf("Time = %d: %d", G[end].Time, begin);
        PrintPath(G, end, 0);
        printf("\nDistance = %d: %d", G[end].Dist, begin);
        PrintPath(G, end, 1);
    }
}

int main(void)
{
    int n, m, begin, end;
    scanf("%d %d", &n, &m);
    struct Vertex G[n];
    ReadGraph(G, n, m);
    scanf("%d %d", &begin, &end);
    Dijkstra(G, n, begin);
    Output(G, begin, end);
    return 0;
}