H - Funny Car Racing

There is a funny car racing in a city with n junctions and m directed roads.

The funny part is: each road is open and closed periodically. Each road is associate with two integers (a, b), that means the road will be open for a seconds, then closed for b seconds, then open for a seconds. . . All these start from the beginning of the race. You must enter a road when it’s open, and leave it before it’s closed again.

Your goal is to drive from junction s and arrive at junction t as early as possible. Note that you can wait at a junction even if all its adjacent roads are closed.

Input

There will be at most 30 test cases. The first line of each case contains four integers n, m, s, t (1 ≤ n ≤ 300, 1 ≤ m ≤ 50, 000, 1 ≤ s, t ≤ n). Each of the next m lines contains five integers u, v, a, b, t (1 ≤ u, v ≤ n, 1 ≤ a, b, t ≤ 105 ), that means there is a road starting from junction u ending with junction v. It’s open for a seconds, then closed for b seconds (and so on). The time needed to pass this road, by your car, is t. No road connects the same junction, but a pair of junctions could be connected by more than one road.

Output

For each test case, print the shortest time, in seconds. It’s always possible to arrive at t from s.

Sample Input

3 2 1 3

1 2 5 6 3

2 3 7 7 6

3 2 1 3

1 2 5 6 3

2 3 9 5 6

Sample Output

Case 1: 20

Case 2: 9

题意：就是有一个赛车比赛，比赛的路径上就是有关卡，然后给你你通过关卡所需要的时间，但是这关卡是有限制的，它会定时开放a秒，接着关闭b秒，现在给你起点、终点、开放的时间、关闭的时间、以及通过关卡所需时间，让你求到达终点所需的最短时间。

分析：用迪杰斯特拉算法的优化队列解决此问题

AC代码：

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<limits.h>
using namespace std;
#define maxn 300
#define maxm 50000
struct node
{
    int x,y,l,r,s;
}edge[2*maxm+5];

int sum[maxn+5];
int vis[maxn+5];
int dis[maxn+5];
int n,m,be,end;
int cmp(node x,node y)
{
    return x.x<y.x;
}

void dijkstra()
{
    for(int c=1;c<=n;c++)
    {
        int min=INT_MAX;/*整型最大值，不用定义，可直接调用。INT_MAX定义在LIMITS.H中，浮点数对应的是FLOAT.H,部分类型的定义对应的是STDDEF.H*/
        int pos=0;
        for(int i=1;i<=n;i++)
            if(!vis[i]&&dis[i]<min)
        {
            min=dis[i];
            pos=i;
        }
      if(min==INT_MAX) break;
      vis[pos]=1;//加入集合
      for(int i=sum[pos-1]+1;i<=sum[pos];i++)
      {
          if(!vis[edge[i].y]&&edge[i].l>=edge[i].s)//少写了等号
          {
              int lt=edge[i].l-dis[pos]%(edge[i].l+edge[i].r);//路开启所剩时间
              int cost;//通过这条路需要的时间
              if(lt>=edge[i].s)//剩余时间足够通过这条路
                cost=edge[i].s;
              else
                 cost=lt+edge[i].r+edge[i].s;//时间不够等待下次开路
              if(dis[pos]+cost<dis[edge[i].y])//更新最短路
                dis[edge[i].y]=dis[pos]+cost;
          }
      }
    }
}

int main()
{
    int T=0,end;
    while(~scanf("%d %d %d %d",&n,&m,&be,&end))
    {
        int u,v,a,b,t;
        memset(sum,0,sizeof(sum));
        for(int i=1;i<=m;i++)
        {
            scanf("%d %d %d %d %d",&u,&v,&a,&b,&t);
            edge[i]=(node){u,v,a,b,t};
            //edge[i+m]=(node){u,v,a,b,t};
            sum[u]++;//是单向边还是不是单向边
            //sum[v]++;
        }
        //sort(edge+1,edge+2*m+1,cmp);
        sort(edge+1,edge+m+1,cmp);
        for(int i=2;i<=n;i++)//i=2
            sum[i]=sum[i]+sum[i-1];
        for(int i=1;i<=n;i++)
            dis[i]=123456789;
        for(int i=sum[be-1]+1;i<=sum[be];i++)
        {
            if(edge[i].l>=edge[i].s&&dis[edge[i].y]>edge[i].s)//时间够通过这条路
                dis[edge[i].y]=edge[i].s;
        }
        memset(vis,0,sizeof(vis));
        vis[be]=1;//标记起点已经走过
        dijkstra();
        T++;
        printf("Case %d: %d\n",T,dis[end]);
    }
    return 0;
}