1131 Subway Map (30 分)

2019-05-08

1131 Subway Map (30 分)

In the big cities, the subway systems always look so complex to the visitors. To give you some sense, the following figure shows the map of Beijing subway. Now you are supposed to help people with your computer skills! Given the starting position of your user, your task is to find the quickest way to his/her destination.

Input Specification:

Each input file contains one test case. For each case, the first line contains a positive integer N (≤ 100), the number of subway lines. Then N lines follow, with the i-th (i=1,⋯,N) line describes the i-th subway line in the format:

M S[1] S[2] … S[M]

where M (≤ 100) is the number of stops, and S[i]’s (i=1,⋯,M) are the indices of the stations (the indices are 4-digit numbers from 0000 to 9999) along the line. It is guaranteed that the stations are given in the correct order — that is, the train travels between S[i] and S[i+1] (i=1,⋯,M−1) without any stop.

Note: It is possible to have loops, but not self-loop (no train starts from S and stops at S without passing through another station). Each station interval belongs to a unique subway line. Although the lines may cross each other at some stations (so called “transfer stations”), no station can be the conjunction of more than 5 lines.

After the description of the subway, another positive integer K (≤ 10) is given. Then K lines follow, each gives a query from your user: the two indices as the starting station and the destination, respectively.

The following figure shows the sample map.

Note: It is guaranteed that all the stations are reachable, and all the queries consist of legal station numbers.

Output Specification:

For each query, first print in a line the minimum number of stops. Then you are supposed to show the optimal path in a friendly format as the following:

1
2
3

Take Line#X1 from S1 to S2.
Take Line#X2 from S2 to S3.
......

where Xi‘s are the line numbers and Si‘s are the station indices. Note: Besides the starting and ending stations, only the transfer stations shall be printed.

If the quickest path is not unique, output the one with the minimum number of transfers, which is guaranteed to be unique.

Sample Input:

4
7 1001 3212 1003 1204 1005 1306 7797
9 9988 2333 1204 2006 2005 2004 2003 2302 2001
13 3011 3812 3013 3001 1306 3003 2333 3066 3212 3008 2302 3010 3011
4 6666 8432 4011 1306
3
3011 3013
6666 2001
2004 3001

Sample Output:

2
Take Line#3 from 3011 to 3013.
10
Take Line#4 from 6666 to 1306.
Take Line#3 from 1306 to 2302.
Take Line#2 from 2302 to 2001.
6
Take Line#2 from 2004 to 1204.
Take Line#1 from 1204 to 1306.
Take Line#3 from 1306 to 3001.

作者: CHEN, Yue

单位: 浙江大学

时间限制: 400 ms

内存限制: 64 MB

代码长度限制: 16 KB

题目大意

给出地铁线路图，要求输出两站之间的最短换乘路径。如果最短路径相同，选择换乘次数最小的。

分析

之前没碰到过类似的题，比较棘手。可以使用dfs，遍历所有的路径选择满足条件的。

使用vector数组v，存储第i个结点能到达的车站。line数组存储两站之间的路线。遍历时将路径暂存至tempath，至终点时与path比较，选择较好的路径。输出结果时，计算路径上相邻两点的线路，与之前线路不同则为一次换乘。

代码

#include <iostream>
#include <vector>

using namespace std;
int n,k,a,b,mintransf,visit[10000],mincnt;
vector<int> v[10000];
vector<int> path,tempath;
int line[10000][10000];
int getransf(){
    int cnt=0,preline,curline;
    preline=line[tempath[0]][tempath[1]];
    for(int i=2;i<tempath.size();i++){
        curline=line[tempath[i-1]][tempath[i]];
        if(curline!=preline){
            cnt++;
            preline=curline;
        }
    }
    return cnt;
}
void dfs(int cur,int cnt){
    if(cur==b){
        int transf=getransf();//得到换乘数
        if(cnt<mincnt||(cnt==mincnt&&transf<mintransf)){
            path=tempath;
            mintransf=transf;
            mincnt=cnt;
        }
        return;
    }
    for(int i:v[cur]){
        if(!visit[i]){
            visit[i]=1;
            tempath.push_back(i);
            dfs(i,cnt+1);
            tempath.pop_back();
            visit[i]=0;
        }
    }
}
void printpath(){
    printf("%d\n",path.size()-1);
    int preline=line[path[0]][path[1]];
    int last=a;
    int curline;
    for(int i=2;i<path.size();i++){
        curline=line[path[i-1]][path[i]];
        if(curline!=preline){
            printf("Take Line#%d from %04d to %04d.\n",preline,last,path[i-1]);
            preline=curline;
            last=path[i-1];
        }
    }
    printf("Take Line#%d from %04d to %04d.\n",preline,last,path.back());
}
int main() {
    cin>>n;
    int m,cur,pre;
    for(int i=1;i<=n;i++){
        cin>>m;
        pre=-1;
        for(int j=0;j<m;j++){
            cin>>cur;
            if(pre!=-1){
                v[pre].push_back(cur);
                v[cur].push_back(pre);
                line[cur][pre]=i;
                line[pre][cur]=i;
            }
            pre=cur;
        }
    }
    cin>>k;
    for(int i=0;i<k;i++){
        tempath.clear();
        mincnt=99999999;
        cin>>a>>b;
        visit[a]=1;
        tempath.push_back(a);
        dfs(a,0);//搜索
        visit[a]=0;
        printpath();//输出结果
    }
    return 0;
}