L - Subway(最短路spfa)

L - Subway(最短路spfa)

You have just moved from a quiet Waterloo neighbourhood to a big,

noisy city. Instead of getting to ride your bike to school every day,

you now get to walk and take the subway. Because you don’t want to be

late for class, you want to know how long it will take you to get to

school. You walk at a speed of 10 km/h. The subway travels at 40

km/h. Assume that you are lucky, and whenever you arrive at a subway

station, a train is there that you can board immediately. You may get

on and off the subway any number of times, and you may switch between

different subway lines if you wish. All subway lines go in both

directions. Input Input consists of the x,y coordinates of your home

and your school, followed by specifications of several subway lines.

Each subway line consists of the non-negative integer x,y coordinates

of each stop on the line, in order. You may assume the subway runs in

a straight line between adjacent stops, and the coordinates represent

an integral number of metres. Each line has at least two stops. The

end of each subway line is followed by the dummy coordinate pair

-1,-1. In total there are at most 200 subway stops in the city. Output Output is the number of minutes it will take you to get to school,

rounded to the nearest minute, taking the fastest route.

Sample Input
0 0 10000 1000
0 200 5000 200 7000 200 -1 -1
2000 600 5000 600 10000 600 -1 -1
Sample Output
21

思路

• 这一题难在输入和建图，，，，，
• 对于建图，我说一些需要注意的地方：
  
  1.首先 起点要与所有的火车站 建了一条边（起点 -> 火车站）权值为人走过这段距离所用的时间
  
  2.汽车 所有的火车站与终点 建了一条边 （火车站-> 终点）权值为人走过这段距离所用的时间
  
  3. 这题一条最需要注意： 在任意一组 车站点之间，相邻的 站点之间 要建立双向边（权值为：火车的行走的时间）
  
  4. 所有火车站之间应该 也应该建了 双向边，这个边的权值（时间），一定是人走过两个车站的时间

题解一

#include<iostream>
#include<algorithm>
#include<cstring>
#include<queue>
#include<cmath>
using namespace std;

#define INF 0x3f3f3f3f
#define Pir pair<double, double>
const int maxm = 100005;

struct Pos
{
    double x,y;
} pos[maxm];
int k = 2;
double Dis(Pos a, Pos b)
{
    return sqrt( (a.x - b.x)*(a.x - b.x) + (a.y - b.y)*(a.y - b.y) );
}

struct Edge
{
    int v;
    double w;
    int next;
} edge[maxm];
int head[maxm];
double dis[maxm];
int cnt = 0;

void Add(int u, int v, double w)
{
    edge[++ cnt] = (Edge){ v, w, head[u]}; head[u] = cnt;
}

double Spfa(int s, int e)
{
    int use[maxm];
    for(int i = 0; i <= k; i ++)
        dis[i] = INF, use[i] = 0;
    dis[s] = 0;
    queue<int> q;
    q.push(s);
    int u,v;
    double w;
    while(! q.empty())
    {
        u = q.front(); q.pop();
        use[u] = 0;

        for(int i = head[u]; i; i = edge[i].next)
        {
            v = edge[i].v;
            w = edge[i].w;
            if(dis[v] > dis[u] + w)
            {
                dis[v] = dis[u] + w;
                if(! use[v])
                {
                    q.push(v);
                    use[v] = 1;
                }
            }
        }
    }
    return dis[e];
}

int main()
{
    ios::sync_with_stdio(false); cin.tie(0);
    //freopen("T.txt","r",stdin);
    cin >> pos[0].x >> pos[0].y >> pos[1].x >> pos[1].y;
    double x,y;
    while(cin >> x >> y)
    {
        pos[k].x = x; pos[k ++].y = y;
        while(cin >> x >> y && (x!=-1 && y!=-1))
        {
            pos[k].x = x; pos[k].y = y;
            Add(k - 1, k, Dis(pos[k-1], pos[k])/2000*3);
            Add(k, k - 1, Dis(pos[k], pos[k-1])/2000*3);
            k ++;
        }
    }

    for(int i = 0; i < 2; i ++)
    {
        for(int j = 2; j < k-1; j ++)
        {
            if(i == 0)
                Add(i, j, Dis(pos[i], pos[j])/500*3);
            if(i == 1)
                Add(j, i, Dis(pos[i], pos[j])/500*3);
        }
    }

    for(int i = 0; i < k; i ++)
        for(int j = i + 1; j < k; j ++)
        {
            Add(i, j, Dis(pos[i], pos[j])/500*3);
            Add(j, i, Dis(pos[i], pos[j])/500*3);
        }
    Add(0, 1, Dis(pos[0], pos[1])/500*3);
    cout << int( Spfa(0, 1) + 0.5) << endl;

    return 0;
}

题解二（别人的）

#include<iostream>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<map>
#include<cstdio>
#include<queue>
#include<stack>

using namespace std;

const int INF = 0x3f3f3f3f;
const int MAXN = 205;
const double wsp = 10 * 1000 / 60;
const double ssp = 40 * 1000 / 60;

struct Node{
    double x, y;
}node[MAXN];

struct ff{
    int x, d;
    ff(){}
    ff( int a, double b ){ x = a; d = b; }
    bool operator <( const ff & a )const{
        return d > a.d;
    }
};

int cnt;
double cost[MAXN][MAXN];
double dis[MAXN];

double gdis( int pre, int pos ){
    double dx = node[pre].x - node[pos].x;
    double dy = node[pre].y - node[pos].y;
    return sqrt( dx * dx + dy * dy );
}

void dij(){
    for( int i = 1; i < MAXN; i++ )
        dis[i] = INF;
    dis[1] = 0;

    priority_queue<ff> Q;
    Q.push( ff( 1, dis[1]) );

    while( !Q.empty() ){
        ff temp = Q.top(); Q.pop();
        int x = temp.x;
        if( temp.d > dis[x] ) continue;
        for( int i = 1; i < cnt; i++ ){
            if( dis[i] > dis[x] + cost[x][i] ){
                dis[i] = dis[x] + cost[x][i];
                Q.push( ff( i, dis[i] ) );
            }
        }
    }
}

int main(){
    ios::sync_with_stdio( false );

    for( int i = 0; i < MAXN; i++ )
        for( int j = 0; j < MAXN; j++ )
            cost[i][j] = INF;

    cin >> node[1].x >> node[1].y >> node[2].x >> node[2].y;
    cnt = 3;

    while( cin >> node[cnt].x >> node[cnt].y ){
        cnt++;
        while( cin >> node[cnt].x >> node[cnt].y, !( node[cnt].x == -1 && node[cnt].y == -1 ) ){
            cost[cnt][cnt - 1] = cost[cnt - 1][cnt] = gdis( cnt - 1, cnt ) / ssp;
            cnt++;
        }
    }

    for( int i = 1; i < cnt - 1; i++ ){
        cost[i][i] = 0;
        for( int j = i + 1; j < cnt; j++ ){
            cost[i][j] = cost[j][i] = min( cost[i][j], gdis( i, j ) / wsp );
        }
    }

    dij();

    cout << int( dis[2] + 0.5 );
    return 0;
}