UVa 10075

航线算球面距离，需要经纬度转空间坐标。

任意两点间距离用Floyd求出来，查询时直接查表。

#include <cstdio>
#include <map>
#include <cmath>
#include <string>
#include <cstring>
#include <cstdlib>

using namespace std;

const int MAXN = 110;
const double INF = 1e30;
const double eps = 1e-8;
const double PI = acos( -1.0 );

struct Point
{
    double x, y;
    Point( int x = 0, int y = 0 ): x(x), y(y) {}
};

struct Coordinate   //空间坐标
{
    double x, y, z;
};

double dist[MAXN][MAXN];
Coordinate C[MAXN];

double Cha( double a, double b )
{
    return (a - b)*(a - b);
}

double GetDis( Coordinate a, Coordinate b )   //三维空间直线距离
{
    return sqrt( Cha( a.x, b.x ) + Cha( a.y, b.y ) + Cha( a.z, b.z ) );
}

double toRad( double deg )    //角度转弧度
{
    return deg / 180.0 * acos( -1.0 );
}

void get_coord( double R, double lat, double lng, double &x, double &y, double &z ) //经纬度转空间坐标
{
    lat = toRad(lat);
    lng = toRad(lng);
    x = R*cos(lat)*cos(lng);
    y = R*cos(lat)*sin(lng);
    z = R*sin(lat);
    return;
}

void Floyd( int n )    //弗洛伊德算任意两点最短路
{
    for ( int k = 0; k < n; ++k )
        for ( int i = 0; i < n; ++i )
        for ( int j = 0; j < n; ++j )
        {
            double temp = dist[i][k] + dist[k][j];
            if ( temp < dist[i][j] ) dist[i][j] = temp;
        }
    return;
}

int main()
{
    int n, m, Q;
    double r = 6378;
    int cas = 0;
    bool flag = false;
    while ( scanf( "%d%d%d", &n, &m, &Q ), n || m || Q )
    {
        map<string, int> Map;
        for ( int i = 0; i < n; ++i )
        {
            char str[100];
            Point P;
            scanf("%s%lf%lf", str, &P.x, &P.y );
            get_coord( r, P.x, P.y, C[i].x, C[i].y, C[i].z );
            Map[ str ] = i;
        }

        for ( int i = 0; i <= n; ++i )
        for ( int j = 0; j <= n; ++j )
            dist[i][j] = INF;

        for ( int i = 0; i < m; ++i )
        {
            char str1[100], str2[100];
            scanf( "%s%s", str1, str2 );
            int u = Map[ str1 ];
            int v = Map[ str2 ];
            dist[u][v] = (int)( 2.0 * asin( GetDis( C[u], C[v] ) / ( 2.0 * r ) ) * r + 0.5 );  //四舍五入
        }

        Floyd( n );

        if ( flag ) puts("");

        printf( "Case #%d
", ++cas );

        while ( Q-- )
        {
            char str1[100], str2[100];
            scanf( "%s%s", str1, str2 );
            int u = Map[ str1 ];
            int v = Map[ str2 ];
            if ( dist[u][v] >= INF - eps ) puts( "no route exists" );
            else printf( "%.0f km
", dist[u][v] );
        }

        flag = true;
    }
    return 0;
}