HDU 4643 GSM 算术几何

当火车处在换基站的临界点时，它到某两基站的距离相等。因此换基站的位置一定在某两个基站的中垂线上，

我们预处理出任意两基站之间的中垂线，对于每次询问，求询问线段与所有中垂线的交点。

检验这些交点是否满足条件（详见代码），如果满足，那么它是一个交换点。

 

#include <cstdio>

#include <cmath>

#include <vector>

#include <algorithm>



using namespace std;



const int MAXN = 60;



const double eps = 1e-7;



struct Point

{

    double x, y;

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

};



typedef Point Vector;



struct Line

{

    Point s;

    Vector v;

    Line( Point s = Point(), Point v = Point() ):

        s(s), v(v) { }

};



int dcmp( double x )    //控制精度

{

    if ( fabs(x) < eps ) return 0;

    else return x < 0 ? -1 : 1;

}



Vector operator+( Vector A, Vector B )       //向量加

{

    return Vector( A.x + B.x, A.y + B.y );

}



Vector operator-( Vector A, Vector B )       //向量减

{

    return Vector( A.x - B.x, A.y - B.y );

}



Vector operator*( Vector A, double p )      //向量数乘

{

    return Vector( A.x * p, A.y * p );

}



Vector operator/( Vector A, double p )      //向量数除

{

    return Vector( A.x / p, A.y / p );

}



bool operator<( const Point& A, const Point& B )   //两点比较

{

    return dcmp( A.x - B.x ) < 0 || ( dcmp( A.x - B.x ) == 0 && dcmp( A.y - B.y ) < 0 );

}



bool operator==( const Point& a, const Point& b )   //两点相等

{

    return dcmp( a.x - b.x ) == 0 && dcmp( a.y - b.y ) == 0;

}



double Dot( Vector A, Vector B )    //向量点乘

{

    return A.x * B.x + A.y * B.y;

}



double Length( Vector A )           //向量模

{

    return sqrt( Dot( A, A ) );

}



double Angle( Vector A, Vector B )    //向量夹角

{

    return acos( Dot(A, B) / Length(A) / Length(B) );

}



double Cross( Vector A, Vector B )   //向量叉积

{

    return A.x * B.y - A.y * B.x;

}



double Area2( Point A, Point B, Point C )    //向量有向面积

{

    return Cross( B - A, C - A );

}



Vector Rotate( Vector A, double rad )    //向量旋转

{

    return Vector( A.x * cos(rad) - A.y * sin(rad), A.x * sin(rad) + A.y * cos(rad) );

}



Vector Normal( Vector A )    //向量单位法向量

{

    double L = Length(A);

    return Vector( -A.y / L, A.x / L );

}



Point GetLineIntersection( Point P, Vector v, Point Q, Vector w )   //两直线交点

{

    Vector u = P - Q;

    double t = Cross( w, u ) / Cross( v, w );

    return P + v * t;

}



double DistanceToLine( Point P, Point A, Point B )    //点到直线的距离

{

    Vector v1 = B - A, v2 = P - A;

    return fabs( Cross( v1, v2 ) ) / Length(v1);

}



double DistanceToSegment( Point P, Point A, Point B )   //点到线段的距离

{

    if ( A == B ) return Length( P - A );

    Vector v1 = B - A, v2 = P - A, v3 = P - B;

    if ( dcmp( Dot(v1, v2) ) < 0 ) return Length(v2);

    else if ( dcmp( Dot(v1, v3) ) > 0 ) return Length(v3);

    else return fabs( Cross( v1, v2 ) ) / Length(v1);

}



Point GetLineProjection( Point P, Point A, Point B )    // 点在直线上的投影

{

    Vector v = B - A;

    return A + v*( Dot(v, P - A) / Dot( v, v ) );

}



bool SegmentProperIntersection( Point a1, Point a2, Point b1, Point b2 )  //线段相交，交点不在端点

{

    double c1 = Cross( a2 - a1, b1 - a1 ), c2 = Cross( a2 - a1, b2 - a1 ),

                c3 = Cross( b2 - b1, a1 - b1 ), c4 = Cross( b2 - b1, a2 - b1 );

    return dcmp(c1)*dcmp(c2) < 0 && dcmp(c3) * dcmp(c4) < 0;

}



bool OnSegment( Point p, Point a1, Point a2 )   //点在线段上，不包含端点

{

    return dcmp( Cross(a1 - p, a2 - p) ) == 0 && dcmp( Dot( a1 - p, a2 - p ) ) < 0;

}



/****************以上模板******************/



int N, M;

Point city[MAXN];      //城市

Point GSM[MAXN];       //基站

Line L[MAXN][MAXN];    //点[i][j]之间的中垂线



void init()

{

    for ( int i = 1; i <= M; ++i )

        for ( int j = i + 1; j <= M; ++j )

        {

            Point mid = Point( (GSM[i].x+GSM[j].x)/2.0, (GSM[i].y+GSM[j].y)/2.0 );

            L[i][j] = Line( mid, Normal( GSM[j] - GSM[i] ) );

            L[j][i] = L[i][j];

        }

    return;

}



//判断交点是否在线段上

bool check( Point st, Point ed, Point cp )

{

    return ( st < cp || st == cp ) && ( cp < ed || cp == ed );

}



//假设我在此交点交换基站

//那么交点到形成 该中垂线的线段的其中一端点 的距离 L 应该是最小的

//判断是否有点到交点的距离小于L，如果有，则不是在这一点交换的基站

bool check2( double limit, Point jiao )

{

    for ( int i = 1; i <= M; ++i )

    {

        double dis = Length( GSM[i] - jiao );

        if ( dcmp( dis - limit ) < 0 ) return false;

    }

    return true;

}



int main()

{

    //freopen( "in.txt", "r", stdin );

    //freopen( "s.txt", "w", stdout );

    while ( ~scanf( "%d%d", &N, &M ) )

    {

        for ( int i = 1; i <= N; ++i )

            scanf( "%lf%lf", &city[i].x, &city[i].y );



        for ( int i = 1; i <= M; ++i )

            scanf( "%lf%lf", &GSM[i].x, &GSM[i].y );



        init();   //初始化所有中垂线

        int Q;

        scanf( "%d", &Q );

        while ( Q-- )

        {

            int a, b;

            scanf( "%d%d", &a, &b );

            if ( a > b ) swap( a, b );

            Line train = Line( city[a], city[b] - city[a] );  //火车行进路线

            int huan = 0;         //换基站次数

            for ( int i = 1; i <= M; ++i )

                for ( int j = i + 1; j <= M; ++j )

                {

                    if ( dcmp( Cross( train.v, L[i][j].v ) ) == 0 ) //如果中垂线与火车行进路线平行

                        continue;

                    Point tmp = GetLineIntersection( train.s, train.v, L[i][j].s, L[i][j].v );  //求交点//交点到形成中垂线的线段的其中一个端点的距离

                    double limit = Length( GSM[i] - tmp );

                    Point st = city[a], ed = city[b];

                    if ( ed < st ) swap( st, ed );



                    if ( check( st, ed, tmp ) )  //如果在线段上

                    {

                        if ( check2( limit, tmp ) ) //如果确实在这点交换基站

                            ++huan;

                    }

                }

            printf( "%d\n", huan );

        }

    }

    return 0;

}