UVa 10256 - The Great Divide 判断凸包相交

模板敲错了于是WA了好几遍……

判断由红点和蓝点分别组成的两个凸包是否相离，是输出Yes，否输出No。

训练指南上的分析：

1.任取红凸包上的一条线段和蓝凸包上的一条线段，判断二者是否相交。如果相交（不一定是规范相交，有公共点就算相交），则无解

2.任取一个红点，判断是否在蓝凸包内。如果是，则无解。蓝点红凸包同理。

其中任何一个凸包退化成点或者线段时需要特判。

其实只需要把上面两个判断顺序颠倒一下，就可以不需要特判。

先判断点是否在凸包内，因为这个考虑了点在凸包边界上的情况，所以后面判凸包线段是否相交时直接用规范相交判断即可。

此时特殊情况包含在了上两种情况中，因此不需要特判。

 

#include <cstdio>
#include <cmath>
#include <algorithm>

using namespace std;

const int MAXN = 540;

const double eps = 1e-10;

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

typedef Point Vector;

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 A.x < B.x || ( A.x == B.x && A.y < B.y );
}

int dcmp( double x )    //控制精度
{
    if ( fabs(x) < eps ) return 0;
    else return x < 0 ? -1 : 1;
}

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;
}

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

int ConvexHull( Point *p, int n, Point *ch )    //求凸包
{
    sort( p, p + n );
    n = unique( p, p + n ) - p;
    int m = 0;
    for ( int i = 0; i < n; ++i )
    {
        while ( m > 1 && Cross( ch[m - 1] - ch[m - 2], p[i] - ch[m - 2] ) <= 0 ) --m;
        ch[m++] = p[i];
    }

    int k = m;
    for ( int i = n - 2; i >= 0; --i )
    {
        while ( m > k && Cross( ch[m - 1] - ch[m - 2], p[i] - ch[m - 2] ) <= 0 ) --m;
        ch[m++] = p[i];
    }

    if ( n > 1 ) --m;
    return m;
}

int isPointInPolygon( Point p, Point *poly, int n )   //判断一点是否在凸包内
{
    int wn = 0;

    for ( int i = 0; i < n; ++i )
    {
        Point& p1 = poly[i], p2 = poly[ (i + 1)%n ];
        if ( p == p1 || p == p2 || OnSegment( p, p1, p2 ) ) return -1;  //在边界上
        int k = dcmp( Cross( p2 - p1, p - p1 ) );
        int d1 = dcmp( p1.y - p.y );
        int d2 = dcmp( p2.y - p.y );
        if ( k > 0 && d1 <= 0 && d2 > 0 ) ++wn;
        if ( k < 0 && d2 <= 0 && d1 > 0 ) --wn;
    }

    if ( wn ) return 1;   //内部
    return 0;             //外部
}

double PolygonArea( Point *p, int n )   //多边形有向面积
{
    double area = 0;
    for ( int i = 1; i < n - 1; ++i )
        area += Cross( p[i] - p[0], p[i + 1] - p[0] );
    return area / 2.0;
}

bool checkConvexHullIntersection( Point *a, Point *b, int na, int nb )
{
    for ( int i = 0; i < na; ++i )
        if ( isPointInPolygon( a[i], b, nb ) ) return true;

    for ( int i = 0; i < nb; ++i )
        if ( isPointInPolygon( b[i], a, na ) ) return true;

    for ( int i = 0; i < na; ++i )
        for ( int j = 0; j < nb; ++j )
            if ( SegmentProperIntersection(a[i], a[ (i + 1) % na ], b[j], b[ (j + 1) % nb ] ) ) return true;

    return false;
}

Point M[MAXN], chM[MAXN];
Point C[MAXN], chC[MAXN];

int main()
{
    int Mn, Cn;
    while ( scanf( "%d%d", &Mn, &Cn ), Mn || Cn )
    {
        for ( int i = 0; i < Mn; ++i )
            scanf( "%lf%lf", &M[i].x, &M[i].y );

        for ( int i = 0; i < Cn; ++i )
            scanf( "%lf%lf", &C[i].x, &C[i].y );

        int Mcnt = ConvexHull( M, Mn, chM );
        int Ccnt = ConvexHull( C, Cn, chC );

        if ( checkConvexHullIntersection( chM, chC, Mcnt, Ccnt ) ) puts("No");
        else puts("Yes");
    }
    return 0;
}