UVA 10256 - The Great Divide

这个题 就是把两个颜色的凸包全部求出来。 然后判断 凸包之间是否有重叠。

在判断凸包之间时候有重叠的时候 有两个方面。 1   判断  某一个点 是否在另一个凸包内部  2   判断 凸包的线段是否出现相交。

#include <cstdio>
#include <algorithm>
#include <iostream>
#include <cstring>
#include <cmath>
#include <cstdlib>
#include <string>
#include <map>
#include <vector>
#include <set>
#include <queue>
#include <stack>
#include <cctype>
using namespace std;
#define ll long long
typedef unsigned long long ull;
#define maxn 10010
#define INF 1<<30
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){ return Vector(A.x + B.x, A.y + B.y);}
Vector operator - (Vector A, Point B){return Vector(A.x - B.x, A.y - B.y);}
Vector operator * (Vector A, double p){return Vector(A.x * p, A.y * p);}
Vector operator / (Vector A, double p){return Vector(A.x / p, A.y / p);}
bool operator < (const Point & a, const Point & b){
    return a.x < b.x || (a.x == b.x && a.y < b.y);
}
const double eps = 1e-10;
int dcmp(double x){
    if(fabs(x) < eps) return 0;
    else return x < 0 ? -1 : 1;
}
bool operator == (const Point & a, const Point & b){
    return dcmp(a.x - b.x) == 0 && dcmp(a.y - b.y) == 0;
}
double Dot(Vector A, Vector B){ return A.x * B.x + A.y * B.y;} // 点积
double Length(Vector A) { return sqrt(Dot(A, A));}             //向量长度
double Angle(Vector A, Vector B){ return acos(Dot(A, B)/Length(A)/Length(B));}
                                                                //夹角
double Cross(Vector A, Vector B){return A.x*B.y - A.y * B.x;}   //叉积（面积两倍）
double Area2(Point A, Point B, Point C){return Cross(B-A,C-A);} // 面积两倍
Vector Rotate(Vector A, double rad){return Vector(A.x*cos(rad) - A.y*sin(rad), A.x*sin(rad)+A.y*cos(rad));}// 旋转后的直线</span>


Vector Normal(Vector A){
    double L = Length(A);
    return Vector(-A.y/L, A.x/L);
}
Point GetLineIntersection(Point P, Point v, Point Q, Point w){  //求直线 pv 与qw的交点
    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 DistanceTpsegment(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 GetLinePrijection(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){ // 线段相交判定（不包括在端点处的情况）
    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){                              //线段在端点处是否可能相交
    return dcmp(Cross(a1-p, a2-p)) == 0 && dcmp(Dot(a1-p, a2-p)) < 0;
}
double ConvexPolygonArea(Point * p,int n){                         // 多边形的有向面积
    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;
}
int ConvexHull(Point *p, int n, Point * ch){                 // 求凸包。 点保存在 ch中
    sort(p, p+n);
    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 q[], int n){ // 判断p 是否在q这个凸包的内部， n为 q的数量
    int w = 0;
    for(int i = 0; i < n; i++){
        if(OnSegment(p, q[i], q[(i+1) % n]))
            return -1;
        int k = dcmp(Cross(q[(i+1)%n] - q[i], p-q[i]));
        int d1 = dcmp(q[i].y - p.y);
        int d2 = dcmp(q[(i+1)%n].y - p.y);
        if(k > 0 && d1 <= 0 && d2 > 0)
            w++;
        if(k < 0 && d2 <= 0 && d1 > 0)
            w--;
    }
    if(w != 0) return 1; // 在内部
    return 0;    // 在外部
}
int pan(Point af1[], int p1n, Point af2[], int p2n){
    for(int i = 0; i < p1n; i++)
        if(isPointInPolygon(af1[i], af2, p2n))
            return 0;
    for(int i = 0; i < p2n; i++)
        if(isPointInPolygon(af2[i], af1, p1n))
            return 0;
    for(int i = 0; i < p1n; i++){
        for(int j = 0; j < p2n; j++){
            if(SegmentProperIntersection(af1[i], af1[(i+1)%p1n], af2[i], af2[(j+1)%p2n]))
                return 0;
        }
    }
    return 1;
}
int main (){
    int m,n;
    while(scanf("%d%d",&m,&n)){
        if(m == 0 && n == 0)
            break;
        Point p1[maxn];
        Point p2[maxn];
        Point af1[maxn];
        Point af2[maxn];
        for(int i = 0; i < m; i++){
            double x, y;
            scanf("%lf%lf",&x, &y);
            p1[i] = Point(x,y);
        }
        for(int i = 0; i < n; i++){
            double x, y;
            scanf("%lf%lf",&x, &y);
            p2[i] = Point(x,y);
        }
        int p1n = ConvexHull(p1, m, af1);
        int p2n = ConvexHull(p2, n, af2);
        if(pan(af1, p1n, af2, p2n)) printf("Yes\n");
        else printf("No\n");
    }
    return 0;
}