UVA 10256 The Great Divide

大意：平面上有n个Majestix（红点）和m个Cleverdix（蓝点），是否存在一条直线，使得任取一个红点和一个蓝点都在直线的异侧？这条直线不能穿过红点或蓝点？

思路：分离两个点集的充要条件是分离两个凸包，首先求出两个凸包。

然后判断这两个凸包是否有公共部分，则只需：

1、判断任何一个红点不在蓝点的内部，蓝点类似。

2、红凸包上的任意一条边与蓝凸包没有交点（包括端点）。

判断1时，判断是否在凸包内外部的同时还判断端点是否相等，这样在判断2时可以直接判断是不是规范相交。

判断2时，直接判断是否规范相交即可。

如果有1个凸包退化成了点或者线也没关系，因为上面两种判断覆盖了这种情况。

#include <iostream>#include <cstdlib>#include <cstdio>#include <string>#include <cstring>#include <cmath>#include <vector>#include <queue>#include <stack>#include <algorithm>using namespace std;const double eps = 1e-10;const double PI = acos(-1.0);struct Point{double x, y;Point(double x = 0, double y = 0) : x(x), y(y) { }bool operator < (const Point& a) const{if(a.x != x) return x < a.x;return y < a.y;}};typedef Point Vector;Vector operator + (Vector A, Vector B) { return Vector(A.x+B.x, A.y+B.y); }Vector operator - (Point 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); }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; }double Length(Vector A) { return sqrt(Dot(A, A)); }double Angle(Vector A, Vector B) { return acos(Dot(A, B) / Length(A) / Length(B)); }double Cross(Vector A, Vector B) { return A.x*B.y - A.y*B.x; }double Area2(Point A, Point B, Point C) { return fabs(Cross(B-A, C-A)) / 2; }Vector Rotate(Vector A, double rad){return Vector(A.x*cos(rad)-A.y*sin(rad), A.x*sin(rad) + A.y*cos(rad));}Point GetLineIntersection(Point P, Vector v, Point Q, Vector w){Vector u = P-Q;double t = Cross(w, u) / Cross(v, w);return P+v*t;}bool SegmentProperIntersection(Point a1, Point a2, Point b1, Point b2){double c1 = Cross(a2-a1, b1-a1), c2 = Cross(a2-a1, b2-a1);double 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){return dcmp(Cross(a1-p, a2-p)) == 0 && dcmp(Dot(a1-p, a2-p)) < 0;}double PolygonArea(Point* p, int n){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;}double PointDistanceToLine(Point P, Point A, Point B){Vector v1 = B-A, v2 = P-A;return fabs(Cross(v1, v2)) / Length(v1);}double PointDistanceToSegment(Point P, Point A, Point B){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);}int isPointInPolygon(Point p, Point *poly, int n){int wn = 0;for(int i = 0; i < n; i++){const Point& p1 = poly[i], p2 = poly[(i+1)%n];if(p == p1 || p == p2 || OnSegment(p, p1, p2)) return -1;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 != 0) return 1;return 0;}int ConvexHull(Point *p, int n, Point *ch) //凸包{sort(p, p+n);n = unique(p, p+n) - p; //去重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 n, m;const int maxn = 1010;Point P[maxn], red[maxn], Q[maxn], blue[maxn];Point read_point(){Point A;scanf("%lf%lf", &A.x, &A.y);return A;}int read_case(){scanf("%d%d", &n, &m);if(!n && !m) return 0;for(int i = 0; i < n; i++) P[i] = read_point();for(int i = 0; i < m; i++) Q[i] = read_point();return 1;}int CheckConvexHullDisjoint(){int newn = ConvexHull(P, n, red);int newm = ConvexHull(Q, m, blue);for(int i = 0; i < newn; i++) if(isPointInPolygon(red[i], blue, newm)) return 0;for(int i = 0; i < newm; i++) if(isPointInPolygon(blue[i], red, newn)) return 0;for(int i = 0; i < newn; i++){for(int j = 0; j < newm; j++){if(SegmentProperIntersection(red[i], red[(i+1)%newn], blue[j], blue[(j+1)%newm])) return 0;}}return 1;}void solve(){if(CheckConvexHullDisjoint()) printf("Yes\n");else printf("No\n");}int main(){while(read_case()){solve();}return 0;}