UVA 10256 The Great Divide(点在多边形内)

The Great Divid

【题目链接】The Great Divid

【题目类型】点在多边形内

&题解：

蓝书274, 感觉我的代码和刘汝佳的没啥区别,可是我的就是wa,所以贴一发刘汝佳的吧.

感觉这题最好的地方就是让我大致懂了点在多边形内的判断,写的好神奇,没有做一条直线,而是2个if判断就替代了这个,好腻害

&代码：

#include <cstdio>
#include <vector>
#include <cmath>
#include <algorithm>
using namespace std;

const double eps = 1e-10;
int dcmp(double x) {if(fabs(x)<eps) return 0; return x<0?-1:1;}
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); }
double Cross(Vector A,Vector B) {return A.x*B.y-A.y*B.x;}
double Dot(Vector A,Vector B) {return A.x*B.x+A.y*B.y;}
bool operator == (Point a,Point b) {return dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)==0;}
bool operator < (Point a,Point b) {return a.x<b.x||(a.x==b.x&&a.y<b.y);}

bool SegmentProperIntersection(const Point& a1,const Point& a2,const Point& b1,const 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(const Point& p,const Point& a1,const Point& a2) {
	return dcmp(Cross(a1-p , a2-p))==0 && dcmp(Dot(a1-p , a2-p))<0;
}

vector<Point> ConvexHull(vector<Point> p) {
	sort(p.begin(),p.end());
	p.erase(unique(p.begin(), p.end()), p.end());
	int n=p.size();
	int m=0;
	vector<Point> ch(n+1);
	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--;
	ch.resize(m);
	return ch;
}

int IsInPolygon(const Point& p,const vector<Point>& poly) {
	int n = poly.size() , wn=0;
	for(int i=0; i<n; i++) {
		const Point& p1 = poly[i] , p2 = poly[(i+1)%n];
		if(p1==p || p2==p || OnSegment(p, p1, p2)) return -1;
		int k=dcmp(Cross(p2-p1 , p-p1));
		int d1=dcmp(p1.y - p.y) , d2=dcmp(p2.y - p.y);
		if(k>0 && d1<=0 && d2>0) wn++;
		if(k<0 && d2<=0 && d1>0) wn--;
	}
	return wn?1:0;
}
bool ConvexPolygonDisjoint(const vector<Point> ch1,const vector<Point> ch2) {
	int c1=ch1.size(), c2=ch2.size();
	for(int i=0; i<c1; i++) {
		if(IsInPolygon(ch1[i],ch2)) return false;
	}
	for(int i=0; i<c2; i++) {
		if(IsInPolygon(ch2[i],ch1)) return false;
	}
	for(int i=0; i<c1; i++) {
		for(int j=0; j<c2; j++) {
			if(SegmentProperIntersection(ch1[i],ch1[(i+1)%c1],ch2[j],ch2[(j+1)%c2])) return false;
		}
	}
	return true;
}
int main() {
	freopen("e:1.in","r",stdin);
	int n,m;
	while(scanf("%d%d",&n,&m)==2&&n>0&&m>0) {
		vector<Point> P1,P2;
		double x,y;
		for(int i=0; i<n; i++) {
			scanf("%lf%lf",&x,&y);
			P1.push_back(Point(x,y));
		}
		for(int i=0; i<m; i++) {
			scanf("%lf%lf",&x,&y);
			P2.push_back(Point(x,y));
		}
		if(ConvexPolygonDisjoint(ConvexHull(P1), ConvexHull(P2)))
			printf("Yes\n");
		else
			printf("No\n");
	}
}