UVALive 4639 && SPOJ SPOINTS && POJ 3805 && AOJ 1298 Separate Points 求两个凸包是否相交 难度:3

https://icpcarchive.ecs.baylor.edu/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=2640

http://www.spoj.com/problems/SPOINTS/en/

http://poj.org/problem?id=3805

http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=1298

要想有一条直线分两个凸包,两个凸包不相交,不相切是必要的

在没有模板的情况下,我的代码,过了poj,uva,和spoj的,但是过不了aoj的,和正确代码对拍所发现的情况不太符合事实

方法是:

1.判断每个点是否在凸包里面或者边上

2.判断两凸包每两条线段是否相交

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
using namespace std;
const double eps=1e-8;
const int  maxn=205;
int dcmp(double d){
    if(fabs(d)<eps)return 0;
    return d>0?1:-1;
}
struct pnt{
    double x,y;
    pnt():x(0),y(0){}
    pnt(double tx,double ty):x(tx),y(ty){}
    pnt operator -(pnt p2){
        pnt newp(x-p2.x,y-p2.y);
        return newp;
    }
    pnt operator +(pnt p2){
        pnt newp(x+p2.x,y+p2.y);
        return newp;
    }
    pnt operator *(double  d){
        pnt newp(x*d,y*d);
        return newp;
    }
    pnt operator /(double  d){
        pnt newp(x/d,y/d);
        return newp;
    }
    double dis(pnt p2){
        return sqrt((x-p2.x)*(x-p2.x)+(y-p2.y)*(y-p2.y));
    }
    bool operator ==(pnt p2){
        if(dcmp(x-p2.x)==0&&dcmp(y-p2.y)==0)return true;
        return false;
    }
};
double cross(pnt p1,pnt p2){
    return p1.x*p2.y-p1.y*p2.x;
}
bool cmpx(pnt p1,pnt p2){
    if(p1.x!=p2.x)return p1.x<p2.x;
    return p1.y<p2.y;
}
pnt base;
bool cmp(pnt p1,pnt p2){
    return cross(p1-  base,p2-base)<0;
}

int isPointInConvexPolygon(pnt p1,pnt * p,int n){
    for(int i=0;i<n;i++){
        pnt A=pnt(p[(i+1)%n].x-p[i].x,p[(i+1)%n].y-p[i].y);
        pnt B=pnt(p1.x-p[i].x,p1.y-p[i].y);
        int fl=dcmp(cross(A,B));
        if(fl<0)return 0;
        if(fl==0){
            int maxx=max(p[(i+1)%n].x,p[i].x);
            int minx=min(p[(i+1)%n].x,p[i].x);
            int maxy=max(p[(i+1)%n].y,p[i].y);
            int miny=min(p[(i+1)%n].y,p[i].y);
            if(minx<=p1.x&&maxx>=p1.x&&miny<=p1.y&&maxy>=p1.y)return -1;//on the edge
            else return 0;
        }
    }
    return 1;
}
int graham(pnt * p,pnt * h,int n){

        int m=0;
        for(int i=0;i<n;i++){//计算上凸包
                while(m>1&&cross((h[m-1]-h[m-2]),(p[i]-h[m-2]))<=0){m--;}
                h[m++]=p[i];
        }
        int tm=m;
        for(int i=n-2;i>=0;i--){//计算下凸包
                while(m>tm&&cross((h[m-1]-h[m-2]),(p[i]-h[m-2]))<=0){m--;}
                h[m++]=p[i];
        }
        if(n>1)m--;
        return m;
}

bool between(pnt p1,pnt p2,pnt p){
        return (p.x<=max(p1.x,p2.x)&&p.x>=min(p1.x,p2.x))
        &&  (p.y<=max(p1.y,p2.y)&&p.y>=min(p1.y,p2.y));
}
bool isInsert(pnt p11,pnt p12,pnt p21,pnt p22){
        pnt v=p22-p21;
        pnt w=p12-p11;
        pnt u=p21-p11;
        if(cross(v,w)==0){
                if(cross(v,u)!=0)return false;
                if(between(p11,p12,p21))return true;
                if(between(p11,p12,p22))return true;
                return false;
        }
        double t=cross(w,u)/cross(v,w);
        double t2=cross(v,u)/cross(v,w);
        if(t2>1||t2<0)return false;
        if(t>1||t<0)return false;
        return true;
}

pnt bp[maxn],bh[maxn],wp[maxn],wh[maxn];
int bn,wn,btop,wtop;

int main(){
        while(scanf("%d%d",&bn,&wn)==2&&(bn||wn)){
                for(int i=0;i<bn;i++){
                        scanf("%lf%lf",&bp[i].x,&bp[i].y);
                }
                for(int i=0;i<wn;i++){
                        scanf("%lf%lf",&wp[i].x,&wp[i].y);
                }
                bool fl=true;

                if(bn>1){
                        sort(bp,bp+bn,cmpx);
                        base =bp[0];
                        sort(bp+1,bp+bn,cmp);
                        btop=graham(bp,bh,bn);

                        if(fl)for(int i=0;i<wn;i++){
                                if(isPointInConvexPolygon(wp[i],bh,btop)){
                                        fl=false;
                                        break;
                                }
                        }
                }

                if(wn>1){
                        sort(wp,wp+wn,cmpx);
                        base =wp[0];
                        sort(wp+1,wp+wn,cmp);
                        wtop=graham(wp,wh,wn);

                        if(fl){
                                for(int i=0;i<bn;i++){
                                        if(isPointInConvexPolygon(bp[i],wh,wtop)){
                                                fl=false;
                                                break;
                                        }
                                }
                        }
                }

                if(fl&&bn>1&&wn>1){
                        for(int i=0;i<btop;i++){
                                for(int j=0;j<wtop;j++){
                                        if(isInsert(bh[i],bh[(i+1)%btop],wh[j],wh[(j+1)%wtop])){
                                                fl=false;
                                                break;
                                        }
                                }
                        }
                }
                if(wn==1&&bn==1&&bp[0]==wp[0]){fl=false;}

                if(fl)puts("YES");
                else puts("NO");
        }
        return 0;
}

　　这里的代码都可以过:http://pelkira.hatenablog.jp/

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<map>
#include<vector>
#include<queue>
#include<functional>
#include<cstring>
#include<cstdlib>
#include<complex>
using namespace std;
typedef long long ll;
typedef complex < double > Point;

typedef vector < Point > Polygon;
namespace std {
    bool operator < (Point a,Point b) {
        return real(a) != real(b) ? real(a) < real(b) : imag(a) < imag(b);
    }
}
const double EPS = 1e-8;
const double INF = 1e12;

struct Line : Polygon{
    Line(){};
    Line(Point p,Point q){ push_back(p);push_back(q); }
};
double cross(Point p,Point q){
    return imag(conj(p)*q);
}
double dot(Point p,Point q){
    return real(conj(p)*q);
}

int ccw(Point a,Point b,Point c){
    b-=a,c-=a;
    if(cross(b,c)>0)return 1; //反時計回り
    if(cross(b,c)<0)return -1; //時計回り
    if(dot(b,c)<0)return 2; //直線上に c - a - b
    if(norm(b)<norm(c))return -2; // 直線上に a - b - c
    return 0; // 直線上に a - c - b
}

bool intersectSS(Line s, Line t) {
    return ccw(s[0],s[1],t[0])*ccw(s[0],s[1],t[1]) <= 0 &&
         ccw(t[0],t[1],s[0])*ccw(t[0],t[1],s[1]) <= 0;
}
bool intersectSP(Line s, Point p) {
    return abs(s[0]-p)+abs(s[1]-p)-abs(s[1]-s[0]) < EPS; // triangle inequality
}
Polygon ConvexHull(Polygon ps) {//凸包
    int n = ps.size(), k = 0;
    if(n == 1)return ps;
    sort(ps.begin(), ps.end());
    Polygon ch(2*n);
    for (int i = 0; i < n; ch[k++] = ps[i++]) // lower-hull
        while (k >= 2 && ccw(ch[k-2], ch[k-1], ps[i]) <= 0) --k;
    for (int i = n-2, t = k+1; i >= 0; ch[k++] = ps[i--]) // upper-hull
        while (k >= t && ccw(ch[k-2], ch[k-1], ps[i]) <= 0) --k;
    ch.resize(k-1);
    return ch;
}

// Point - Vertex
enum{OUT, ON, IN};
int IsInnerPointVertex(Polygon ps,Point a){
    bool flg = false;
    for(int i = 0;i < ps.size();i++){
        Point p = ps[i] - a,q = ps[(i+1)%ps.size()] - a;
        if(imag(p)>imag(q))swap(p,q);
        if(imag(p)<=0&&0<imag(q)){
            if(cross(p,q) < 0)flg = !flg;
        }
        if(cross(p,q) == 0 && dot(p,q) <= 0)return ON;
    }
    return flg ? IN : OUT;
}
int main(){
    int n,m;
    while(cin>>n>>m,n){
        Polygon G,H;
        for(int i = 0;i < n;i++){
            double x,y;
            cin>>x>>y;
            G.push_back(Point(x,y));
        }
        for(int i = 0;i < m;i++){
            double x,y;
            cin>>x>>y;
            H.push_back(Point(x,y));
        }
        G = ConvexHull(G);
        H = ConvexHull(H);
        int g = G.size(),h = H.size();
        //cout<<g<<" "<<h<<endl;
        if(g > h)swap(G,H);
        g = G.size(),h = H.size();
        bool flg = true;
        for(int i = 0;i < g;i++){
            if(IsInnerPointVertex(H,G[i]) != OUT){
                flg = false;
                break;
            }
        }
        for(int i = 0;i < h;i++){
            if(IsInnerPointVertex(G,H[i]) != OUT){
                flg = false;
                break;
            }
        }

        if(h == 1)flg = true;
        else if(g == 1 && h == 2){
            flg = !(intersectSP(Line(H[0],H[1]),G[0]));
        }
        else if(g == 2 && h == 2){
            flg = !(intersectSS(Line(G[0],G[1]),Line(H[0],H[1])));
        }
        else if(g == 2){
            flg = true;
            for(int i = 0;i < h;i++){
                int j = (i+1)%h;
                if(intersectSS(Line(G[0],G[1]),Line(H[i],H[j])))flg = false;
            }
        }
        if(flg)cout<<"YES"<<endl;
        else cout<<"NO"<<endl;
    }
    return 0;
}