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  • hdu 6617

    我人傻了,我两份半平面交的板子都错了??
    然后粘了网友的板子过了????
    我他妈????
    这现场赛万一出个半平面交我都不知道粘哪份板子了
    其实题目本身还挺简单的,
    维护一下小凸包每条边切的点,
    然后二分半平面交就行了。
    代码几乎照着网友的抄的。。。。。。好像一共也就几行代码

    #include <bits/stdc++.h>
    #define mp make_pair
    #define fi first
    #define se second
    #define pb push_back
    using namespace std;
    typedef double db;
    const int maxn = 4e5+5;
    const db eps=1e-13;
    const db pi=acos(-1);
    int sign(db k){
        if (k>eps) return 1; else if (k<-eps) return -1; return 0;
    }
    int cmp(db k1,db k2){return sign(k1-k2);}
    int inmid(db k1,db k2,db k3){return sign(k1-k3)*sign(k2-k3)<=0;}// k3 在 [k1,k2] 内
    struct point{
        db x,y;
        point operator + (const point &k1) const{return (point){k1.x+x,k1.y+y};}
        point operator - (const point &k1) const{return (point){x-k1.x,y-k1.y};}
        point operator * (db k1) const{return (point){x*k1,y*k1};}
        point operator / (db k1) const{return (point){x/k1,y/k1};}
        int operator == (const point &k1) const{return cmp(x,k1.x)==0&&cmp(y,k1.y)==0;}
        // 逆时针旋转
        point turn(db k1){return (point){x*cos(k1)-y*sin(k1),x*sin(k1)+y*cos(k1)};}
        point turn90(){return (point){-y,x};}
        bool operator < (const point k1) const{
            int a=cmp(x,k1.x);
            if (a==-1) return 1; else if (a==1) return 0; else return cmp(y,k1.y)==-1;
        }
        db abs(){return sqrt(x*x+y*y);}
        db abs2(){return x*x+y*y;}
        db dis(point k1){return ((*this)-k1).abs();}
        point unit(){db w=abs(); return (point){x/w,y/w};}
        void scan(){double k1,k2; scanf("%lf%lf",&k1,&k2); x=k1; y=k2;}
        void print(){printf("%.11lf %.11lf
    ",x,y);}
        db getw(){return atan2(y,x);}
        point getdel(){if (sign(x)==-1||(sign(x)==0&&sign(y)==-1)) return (*this)*(-1); else return (*this);}
        int getP() const{return sign(y)==1||(sign(y)==0&&sign(x)==-1);}
    };
    int inmid(point k1,point k2,point k3){return inmid(k1.x,k2.x,k3.x)&&inmid(k1.y,k2.y,k3.y);}
    db cross(point k1,point k2){return k1.x*k2.y-k1.y*k2.x;}
    db dot(point k1,point k2){return k1.x*k2.x+k1.y*k2.y;}
    db rad(point k1,point k2){return atan2(cross(k1,k2),dot(k1,k2));}
    // -pi -> pi
    int compareangle (point k1,point k2){//极角排序+
        return k1.getP()<k2.getP()||(k1.getP()==k2.getP()&&sign(cross(k1,k2))>0);
    }
    point proj(point k1,point k2,point q){ // q 到直线 k1,k2 的投影
        point k=k2-k1;return k1+k*(dot(q-k1,k)/k.abs2());
    }
    point reflect(point k1,point k2,point q){return proj(k1,k2,q)*2-q;}
    int clockwise(point k1,point k2,point k3){// k1 k2 k3 逆时针 1 顺时针 -1 否则 0
        return sign(cross(k2-k1,k3-k1));
    }
    int checkLL(point k1,point k2,point k3,point k4){// 求直线 (L) 线段 (S)k1,k2 和 k3,k4 的交点
        return cmp(cross(k3-k1,k4-k1),cross(k3-k2,k4-k2))!=0;
    }
    point getLL(point k1,point k2,point k3,point k4){
        db w1=cross(k1-k3,k4-k3),w2=cross(k4-k3,k2-k3); return (k1*w2+k2*w1)/(w1+w2);
    }
    int intersect(db l1,db r1,db l2,db r2){
        if (l1>r1) swap(l1,r1); if (l2>r2) swap(l2,r2); return cmp(r1,l2)!=-1&&cmp(r2,l1)!=-1;
    }
    int checkSS(point k1,point k2,point k3,point k4){
        return intersect(k1.x,k2.x,k3.x,k4.x)&&intersect(k1.y,k2.y,k3.y,k4.y)&&
               sign(cross(k3-k1,k4-k1))*sign(cross(k3-k2,k4-k2))<=0&&
               sign(cross(k1-k3,k2-k3))*sign(cross(k1-k4,k2-k4))<=0;
    }
    db disSP(point k1,point k2,point q){
        point k3=proj(k1,k2,q);
        if (inmid(k1,k2,k3)) return q.dis(k3); else return min(q.dis(k1),q.dis(k2));
    }
    db disSS(point k1,point k2,point k3,point k4){
        if (checkSS(k1,k2,k3,k4)) return 0;
        else return min(min(disSP(k1,k2,k3),disSP(k1,k2,k4)),min(disSP(k3,k4,k1),disSP(k3,k4,k2)));
    }
    int onS(point k1,point k2,point q){return inmid(k1,k2,q)&&sign(cross(k1-q,k2-k1))==0;}
    struct circle{
        point o; db r;
        void scan(){o.scan(); scanf("%lf",&r);}
        int inside(point k){return cmp(r,o.dis(k));}
    };
    struct line{
        // p[0]->p[1]
        point p[2];
        line(point k1,point k2){p[0]=k1; p[1]=k2;}
        line(){}
        point& operator [] (int k){return p[k];}
        int include(point k){return sign(cross(p[1]-p[0],k-p[0]))>0;}
        point dir(){return p[1]-p[0];}
        line push(){ // 向外 ( 左手边 ) 平移 eps
            const db eps = 1e-6;
            point delta=(p[1]-p[0]).turn90().unit()*eps;
            return {p[0]-delta,p[1]-delta};
        }
    };
    point getLL(line k1,line k2){return getLL(k1[0],k1[1],k2[0],k2[1]);}
    int parallel(line k1,line k2){return sign(cross(k1.dir(),k2.dir()))==0;}
    int sameDir(line k1,line k2){return parallel(k1,k2)&&sign(dot(k1.dir(),k2.dir()))==1;}
    int operator < (line k1,line k2){
        if (sameDir(k1,k2)) return k2.include(k1[0]);
        return compareangle(k1.dir(),k2.dir());
    }
    int checkpos(line k1,line k2,line k3){return k3.include(getLL(k1,k2));}
    vector<line> getHL(vector<line> &L){ // 求半平面交 , 半平面是逆时针方向 , 输出按照逆时针
        sort(L.begin(),L.end()); deque<line> q;
        for (int i=0;i<(int)L.size();i++){
            if (i&&sameDir(L[i],L[i-1])) continue;
            while (q.size()>1&&!checkpos(q[q.size()-2],q[q.size()-1],L[i])) q.pop_back();
            while (q.size()>1&&!checkpos(q[1],q[0],L[i])) q.pop_front();
            q.push_back(L[i]);
        }
        while (q.size()>2&&!checkpos(q[q.size()-2],q[q.size()-1],q[0])) q.pop_back();
        while (q.size()>2&&!checkpos(q[1],q[0],q[q.size()-1])) q.pop_front();
        vector<line>ans; for (int i=0;i<q.size();i++) ans.push_back(q[i]);
        return ans;
    }
    vector<point> ConvexHull(vector<point>A,int flag=1){ // flag=0 不严格 flag=1 严格
        int n=A.size(); vector<point>ans(n*2);
        sort(A.begin(),A.end()); int now=-1;
        for (int i=0;i<A.size();i++){
            while (now>0&&sign(cross(ans[now]-ans[now-1],A[i]-ans[now-1]))<flag) now--;
            ans[++now]=A[i];
        } int pre=now;
        for (int i=n-2;i>=0;i--){
            while (now>pre&&sign(cross(ans[now]-ans[now-1],A[i]-ans[now-1]))<flag) now--;
            ans[++now]=A[i];
        } ans.resize(now); return ans;
    }
    bool cclock(vector<point> &p){
        int n = p.size();
        for(int i=1;i<n-1;i++){
            if(sign(cross(p[i]-p[i-1],p[i+1]-p[i-1]))>0)    return 0;
            else if(sign(cross(p[i]-p[i-1],p[i+1]-p[i-1]))<0){
                reverse(p.begin(),p.end());
                return 1;
            }
        }
        return 1;
    }
    //117-151 更可靠的半平面交板子 from matthew99 upd 9-29
    bool on_left(line l,point p){
        return sign(cross(l.dir(),p-l[0]))>0;
    }
    inline bool half_plane(line *plane, const int &n_plane, point *poly, int &n_poly){
        static int pos[maxn + 5];
        static double ang[maxn + 5];
        for(int i=0;i<n_plane;i++) ang[i] = atan2(plane[i].dir().y, plane[i].dir().x), pos[i] = i;
        sort(pos, pos + n_plane, [&](int x, int y) { return ang[x] < ang[y]; });
        int head, rear;
        static point p[maxn + 5];
        static line q[maxn + 5];
        head = rear = 0;
        q[rear++] = plane[pos[0]];
        for(int i=0;i<n_plane;i++){
            while (head < rear - 1 && !on_left(plane[pos[i]], p[rear - 2])) --rear;
            while (head < rear - 1 && !on_left(plane[pos[i]], p[head])) ++head;
            q[rear++] = plane[pos[i]];
            if (abs(cross(q[rear - 1].dir() , q[rear - 2].dir())) < eps){
                --rear;
                if (on_left(q[rear - 1], plane[pos[i]][0])) q[rear - 1] = plane[pos[i]];
            }
            if (head + 1 < rear) p[rear - 2] = getLL(q[rear - 2], q[rear - 1]);
        }
        while (head < rear - 1 && !on_left(q[head], p[rear - 2])) --rear;
        if (abs(cross(q[head].dir() , q[rear - 1].dir())) < eps){
            if (on_left(q[rear - 1], q[head][0])) --rear;
            else ++head;
        }
        if (head + 1 >= rear) return 0;
        p[rear - 1] = getLL(q[rear - 1], q[head]);
        n_poly = 0;
        for(int i=head;i<rear;i++) poly[n_poly++] = p[i];
        return 1;
    }
    
    int relation(point p,line l){    //点和向量关系   1:左侧   2:右侧   3:在线上
        int c=sign(cross(p-l[0],l[1]-l[0]));
        if(c<0)    return 1;
        else if(c>0)    return 2;
        else    return 3;
    }
    line que[maxn];
    int half_plane_intersection(line *L,int n){    //以逆时针方向 半平面交求多边形的核  ch表示凸包的顶点  返回顶点数 -1则表示不存在
        int head=0,tail=1;
        que[0]=L[0],que[1]=L[1];
        for(int i=2;i<n;i++){
            while(tail>head&&relation(getLL(que[tail],que[tail-1]),L[i])==2)   tail--;
            while(tail>head&&relation(getLL(que[head],que[head+1]),L[i])==2)   head++;
            que[++tail]=L[i];
        }
        while(tail>head&&relation(getLL(que[tail],que[tail-1]),que[head])==2)  tail--;
        while(tail>head&&relation(getLL(que[head],que[head+1]),que[tail])==2)  head++;
        for(int i=head;i<=tail;i++){
            int j=(i==tail? head: i+1);
            if(sign(cross(que[i][1]-que[i][0],que[j][1]-que[j][0]))<=0)
                return 0;
        }
        return 1;
    }
    
    int T,n,m,id[400005];
    vector<point> p,q;
    line l[400005];int cnt=0;point s[400005];int y;
    bool check(db x){
        cnt=0;
        for(int i=0;i<n;i++){
            l[cnt++]=line(p[i]*x-q[id[i]],p[(i+1)%n]*x-q[id[i]]);
        }
        return half_plane_intersection(l,cnt);
    }
    void log(vector<point>&v){for(auto x:v)x.print();}
    int main(){
        scanf("%d",&T);
        while (T--){
            scanf("%d",&n);p.resize(n);
            for(int i=0;i<n;i++)scanf("%lf%lf",&p[i].x,&p[i].y);
            cclock(p);n=p.size();
            scanf("%d",&m);q.resize(m);
            for(int i=0;i<m;i++)scanf("%lf%lf",&q[i].x,&q[i].y);
            if(m==1){
                printf("%.6f
    ",0.0);
                continue;
            }
    //      log(q);
            q=ConvexHull(q);m=q.size();
    //      log(q);
    //      log(q);
            db ans = 1e18;
            for(int cas=1;cas<=2;cas++){
                for(int i=0;i<n;i++)p[i]=p[i]*-1;
    //           p=ConvexHull(p);
    //          log(p);
                int j=0;
                for(int i=0;i<n;i++){
                    while (sign(cross(p[(i+1)%n]-p[i],q[(j+1)%m]-q[j]))<0||sign(cross(p[(i+1)%n]-p[i],q[(j-1+m)%m]-q[j]))<0){
                        j=(j+1)%m;
                    }
                    id[i]=j;//这条边无限外移切到的点
                    // cout<<i<<' '<<j<<endl;
                }
                db l=0,r=1e10;
                for(int i=0;i<=70;i++){
                    db mid = (l+r)/2;
                    if(check(mid))
                        r=mid;
                    else
                        l=mid;
                }
                ans = min(ans,l);
            }
            printf("%.11f
    ",ans);
        }
    }
    
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  • 原文地址:https://www.cnblogs.com/MXang/p/11773035.html
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