BZOJ 2961: 共点圆

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突然想起来论文还没刷完QAQ简直智障

2013年xhr论文

卡斜率的时候用点积

#include<iostream>#include<cstdio>#include<cstring>#include<cmath>#include<algorithm>using namespace std;#define rep(i,l,r) for(int i=l;i<=r;i++)#define per(i,r,l) for(int i=r;i>=l;i--)#define mmt(a,v) memset(a,v,sizeof(a))#define tra(i,u) for(int i=head[u];i;i=e[i].next)const int N=500000+5;const double eps=1e-9;const double pi=acos(-1.0);const double inf=1e12;int dcmp(double x){if(fabs(x)<eps)return 0;return x<0?-1:1;}struct point{double x,y;bool operator < (const point &p)const{return dcmp(x-p.x)?x<p.x:y<p.y;}void print(){printf("%lf %lf\n",x,y);}};point operator - (point a,point b){return (point){a.x-b.x,a.y-b.y};}point operator + (point a,point b){return (point){a.x+b.x,a.y+b.y};}double cross(point a,point b){return a.x*b.y-a.y*b.x;}double cross(point a,point b,point c){return cross(b-a,c-a);}double dot(point a,point b){return a.x*b.x+a.y*b.y;}double sqr(double x){return x*x;}struct Query{int k;double x,y;bool ans;}q[N];point p[N],up[N],dw[N];void cdq(int l,int r){if(l==r)return;int mid=l+r>>1;cdq(l,mid);cdq(mid+1,r);int n=0;rep(i,l,mid)if(!q[i].k)p[++n]=(point){q[i].x,q[i].y};if(!n)return;sort(p+1,p+1+n);int t1=0,t2=0;rep(i,1,n){while(t1>=2&&dcmp(cross(up[t1-1],up[t1],p[i]))>=0)t1--;up[++t1]=p[i];}per(i,n,1){while(t2>=2&&dcmp(cross(dw[t2-1],dw[t2],p[i]))>=0)t2--;dw[++t2]=p[i];}up[t1+1]=(point){up[t1].x+eps,-inf};dw[t2+1]=(point){dw[t2].x-eps,inf};rep(i,mid+1,r)if(q[i].k&&q[i].ans){point t,tt=(point){q[i].x,q[i].y};if(q[i].y<0){int x=1,y=t1;while(x<=y){int mid=x+y>>1;if(dcmp(dot(tt,up[mid+1]-up[mid]))>=0)y=mid-1,t=up[mid];else x=mid+1;}}else{int x=1,y=t2;while(x<=y){int mid=x+y>>1;if(dcmp(dot(tt,dw[mid]-dw[mid+1]))<=0)y=mid-1,t=dw[mid];else x=mid+1;}}q[i].ans&=dcmp(2*tt.x*t.x+2*tt.y*t.y-sqr(tt.x)-sqr(tt.y))>=0;}}int main(){//freopen("a.in","r",stdin);//freopen("a.out","w",stdout);int n;scanf("%d",&n);bool cir=false;rep(i,1,n){scanf("%d%lf%lf",&q[i].k,&q[i].x,&q[i].y);if(q[i].k)q[i].ans=cir;else cir=1;}cdq(1,n);rep(i,1,n)if(q[i].k)puts(q[i].ans?"Yes":"No");return 0;}

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