Description

Input

Output

Sample Input

Sample Output

HINT

Source

題解：半平面交求解不等式組

#include<iostream>#include<cstdio>#include<algorithm>#include<cstring>#include<cmath>#define N 103#define eps 1e-16#define inf 1000000000using namespace std;struct vector {    double x,y;    vector (double X=0,double Y=0){        x=X,y=Y;    }}a1[N],p[N],tmp[N];typedef vector point;vector Operator -(vector a,vector b){    return vector (a.x-b.x,a.y-b.y);}vector operator +(vector a,vector b){    return vector (a.x+b.x,a.y+b.y);}vector operator *(vector a,double t){    return vector (a.x*t,a.y*t);}vector operator !=(vector a,vector b){    return a.x!=b.x||a.y!=b.y;}struct data{    point a,b;}line[N];double a[N],b[N],c[N];int n,m;void init(){    m=0;    p[m++]=point(inf,inf);    p[m++]=point(eps,inf);    p[m++]=point(eps,eps);    p[m++]=point(inf,eps);}int dcmp(double x){    if (fabs(x)<eps) return 0;    return x<0?-1:1;}double cross(vector a,vector b){    return a.x*b.y-a.y*b.x;}point glt(point a,point a0,point b,point b0){    double a1,b1,c1,a2,b2,c2;      a1 = a.y - a0.y;      b1 = a0.x - a.x;      c1 = cross(a,a0);      a2 = b.y - b0.y;      b2 = b0.x - b.x;      c2 = cross(b,b0);      double d = a1 * b2 - a2 * b1;      return point((b1 * c2 - b2 * c1) / d,(c1 * a2 - c2 * a1) / d);   }void cut(point a,point b){    int cnt=0;    memset(tmp,0,sizeof(tmp));    for (int i=0;i<m;i++){        double c=cross(b-a,p[i]-a);        double d=cross(b-a,p[(i+1)%m]-a);        if (dcmp(c)>=0)           tmp[cnt++]=p[i];        if (dcmp(c)*dcmp(d)<0)          tmp[cnt++]=glt(a,b,p[i],p[(i+1)%m]);    }    m=0;    for (int i=0;i<cnt;i++)      if (m==0 || (tmp[i].x!=p[m-1].x||tmp[i].y!=p[m-1].y))        p[m++]=tmp[i];}int main(){    scanf("%d",&n);    for (int i=1;i<=n;i++) scanf("%lf%lf%lf",&a[i],&b[i],&c[i]);    for (int i=1;i<=n;i++){        int k=0;        bool mark=true;        for (int j=1;j<=n;j++){            if (i==j) continue;            double nowa=1.0/a[j]-1.0/a[i];            double nowb=1.0/b[j]-1.0/b[i];            double nowc=1.0/c[j]-1.0/c[i];            if (dcmp(nowa)==0&&dcmp(nowb)==0) {                if (dcmp(nowc)>0) continue;                else {                    mark=false;                    break;                }            }            k++;            if (dcmp(nowb)==0) {                double t=-nowc/nowa;                line[k].a.x=t; line[k].b.x=t;                line[k].a.y=1; line[k].b.y=2;                if (dcmp(nowa)>0) swap(line[k].a,line[k].b);                continue;            }            line[k].a.x=1;            line[k].a.y=-(nowa+nowc)/nowb;            line[k].b.x=2;            line[k].b.y=-(nowa*2.0+nowc)/nowb;            if (dcmp(nowb)<0) swap(line[k].a,line[k].b);        }        if (!mark){            PRintf("No/n");            continue;        }        init();        for (int  j=1;j<=k;j++)         cut(line[j].a,line[j].b);        double area=0; p[m]=p[0];        for (int j=1;j<m;j++) area+=cross(p[j]-p[0],p[j+1]-p[0]);        area=fabs(area);        if (m>2&&dcmp(area)>0) printf("Yes/n");        else printf("No/n");    }}