【半平面交】 POJ 1755 Triathlon

#include <iostream>
#include <queue>
#include <stack>
#include <map>
#include <set>
#include <bitset>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <climits>
#include <cstdlib>
#include <cmath>
#include <time.h>
#define maxn 50005
#define maxm 3000005
#define eps 1e-10
#define mod 998244353
#define INF 999999999
#define lowbit(x) (x&(-x))
#define mp mark_pair
#define ls o<<1
#define rs o<<1 | 1
#define lson o<<1, L, mid
#define rson o<<1 | 1, mid+1, R
#define debug(x) printf("AA x = %d BB\n", x);
//#pragma comment (linker,"/STACK:102400000,102400000")
typedef long long LL;
//typedef int LL;
using namespace std;
LL powmod(LL a, LL b){LL res=1,base=a;while(b){if(b%2)res=res*base%mod;base=base*base%mod;b/=2;}return res;}
void scanf(int &__x){__x=0;char __ch=getchar();while(__ch==' '||__ch=='\n')__ch=getchar();while(__ch>='0'&&__ch<='9')__x=__x*10+__ch-'0',__ch = getchar();}
// head

struct Point
{
double x, y;
Point(double x = 0, double y = 0) : x(x), y(y) { }
bool operator < (const Point &a) const {
return a.x < x || (a.x == x && a.y < y);
}
};
typedef Point Vector;
struct Line
{
Point P;
Vector v;
double ang;
Line() {}
Line(Point P, Vector v) : P(P), v(v) { ang = atan2(v.y, v.x); }
bool operator < (const Line &L) const {
return ang < L.ang;
}
};

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 p)
{
return Vector(A.x * p, A.y * p);
}
Vector operator / (Vector A, double p)
{
return Vector(A.x / p, A.y / p);
}
int dcmp(double x)
{
if(fabs(x) < eps) return 0;
else return x < 0 ? -1 : 1;
}
double Dot(Vector A, Vector B)
{
return A.x * B.x + A.y * B.y;
}
double Length(Vector A)
{
return sqrt(Dot(A, A));
}
double Angle(Vector A, Vector B)
{
return acos(Dot(A, B) / Length(A) / Length(B));
}
double Cross(Vector A, Vector B)
{
return A.x * B.y - A.y * B.x;
}
double Area2(Point A, Point B, Point C)
{
return Cross(B - A, C - A);
}
double PolyonArea(Point *p, int n)
{
double area = 0;
for(int i = 1; i < n-1; i++)
area += Cross(p[i] - p[0], p[i+1] - p[0]);
return area / 2;
}
Vector Rotate(Vector A, double rad)
{
return Vector(A.x * cos(rad) - A.y * sin(rad), A.x * sin(rad) + A.y * cos(rad));
}
Vector Normal(Vector A)
{
double L = Length(A);
return Vector(-A.y / L, A.x / L);
}

bool OnLeft(Line L, Point p)
{
return Cross(L.v, p - L.P) > 0;
}

Point GetIntersection(Line a, Line b)
{
Vector u = a.P - b.P;
double t = Cross(b.v, u) / Cross(a.v, b.v);
return a.P + a.v * t;
}
int ConvexHull(Point *p, int n, Point *ch)
{
sort(p, p+n);
int m = 0;
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--;
return m;
}
Point p[maxn];
Line q[maxn];
int HalfplaneInersection(Line* L, int n, Point* poly)
{
sort(L, L+n);
int first, last;
q[first = last = 0] = L[0];
for(int i = 1; i < n; i++) {
while(first < last && !OnLeft(L[i], p[last - 1])) last--;
while(first < last && !OnLeft(L[i], p[first])) first++;
q[++last] = L[i];
if(fabs(Cross(q[last].v, q[last-1].v)) < eps) {
last--;
if(OnLeft(q[last], L[i].P)) q[last] = L[i];
}
if(first < last) p[last-1] = GetIntersection(q[last-1], q[last]);
}
while(first < last && !OnLeft(q[first], p[last-1])) last--;
if(last - first <= 1) return 0;
p[last] = GetIntersection(q[last], q[first]);
int m = 0;
for(int i = first; i <= last; i++) poly[m++] = p[i];
return m;
}

struct node
{
int v, u, w;
}po[maxn];
Point poly[maxn], point, v;
Line line[maxn];
int n, cnt;
void read(void)
{
for(int i = 0; i < n; i++) scanf("%d%d%d", &po[i].v, &po[i].u, &po[i].w);
}
void work(void)
{
int ok;
double pp = 10000, A, B, C;
for(int i = 0; i < n; i++) {
cnt = ok = 0;
for(int j = 0; j < n; j++) {
if(i == j) continue;
if(po[i].v <= po[j].v && po[i].u <= po[j].u && po[i].w <= po[j].w) ok = 1;
if(po[i].v >= po[j].v && po[i].u >= po[j].u && po[i].w >= po[j].w) continue;
A = (pp / po[j].v - pp / po[j].w) - (pp / po[i].v - pp / po[i].w);
B = (pp / po[j].u - pp / po[j].w) - (pp / po[i].u - pp / po[i].w);
C = pp / po[j].w - pp / po[i].w;
v.x = B, v.y = -A;
if(fabs(A) < fabs(B)) point.x = 0, point.y = -C/B;
else point.x = -C/A, point.y = 0;
line[cnt++] = Line(point, v);
}
v.x = 0, v.y = -1, point.x = 0, point.y = 0;
line[cnt++] = Line(point, v);
v.x = 1, v.y = 0, point.x = 0, point.y = 0;
line[cnt++] = Line(point, v);
v.x = -1, v.y = 1, point.x = 0, point.y = 1;
line[cnt++] = Line(point, v);
int k = HalfplaneInersection(line, cnt, poly);
if(k && !ok) printf("Yes\n");
else printf("No\n");
}
}
int main(void)
{
while(scanf("%d", &n)!=EOF){
read();
work();
}
return 0;
}