线段和矩形相交 POJ 1410

// 线段和矩形相交 POJ 1410

// #include <bits/stdc++.h>
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <vector>
#include <math.h>
using namespace std;
#define LL long long
typedef pair<int,int> pii;
const int inf = 0x3f3f3f3f;
const LL MOD =100000000LL;
const int N =110;
#define clc(a,b) memset(a,b,sizeof(a))
const double eps = 1e-8;
void fre() {freopen("in.txt","r",stdin);}
void freout() {freopen("out.txt","w",stdout);}
inline int read() {int x=0,f=1;char ch=getchar();while(ch>'9'||ch<'0') {if(ch=='-') f=-1; ch=getchar();}while(ch>='0'&&ch<='9') {x=x*10+ch-'0';ch=getchar();}return x*f;}

int sgn(double x){
    if(fabs(x) < eps)return 0;
    if(x < 0)return -1;
    else return 1;
}
struct Point{
    double x,y;
    Point(){}
    Point(double _x,double _y){
        x = _x;y = _y;
    }
    Point operator -(const Point &b)const{
        return Point(x - b.x,y - b.y);
    }
    double operator ^(const Point &b)const{
        return x*b.y - y*b.x;
    }
    double operator *(const Point &b)const{
        return x*b.x + y*b.y;
    }
};

struct Line{
    Point s,e;
    int inx;
    Line(){}
    Line(Point _s,Point _e){
        s=_s;e=_e;
    }
};

// Line line[N];
bool inter(Line l1,Line l2){
    return 
        max(l1.s.x,l1.e.x) >= min(l2.s.x,l2.e.x) &&
        max(l2.s.x,l2.e.x) >= min(l1.s.x,l1.e.x) &&
        max(l1.s.y,l1.e.y) >= min(l2.s.y,l2.e.y) &&
        max(l2.s.y,l2.e.y) >= min(l1.s.y,l1.e.y) &&
        sgn((l2.s-l1.s)^(l1.e-l1.s))*sgn((l2.e-l1.s)^(l1.e-l1.s)) <= 0 &&
        sgn((l1.s-l2.s)^(l2.e-l2.s))*sgn((l1.e-l2.s)^(l2.e-l2.s)) <= 0;
}
bool OnSeg(Point P,Line L){
    return
    sgn((L.s-P)^(L.e-P))==0&&
    sgn((P.x-L.s.x)*(P.x-L.e.x))<=0&&
    sgn((P.y-L.s.y)*(P.y-L.e.y))<=0;
}

int inConvexPoly(Point a,Point p[],int n){
    for(int i=0;i<n;i++){
        if(sgn((p[i]-a)^(p[(i+1)%n]-a))<0) return -1;
        else if (OnSeg(a,Line(p[i],p[(i+1)%n]))) return 0;
    }
    return 1;
}

Point p[4];
int main(){
    int T;
    scanf("%d",&T);
    while(T--){
        double x1,y1,x2,y2;
        scanf("%lf%lf%lf%lf",&x1,&y1,&x2,&y2);
        Line line=Line(Point(x1,y1),Point(x2,y2));
        scanf("%lf%lf%lf%lf",&x1,&y1,&x2,&y2);
        if(x1>x2) swap(x1,x2);
        if(y1>y2) swap(y1,y2);
        p[0]=Point(x1,y1);
        p[1]=Point(x2,y1);
        p[2]=Point(x2,y2);
        p[3]=Point(x1,y2);
        if(inter(Line(p[0],p[1]),line)){
            printf("T
");
            continue;
        }
        if(inter(Line(p[1],p[2]),line)){
            printf("T
");
            continue;
        }
        if(inter(Line(p[2],p[3]),line)){
            printf("T
");
            continue;
        }
        if(inter(Line(p[3],p[0]),line)){
            printf("T
");
            continue;
        }
        if(inConvexPoly(line.s,p,4)>=0||inConvexPoly(line.e,p,4)>=0){
            printf("T
");
            continue;
        }
        else 
            printf("F
");
    }
    return 0;
}