uva191 Intersection

Intersection

Time Limit:3000MS     Memory Limit:0KB     64bit IO Format:%lld & %llu

Submit Status

Description

 Intersection 

You are to write a program that has to decide whether a given line segment intersects a given rectangle.

An example:

 line:  start point:  (4,9)
 end point: (11,2) 
 rectangle: left-top: (1,5) 
 right-bottom: (7,1) 

 
Figure: Line segment does not intersect rectangle

The line is said to intersect the rectangle if the line and the rectangle have at least one point in common. The rectangle consists of four straight lines and the area in between. Although all input values are integer numbers, valid intersection points do not have to lay on the integer grid.

Input

The input consists of n test cases. The first line of the input file contains the number n. Each following line contains one test case of the format:

where (xstart, ystart) is the start and (xend, yend) the end point of the line and (xleft, ytop) the top left and (xright, ybottom) the bottom right corner of the rectangle. The eight numbers are separated by a blank. The terms  and  do not imply any ordering of coordinates.

Output

For each test case in the input file, the output file should contain a line consisting either of the letter "T" if the line segment intersects the rectangle or the letter "F" if the line segment does not intersect the rectangle.

Sample Input

14 9 11 2 1 5 7 1

Sample Output

F

坑点在于，尼玛右上角不是右上角，左下角不是左下角，QNMLGB

#define DeBUG#include <iostream>#include <cstdio>#include <cstring>#include <cmath>#include <cstdlib>#include <algorithm>#include <vector>#include <stack>#include <queue>#include <string>#include <set>#include <sstream>#include <map>#include <bitset>using namespace std ;#define zero {0}#define INF 0x3f3f3f3f#define EPS 1e-9typedef long long LL;const double PI = acos(-1.0);//#pragma comment(linker, "/STACK:102400000,102400000")inline int sgn(double x){    return fabs(x) < EPS ? 0 : (x < 0 ? -1 : 1);}#define N 100005struct Point{    double x, y;    Point () {}    Point(double a, double b)    {        x = a;        y = b;    }};typedef Point Vec;Vec operator - (Vec a, Vec b)//点减法{    return Vec(a.x - b.x, a.y - b.y);}bool operator == (Point a, Point b)//点相等判断{    return sgn(a.x - b.x) == 0 && sgn(a.y - b.y) == 0;}inline double crossDet(Vec a, Vec b)//叉乘{    return a.x * b.y - a.y * b.x;}inline double dotDet(Vec a, Vec b)//点乘{    return a.x * b.x + a.y * b.y;}inline bool onSeg(Point x, Point a, Point b)//判断点在线段ab上,加上||x==a||x==b在端点也算{    return sgn(crossDet(a - x, b - x)) == 0 && sgn(dotDet(a - x, b - x)) < 0 || x == a || x == b;}// 0 : not intersect// 1 : proper intersect// 2 : improper intersectint segIntersect(Point a, Point c, Point b, Point d){    Vec v1 = b - a, v2 = c - b, v3 = d - c, v4 = a - d;    int a_bc = sgn(crossDet(v1, v2));    int b_cd = sgn(crossDet(v2, v3));    int c_da = sgn(crossDet(v3, v4));    int d_ab = sgn(crossDet(v4, v1));    if (a_bc * c_da > 0 && b_cd * d_ab > 0) return 1;    if (onSeg(b, a, c) && c_da) return 2;    if (onSeg(c, b, d) && d_ab) return 2;    if (onSeg(d, c, a) && a_bc) return 2;    if (onSeg(a, d, b) && b_cd) return 2;    return 0;}bool inrec(Point a, Point tl, Point br){    if (a.x >= tl.x && a.x <= br.x && a.y <= tl.y && a.y >= br.y)        return true;    return false;}int main(){#ifdef DeBUGs    freopen("C:\\Users\\Sky\\Desktop\\1.in", "r", stdin);#endif    int T;    scanf("%d", &T);    while (T--)    {        Point topleft;        Point bottomright;        Point start, end;        scanf("%lf%lf%lf%lf%lf%lf%lf%lf", &start.x, &start.y, &end.x, &end.y, &topleft.x, &topleft.y, &bottomright.x, &bottomright.y);        if(topleft.x>bottomright.x)            swap(topleft.x,bottomright.x);        if(topleft.y<bottomright.y)            swap(topleft.y,bottomright.y);        Point p[5];        p[0].x = topleft.x;        p[0].y = topleft.y;        p[1].x = bottomright.x;        p[1].y = topleft.y;        p[2].x = bottomright.x;        p[2].y = bottomright.y;        p[3].x = topleft.x;        p[3].y = bottomright.y;        p[4] = p[0];        bool flag = false;        for (int i = 0; i < 4; i++)        {            if (segIntersect(p[i], p[i + 1], start, end) != 0)            {                flag = true;            }        }        if (inrec(start, topleft, bottomright) || inrec(end, topleft, bottomright))            flag = true;        if (flag)            printf("T\n");        else            printf("F\n");    }    return 0;}