1 /*
2 * 题目要求：判断线段是否跟矩形相交
3 * 注意：线段完全在矩形内也是相交
4 * 解法：分别判断线段是否跟矩形的四条边相交，再判断线段的两个端点是否都在矩形内
5 */
6
7 #include <cstdio>
8 #include <cstdlib>
9 #include <iostream>
10
11 using namespace std;
12
13 struct point {
14 double x;
15 double y;
16 }A, B, C, D, E, F;
17
18 double crossProd(point A, point B, point C) {
19 return (B.x-A.x)*(C.y-A.y) - (B.y-A.y)*(C.x-A.x);
20 }
21
22 bool segIntersect(point A, point B, point C, point D) {//判断线段是否相交
23 if (max(A.x, B.x) >= min(C.x, D.x) &&
24 max(C.x, D.x) >= min(A.x, B.x) &&
25 max(A.y, B.y) >= min(C.y, D.y) &&
26 max(C.y, D.y) >= min(A.y, B.y) &&
27 crossProd(C, D, A)*crossProd(C, B, D)>=0 &&
28 crossProd(A, B, C)*crossProd(A, D, B)>=0) return true;
29 return false;
30 }
31
32 bool pointInRectangle(point S, point A, point B) {//判断点是否在矩形内
33 if (max(A.x, B.x) >= S.x &&
34 min(A.x, B.x) <= S.x &&
35 max(A.y, B.y) >= S.y &&
36 min(A.y, B.y) <= S.y) return true;
37 return false;
38 }
39
40 bool segXRectangle() {
41 if (segIntersect(A, B, C, E)) return true;//判断线段是否跟矩形的边相交
42 else if (segIntersect(A, B, C, F)) return true;
43 else if (segIntersect(A, B, D, E)) return true;
44 else if (segIntersect(A, B, D, F)) return true;
45 if (pointInRectangle(A, C, D) && pointInRectangle(B, C, D)) return true;//判断线段的两端点是否都在矩形内
46 return false;
47 }
48
49 int main() {
50 int t;
51 scanf ("%d", &t);
52 while (t--) {
53 scanf ("%lf%lf%lf%lf%lf%lf%lf%lf", &A.x, &A.y, &B.x, &B.y, &C.x, &C.y, &D.x, &D.y);
54 E.x = C.x;
55 E.y = D.y;
56 F.x = D.x;
57 F.y = C.y;
58 bool yes = segXRectangle();
59 if (yes) printf ("T\n");
60 else printf ("F\n");
61 }
62 return 0;
63 }
