1 /*
2 fzu_1120
3 判断点q是否在多边形内的一种方法，过q作水平射线L，
4 如果L与多边形P的边界不相交，则q在P的外部。否则，
5 L和P的边界相交，具体地说，交点个数为奇（偶）数
6 时，点q在P的内（外）部。 */
7
8 #include <stdio.h>
9 #include <stdlib.h>
10 #include <math.h>
11
12 #define MaxNode 50
13 #define INF 999999999
14
15 typedef struct TPoint
16 {
17 double x;
18 double y;
19 }TPoiont;
20
21 typedef struct TSegment
22 {
23
24 TPoint p1;
25 TPoint p2;
26 }TSegment;
27
28 typedef struct TPolygon
29 {
30 TPoint point[MaxNode];
31 int n;
32 }TPolygon;
33
34 double multi(TPoint p1, TPoint p2, TPoint p0)
35 {
36 //求矢量[p0, p1], [p0, p2]的叉积
37 //p0是顶点
38 return (p1.x - p0.x) * (p2.y - p0.y) - (p2.x - p0.x) * (p1.y - p0.y);
39 //若结果等于0，则这三点共线
40 //若结果大于0，则p0p2在p0p1的逆时针方向
41 //若结果小于0，则p0p2在p0p1的顺时针方向
42 }
43
44 double max(double x, double y)
45 {
46 //比较两个数的大小，返回大的数
47 if(x > y) return x;
48 else return y;
49 }
50
51 double min(double x, double y)
52 {
53 //比较两个数的大小，返回小的数
54 if(x < y) return x;
55 else return y;
56 }
57
58 bool Intersect(TSegment L1, TSegment L2)
59 {
60 //线段l1与l2相交而且不在端点上时，返回true
61 //判断线段是否相交
62 //1.快速排斥试验判断以两条线段为对角线的两个矩形是否相交
63 TPoint s1 = L1.p1;
64 TPoint e1 = L1.p2;
65 TPoint s2 = L2.p1;
66 TPoint e2 = L2.p2;
67 //2.跨立试验
68 if(
69 (max(s1.x, e1.x) > min(s2.x, e2.x)) &&
70 (max(s2.x, e2.x) > min(s1.x, e1.x)) &&
71 (max(s1.y, e1.y) > min(s2.y, e2.y)) &&
72 (max(s2.y, e2.y) > min(s1.y, e1.y)) &&
73 (multi(s2, e1, s1) * multi(e1, e2, s1) > 0) &&
74 (multi(s1, e2, s2) * multi(e2, e1, s2) > 0)
75 ) return true;
76
77 return false;
78 }
79
80
81 bool Online(TSegment L, TPoint p)
82 {
83 //p在L上(不在端点)时返回true
84 //1.在L所在的直线上
85 //2.在L为对角线的矩形中
86 double dx, dy, dx1, dy1;
87 dx = L.p2.x - L.p1.x;
88 dy = L.p2.y - L.p1.y;
89 dx1 = p.x - L.p1.x;
90 dy1 = p.y - L.p1.y;
91 if(dx * dy1 - dy * dx1 != 0) return false; //叉积
92 if(dx1 * (dx1 - dx) < 0 || dy1 * (dy1 - dy) < 0) return true;
93 return false;
94 }
95
96 bool same1(TSegment L, TPoint p1, TPoint p2)
97 {
98 //判断p1, p2是否在L的同侧
99 if(multi(p1, L.p2, L.p1) * multi(L.p2, p2, L.p1)< 0) return true;
100 return false;
101 }
102
103 bool Inside(TPoint q, TPolygon polygon)
104 {
105 int c, i;
106 TSegment L1, L2;
107 c = 0;
108 L1.p1 = q;
109 L1.p2 = q;
110 L1.p2.x = INF;
111 /*
112 （1）相交
113 1.p[i]和p[i+1]在L的两侧
114 2.p[i]和p[i+2]在L的同侧
115 3.p[u]和p[i+3]在L的同侧或异侧
116 */
117 for(i = 0;i <= polygon.n - 1;i++){
118 L2.p1 = polygon.point[i];
119 L2.p2 = polygon.point[(i + 1) % polygon.n];
120 if(Intersect(L1, L2)){
121 c++;
122 continue;
123 }
124 if(!Online(L1, polygon.point[(i + 1) % polygon.n])) continue;
125 if(!Online(L1, polygon.point[(i + 2) % polygon.n]) &&
126 !same1(L1, polygon.point[i], polygon.point[(i + 2) % polygon.n])){
127 c++;
128 continue;
129 }
130 if(Online(L1, polygon.point[(i + 2) % polygon.n]) &&
131 !same1(L1, polygon.point[i], polygon.point[(i + 3) % polygon.n]))
132 c++;
133 }
134 if(c % 2 == 0) return false;
135 else return true;
136 }
137
138 int main()
139 {
140 int i, test, k;
141 int primp, primq;
142 TPoint p;
143 p.x = 0;
144 p.y = 0;
145 test = 1;
146 TPolygon polygon;
147 while(scanf("%d", &polygon.n) != EOF && polygon.n){
148 printf("Pilot %d\n", test++);
149 for(i = 0;i <= polygon.n - 1;i++){
150 scanf("%lf%lf", &polygon.point[i].x, &polygon.point[i].y);
151 }
152 scanf("%d%d", &primp, &primq);
153 if(Inside(p, polygon)){
154 printf("The pilot is in danger!\n");
155 k = (primp - 1) * (primq - 1) / 2;
156 printf("The secret number is %d.\n", k);
157 }
158 else printf("The pilot is safe.\n");
159 printf("\n");
160 }
161 return 0;
162 }
