poj 2540 Hotter Colder 半平面交 不等式求区域面积
在一个区间内寻找某一个点，每次走法会提示距目标是更近、更远还是相同。每次可确定一个目标必在的区域，求这个区域的面积。
假定寻找者从A点走到B点，做线段AB的中垂线，取距目标近的那一半。用半平面交即可求该区域。
注意Same时区域面积为0；
若有出现面积为0，则之后的都是0；
1 #include <cmath> 2 #include <vector> 3 #include <cstdio> 4 #include <cstdlib> 5 #include <cstring> 6 #include <algorithm> 7 const double eps = 1e-10; 8 int sz; 9 double flag; 10 struct point 11 { 12 double x,y; 13 }p[60],q[60]; 14 void init() 15 { 16 sz = 4; 17 p[1].x=p[1].y=0; 18 p[2].x=10, p[2].y=0; 19 p[3].x=p[3].y=10; 20 p[4].x=0, p[4].y=10; 21 p[0]=p[4], p[5]=p[1]; 22 } 23 24 int dcmp(double x) 25 { 26 if (x < -eps) 27 return -1; 28 else 29 return (x > eps); 30 } 31 point intersect(const point &p1, const point &p2, double a, double b, double c) 32 { 33 point g; 34 double u = fabs(a * p1. x + b * p1. y + c); 35 double v = fabs(a * p2. x + b * p2. y + c); 36 g.x=(p1.x*v + p2.x*u)/(u+v),g.y=(p1.y*v+p2.y*u)/(u+v); 37 return g; 38 } 39 void cut(double a, double b, double c) 40 { 41 int s = 0,i; 42 for ( i = 1; i <= sz; i++) 43 { 44 if (dcmp((a * p[i]. x + b * p[i]. y + c)*flag) >=0) 45 q[++s] = p[i]; 46 else 47 { 48 if (dcmp((a * p[i - 1]. x + b * p[i - 1]. y + c)*flag) > 0) 49 q[++s] = intersect(p[i-1], p[i], a, b, c); 50 if (dcmp((a * p[i + 1]. x + b * p[i + 1]. y + c)*flag) > 0) 51 q[++s] = intersect(p[i], p[i+1], a, b, c); 52 } 53 } 54 for ( i = 1; i <= s; i++) 55 p[i] = q[i]; 56 p[s+1] = p[1]; 57 p[0] = p[s]; 58 sz = s; 59 } 60 void solve(point p0,point t1,point t2) 61 { 62 double a,b,c; 63 a=t2.y-t1.y; 64 b=t1.x-t2.x; 65 c=t2.x*t1.y-t2.y*t1.x; 66 flag=a*p0.x+b*p0.y+c; 67 cut(a,b,c); 68 } 69 int main() 70 { 71 int i,c=1; 72 char s[20]; 73 double area; 74 point p1,p2,t1,t2; 75 p1.x=0;p1.y=0; 76 init(); 77 while(scanf("%lf%lf%s",&p2.x,&p2.y,s)!=EOF) 78 { 79 t1.x=(p1.x+p2.x)/2; 80 t1.y=(p1.y+p2.y)/2; 81 t2.x=t1.x+p1.y-p2.y; 82 t2.y=t1.y+p2.x-p1.x; 83 area=0; 84 if(strcmp("Same",s)==0||!c) 85 { 86 printf("0.00\n"); 87 c=0; 88 continue; 89 } 90 if(strcmp("Colder",s)==0) 91 solve(p1,t1,t2); 92 else if(strcmp("Hotter",s)==0) 93 solve(p2,t1,t2); 94 for(i=1;i<=sz;i++) 95 area+=p[i].x*p[i+1].y-p[i].y*p[i+1].x; 96 printf("%.2f\n",fabs(area)/2); 97 if(fabs(area)/2<eps) 98 c=0; 99 p1=p2; 100 } 101 return 0; 102 }
