poj 2540 Hotter Colder 半平面交 不等式求区域面积

http://poj.org/problem?id=2540

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 }