poj 1265 Area (Pick定理+求面积)

  1 #include <stdio.h>
  2 #include <math.h>
  3 #include <string.h>
  4 #include <stdlib.h>
  5 #include <iostream>
  6 #include <algorithm>
  7 
  8 #define eps 1e-8
  9 #define MAXX 210
 10 using namespace std;
 11 
 12 typedef struct point
 13 {
 14     double x;
 15     double y;
 16 }point;
 17 typedef struct line
 18 {
 19     point st;
 20     point ed;
 21 }line;
 22 
 23 bool dy(double x,double y)
 24 {
 25     return x>y+eps;
 26 }
 27 bool xy(double x,double y)
 28 {
 29     return x<y-eps;
 30 }
 31 bool dyd(double x,double y)
 32 {
 33     return x>y-eps;
 34 }
 35 bool xyd(double x,double y)
 36 {
 37     return x<y+eps;
 38 }
 39 bool dd(double x,double y)
 40 {
 41     return fabs(x-y)<eps;
 42 }
 43 
 44 double crossProduct(point a,point b,point c)//ac -> ab
 45 {
 46     return (c.x-a.x)*(b.y-a.y)-(c.y-a.y)*(b.x-a.x);
 47 }
 48 double dist(point a,point b)
 49 {
 50     return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
 51 }
 52 
 53 bool onSegment_1(point a,point b,point c)
 54 {
 55     double maxx=max(a.x,b.x);
 56     double minx=min(a.x,b.x);
 57     double maxy=max(a.y,b.y);
 58     double miny=min(a.y,b.y);
 59 
 60     if(dd(crossProduct(a,b,c),0.0) && xyd(c.x,maxx) && dyd(c.x,minx)
 61        && xyd(c.y,maxy) && dyd(c.y,miny))
 62         return true;
 63     return false;
 64 }
 65 
 66 bool segIntersect_1(point p1,point p2,point p3,point p4)
 67 {
 68     double d1=crossProduct(p3,p4,p1);
 69     double d2=crossProduct(p3,p4,p2);
 70     double d3=crossProduct(p1,p2,p3);
 71     double d4=crossProduct(p1,p2,p4);
 72 
 73     if(xy(d1*d2,0.0) && xy(d3*d4,0.0))
 74         return true;
 75     if(dd(d1,0.0) && onSegment_1(p3,p4,p1))
 76         return true;
 77     if(dd(d2,0.0) && onSegment_1(p3,p4,p2))
 78         return true;
 79     if(dd(d3,0.0) && onSegment_1(p1,p2,p3))
 80         return true;
 81     if(dd(d4,0.0) && onSegment_1(p1,p2,p4))
 82         return true;
 83     return false;
 84 }
 85 
 86 point p[MAXX];
 87 line li[MAXX];
 88 int n;
 89 
 90 bool inPolygon_1(point pot)
 91 {
 92     int count=0;
 93     line l;
 94     l.st=pot;
 95     l.ed.x=1e10;
 96     l.ed.y=pot.y;
 97     p[n]=p[0];
 98     for(int i=0; i<n; i++)
 99     {
100         if( onSegment_1(p[i],p[i+1],pot ))
101             return true;
102         if(!dd(p[i].y,p[i+1].y))
103         {
104             int tmp=-1;
105             if(onSegment_1(l.st,l.ed,p[i]))
106                 tmp=i;
107             else if(onSegment_1(l.st,l.ed,p[i+1]))
108                 tmp=i+1;
109             if(tmp != -1 && dd(p[tmp].y,max(p[i].y,p[i+1].y)))
110                 count++;
111             else if(tmp == -1 && segIntersect_1(p[i],p[i+1],l.st,l.ed))
112                 count++;
113         }
114     }
115     if(count % 2 ==1)
116         return true;
117     return false;
118 }
119 
120 bool inPolygon_2(point pot)
121 {
122     int count=0;
123     line l;
124     l.st=pot;
125     l.ed.x=1e10;
126     l.ed.y=pot.y;
127     p[n]=p[0];
128     for(int i=0; i<n; i++)
129     {
130         if( onSegment_1(p[i],p[i+1],pot ))
131             return false;
132         if(!dd(p[i].y,p[i+1].y))
133         {
134             int tmp=-1;
135             if(onSegment_1(l.st,l.ed,p[i]))
136                 tmp=i;
137             else if(onSegment_1(l.st,l.ed,p[i+1]))
138                 tmp=i+1;
139             if(tmp != -1 && dd(p[tmp].y,max(p[i].y,p[i+1].y)))
140                 count++;
141                 else if(tmp == -1 && segIntersect_1(p[i],p[i+1],l.st,l.ed))
142                 count++;
143         }
144     }
145     if(count % 2 ==1)
146         return true;
147     return false;
148 }
149 
150 double Area(int n)
151 {
152     if(n<3)return 0;
153     int i;
154     double ret=0.0;
155     for(i=2; i<=n; i++)
156     {
157         ret+=(crossProduct(p[0],p[i-1],p[i]));
158     }
159     return fabs(ret)/2.0;
160 }
161 
162 int main()
163 {
164     int m,i,j;
165     int ttmp=1;
166     scanf("%d",&m);
167     while(m--)
168     {
169         scanf("%d",&n);
170         p[0].x=0;p[0].y=0;
171         double x,y;
172         double maxx=-100,maxy=-100,minx=100,miny=100;
173         for(i=1; i<=n; i++)
174         {
175             scanf("%lf%lf",&x,&y);
176             p[i].x=p[i-1].x+x;
177             p[i].y=p[i-1].y+y;//printf("%lf %lf^^",p[i].x,p[i].y);
178         }
179         for(i=0; i<=n; i++)
180         {
181             maxx=maxx>p[i].x?maxx:p[i].x;
182             maxy=maxy>p[i].y?maxy:p[i].y;
183             minx=minx<p[i].x?minx:p[i].x;
184             miny=miny<p[i].y?miny:p[i].y;
185         }//printf("%lf %lf^^%lf %lf**",minx,maxx,miny,maxy);
186         int in=0,edge=0,sum=0;
187         point cas;
188         for(i=minx; i<=maxx; i++)
189         {
190             for(j=miny; j<=maxy; j++)
191             {
192                 cas.x=i;cas.y=j;
193                 if(inPolygon_1(cas))
194                 {
195                     sum++;
196                 }
197                 if(inPolygon_2(cas))
198                 {
199                     in++;
200                 }
201             }
202         }
203         double area=Area(n);
204         edge=sum-in;
205         printf("Scenario #%d:\n",ttmp++);
206         printf("%d %d %.1lf\n",in,edge,area);
207     }
208     return 0;
209 }