poj 3335 /poj 3130/ poj 1474 半平面交 判断核是否存在 / poj1279 半平面交 求核的面积

  1 /***************
  2 poj 3335  点序顺时针
  3 ***************/
  4 #include <iostream>
  5 #include <cmath>
  6 #include <algorithm>
  7 using namespace std;
  8 const double eps = 1e-8;
  9 const double maxn = 0x7f7f7f7f;
 10 int dcmp(double x){
 11     if(fabs(x)<eps)
 12         return 0;
 13     else
 14         return x<0?-1:1;
 15 }
 16 struct point {
 17     double x,y;
 18     point (double x=0,double y =0):x(x),y(y){}
 19 };
 20 point p[150];
 21 typedef point Vector;
 22 
 23 struct polygon{
 24     point p[150];
 25     int Size;
 26 };
 27 
 28 struct line{
 29     point fir,sec;
 30     line(point a = point(),point b = point()){
 31         fir = a;
 32         sec = b;
 33     }
 34 };
 35 
 36 Vector operator -(point a,point b){
 37     return Vector(a.x-b.x,a.y-b.y);
 38 }
 39 
 40 Vector operator *(Vector a,double p){
 41     return Vector (a.x*p,a.y*p);
 42 }
 43 Vector operator + (Vector a,Vector b){
 44     return Vector (a.x+b.x,a.y+b.y);
 45 }
 46 
 47 double cross(Vector a,Vector b){
 48     return a.x*b.y-a.y*b.x;
 49 }
 50 
 51 double dot(Vector a,Vector b){
 52     return a.x*b.x+a.y*b.y;
 53 }
 54 
 55 point getLineIntersection(point p,Vector v,point q,Vector w){
 56     Vector u = p-q;
 57     double t = cross(w,u)/cross(v,w);
 58     return p+v*t;
 59 }
 60 
 61 bool onsegment(point p,point a1,point a2){
 62     return dcmp(cross(a1-p,a2-p))==0&&dcmp(dot(a1-p,a2-p))<0;
 63 }
 64 
 65 polygon cutploygon(polygon poly,line ln){
 66     polygon newploy;
 67     int m=0;
 68     int n = poly.Size;
 69     point a = ln.fir,b = ln.sec;
 70     for(int i=0;i<n;i++){
 71         point c = poly.p[i];
 72         point d = poly.p[(i+1)%n];
 73         double cc = cross(b-a,c-a);
 74         double dd = cross(b-a,d-a);
 75         if(cc>=0)
 76             newploy.p[m++] = c;
 77         if(cc*dd<0)
 78             newploy.p[m++] = getLineIntersection(a,b-a,c,d-c);
 79     }
 80     newploy.Size = m;
 81     return newploy;
 82 }
 83 
 84 int main()
 85 {
 86     int t;
 87     cin>>t;
 88     int n;
 89     while(t--){
 90         cin>>n;
 91         for(int i=0;i<n;i++)
 92             cin>>p[i].x>>p[i].y;
 93         polygon poly;
 94         poly.Size = 4;
 95         poly.p[0].x = -maxn;
 96         poly.p[0].y = -maxn;
 97         poly.p[1].x = maxn;
 98         poly.p[1].y = -maxn;
 99         poly.p[2].x = maxn;
100         poly.p[2].y = maxn;
101         poly.p[3].x = -maxn;
102         poly.p[3].y = maxn;
103         bool flag = true;
104         for(int i=1;i<=n;i++){
105             line ln;
106             ln.fir = p[i%n];
107             ln.sec = p[i-1];
108             poly = cutploygon(poly,ln);
109             if(poly.Size==0){
110                 flag = false;
111                 break;
112             }
113         }
114         if(!flag)
115             cout<<"NO"<<endl;
116         else
117             cout<<"YES"<<endl;
118     }
119     return 0;
120 }
121 
122 /****************************************/
123 poj 3130  点序逆时针
124 /****************************************/
125 
126 #include <iostream>
127 #include <cmath>
128 #include <algorithm>
129 using namespace std;
130 const double eps = 1e-8;
131 const double maxn = 0x7f7f7f7f;
132 int dcmp(double x){
133     if(fabs(x)<eps)
134         return 0;
135     else
136         return x<0?-1:1;
137 }
138 struct point {
139     double x,y;
140     point (double x=0,double y =0):x(x),y(y){}
141 };
142 point p[150];
143 typedef point Vector;
144 
145 struct polygon{
146     point p[150];
147     int Size;
148 };
149 
150 struct line{
151     point fir,sec;
152     line(point a = point(),point b = point()){
153         fir = a;
154         sec = b;
155     }
156 };
157 
158 Vector operator -(point a,point b){
159     return Vector(a.x-b.x,a.y-b.y);
160 }
161 
162 Vector operator *(Vector a,double p){
163     return Vector (a.x*p,a.y*p);
164 }
165 Vector operator + (Vector a,Vector b){
166     return Vector (a.x+b.x,a.y+b.y);
167 }
168 
169 double cross(Vector a,Vector b){
170     return a.x*b.y-a.y*b.x;
171 }
172 
173 double dot(Vector a,Vector b){
174     return a.x*b.x+a.y*b.y;
175 }
176 
177 point getLineIntersection(point p,Vector v,point q,Vector w){
178     Vector u = p-q;
179     double t = cross(w,u)/cross(v,w);
180     return p+v*t;
181 }
182 
183 bool onsegment(point p,point a1,point a2){
184     return dcmp(cross(a1-p,a2-p))==0&&dcmp(dot(a1-p,a2-p))<0;
185 }
186 
187 polygon cutploygon(polygon poly,line ln){
188     polygon newploy;
189     int m=0;
190     int n = poly.Size;
191     point a = ln.fir,b = ln.sec;
192     for(int i=0;i<n;i++){
193         point c = poly.p[i];
194         point d = poly.p[(i+1)%n];
195         double cc = cross(b-a,c-a);
196         double dd = cross(b-a,d-a);
197         if(cc>=0)
198             newploy.p[m++] = c;
199         if(cc*dd<0)
200             newploy.p[m++] = getLineIntersection(a,b-a,c,d-c);
201     }
202     newploy.Size = m;
203     return newploy;
204 }
205 
206 int main()
207 {
208     int n;
209     while(cin>>n&&n){
210         for(int i=0;i<n;i++)
211             cin>>p[i].x>>p[i].y;
212         polygon poly;
213         poly.Size = 4;
214         poly.p[0].x = -maxn;
215         poly.p[0].y = -maxn;
216         poly.p[1].x = maxn;
217         poly.p[1].y = -maxn;
218         poly.p[2].x = maxn;
219         poly.p[2].y = maxn;
220         poly.p[3].x = -maxn;
221         poly.p[3].y = maxn;
222         bool flag = true;
223         for(int i=0;i<n;i++){
224             line ln;
225             ln.fir = p[i%n];
226             ln.sec = p[(i+1)%n];
227             poly = cutploygon(poly,ln);
228             if(poly.Size==0){
229                 flag = false;
230                 break;
231             }
232         }
233         if(!flag)
234             cout<<"0"<<endl;
235         else
236             cout<<"1"<<endl;
237     }
238     return 0;
239 }
240 
241 
242 /*************************************/
243 poj  1474  点序顺时针
244 /*************************************/
245 #include <iostream>
246 #include <cmath>
247 #include <algorithm>
248 using namespace std;
249 const double eps = 1e-8;
250 const double maxn = 0x7f7f7f7f;
251 int dcmp(double x){
252     if(fabs(x)<eps)
253         return 0;
254     else
255         return x<0?-1:1;
256 }
257 struct point {
258     double x,y;
259     point (double x=0,double y =0):x(x),y(y){}
260 };
261 point p[150];
262 typedef point Vector;
263 
264 struct polygon{
265     point p[150];
266     int Size;
267 };
268 
269 struct line{
270     point fir,sec;
271     line(point a = point(),point b = point()){
272         fir = a;
273         sec = b;
274     }
275 };
276 
277 Vector operator -(point a,point b){
278     return Vector(a.x-b.x,a.y-b.y);
279 }
280 
281 Vector operator *(Vector a,double p){
282     return Vector (a.x*p,a.y*p);
283 }
284 Vector operator + (Vector a,Vector b){
285     return Vector (a.x+b.x,a.y+b.y);
286 }
287 
288 double cross(Vector a,Vector b){
289     return a.x*b.y-a.y*b.x;
290 }
291 
292 double dot(Vector a,Vector b){
293     return a.x*b.x+a.y*b.y;
294 }
295 
296 point getLineIntersection(point p,Vector v,point q,Vector w){
297     Vector u = p-q;
298     double t = cross(w,u)/cross(v,w);
299     return p+v*t;
300 }
301 
302 bool onsegment(point p,point a1,point a2){
303     return dcmp(cross(a1-p,a2-p))==0&&dcmp(dot(a1-p,a2-p))<0;
304 }
305 
306 polygon cutploygon(polygon poly,line ln){
307     polygon newploy;
308     int m=0;
309     int n = poly.Size;
310     point a = ln.fir,b = ln.sec;
311     for(int i=0;i<n;i++){
312         point c = poly.p[i];
313         point d = poly.p[(i+1)%n];
314         double cc = cross(b-a,c-a);
315         double dd = cross(b-a,d-a);
316         if(cc>=0)
317             newploy.p[m++] = c;
318         if(cc*dd<0)
319             newploy.p[m++] = getLineIntersection(a,b-a,c,d-c);
320     }
321     newploy.Size = m;
322     return newploy;
323 }
324 
325 int main()
326 {
327     int n;
328     int cnt =1;
329     while(cin>>n&&n){
330         for(int i=0;i<n;i++)
331             cin>>p[i].x>>p[i].y;
332         polygon poly;
333         poly.Size = 4;
334         poly.p[0].x = -maxn;
335         poly.p[0].y = -maxn;
336         poly.p[1].x = maxn;
337         poly.p[1].y = -maxn;
338         poly.p[2].x = maxn;
339         poly.p[2].y = maxn;
340         poly.p[3].x = -maxn;
341         poly.p[3].y = maxn;
342         bool flag = true;
343         for(int i=1;i<=n;i++){
344             line ln;
345             ln.fir = p[i%n];
346             ln.sec = p[i-1];
347             poly = cutploygon(poly,ln);
348             if(poly.Size==0){
349                 flag = false;
350                 break;
351             }
352         }
353         //cout<<poly.Size<<endl;
354         cout<<"Floor #"<<cnt++<<endl;
355         if(!flag)
356             cout<<"Surveillance is impossible."<<endl;
357         else
358             cout<<"Surveillance is possible."<<endl;
359         cout<<endl;
360     }
361     return 0;
362 }
363 
364 
365 /**********************************
366 poj 1279  点序顺时针
367 **********************************/
368 #include <iostream>
369 #include <cmath>
370 #include <algorithm>
371 #include <cstdio>
372 using namespace std;
373 const double eps = 1e-8;
374 const double maxn = 0x7f7f7f7f;
375 int dcmp(double x){
376     if(fabs(x)<eps)
377         return 0;
378     else
379         return x<0?-1:1;
380 }
381 struct point {
382     double x,y;
383     point (double x=0,double y =0):x(x),y(y){}
384 };
385 point p[2000];
386 typedef point Vector;
387 
388 struct polygon{
389     point p[2000];
390     int Size;
391 };
392 
393 struct line{
394     point fir,sec;
395     line(point a = point(),point b = point()){
396         fir = a;
397         sec = b;
398     }
399 };
400 
401 Vector operator -(point a,point b){
402     return Vector(a.x-b.x,a.y-b.y);
403 }
404 
405 Vector operator *(Vector a,double p){
406     return Vector (a.x*p,a.y*p);
407 }
408 Vector operator + (Vector a,Vector b){
409     return Vector (a.x+b.x,a.y+b.y);
410 }
411 
412 double cross(Vector a,Vector b){
413     return a.x*b.y-a.y*b.x;
414 }
415 
416 double dot(Vector a,Vector b){
417     return a.x*b.x+a.y*b.y;
418 }
419 
420 point getLineIntersection(point p,Vector v,point q,Vector w){
421     Vector u = p-q;
422     double t = cross(w,u)/cross(v,w);
423     return p+v*t;
424 }
425 
426 bool onsegment(point p,point a1,point a2){
427     return dcmp(cross(a1-p,a2-p))==0&&dcmp(dot(a1-p,a2-p))<0;
428 }
429 
430 polygon cutploygon(polygon poly,line ln){
431     polygon newploy;
432     int m=0;
433     int n = poly.Size;
434     point a = ln.fir,b = ln.sec;
435     for(int i=0;i<n;i++){
436         point c = poly.p[i];
437         point d = poly.p[(i+1)%n];
438         double cc = cross(b-a,c-a);
439         double dd = cross(b-a,d-a);
440         if(cc>=0)
441             newploy.p[m++] = c;
442         if(cc*dd<0)
443             newploy.p[m++] = getLineIntersection(a,b-a,c,d-c);
444     }
445     newploy.Size = m;
446     return newploy;
447 }
448 
449 double polyArea(point *p,int n){
450     double area =0;
451     for(int i=1;i<n-1;i++){
452         area += cross(p[i]-p[0],p[i+1]-p[0]);
453     }
454     return area/2;
455 }
456 
457 int main()
458 {
459     int t;
460     cin>>t;
461     int n;
462     while(t--){
463         cin>>n;
464         for(int i=0;i<n;i++)
465             cin>>p[i].x>>p[i].y;
466         polygon poly;
467         poly.Size = 4;
468         poly.p[0].x = -maxn;
469         poly.p[0].y = -maxn;
470         poly.p[1].x = maxn;
471         poly.p[1].y = -maxn;
472         poly.p[2].x = maxn;
473         poly.p[2].y = maxn;
474         poly.p[3].x = -maxn;
475         poly.p[3].y = maxn;
476         bool flag = true;
477         for(int i=1;i<=n;i++){
478             line ln;
479             ln.fir = p[i%n];
480             ln.sec = p[i-1];
481             poly = cutploygon(poly,ln);
482             if(poly.Size==0){
483                 flag = false;
484                 break;
485             }
486         }
487         double res;
488         if(!flag)
489             res =0;
490         else{
491             res = polyArea(poly.p,poly.Size);
492         }
493         printf("%.2lf\n",res);
494     }
495     return 0;
496 }