poj1279 半平面交

题意：没看懂= =
sol：在纸上随便画两下就可以看出，答案即按逆时针方向建立line，求它们的半平面交的面积。
模板题。注意输出答案时输出ans+eps，否则可能会出现结果为-0.00的情况。
  1 #include<vector>
  2 #include<list>
  3 #include<map>
  4 #include<set>
  5 #include<deque>
  6 #include<queue>
  7 #include<stack>
  8 #include<bitset>
  9 #include<algorithm>
 10 #include<functional>
 11 #include<numeric>
 12 #include<utility>
 13 #include<iostream>
 14 #include<sstream>
 15 #include<iomanip>
 16 #include<cstdio>
 17 #include<cmath>
 18 #include<cstdlib>
 19 #include<cctype>
 20 #include<string>
 21 #include<cstring>
 22 #include<cstdio>
 23 #include<cmath>
 24 #include<cstdlib>
 25 #include<ctime>
 26 #include<climits>
 27 #include<complex>
 28 #define mp make_pair
 29 #define pb push_back
 30 using namespace std;
 31 const double eps=1e-6;
 32 const double pi=acos(-1.0);
 33 const double inf=1e20;
 34 const int maxp=1111;
 35 int dblcmp(double d)
 36 {
 37     if (fabs(d)<eps)return 0;
 38     return d>eps?1:-1;
 39 }
 40 inline double sqr(double x){return x*x;}
 41 struct point
 42 {
 43     double x,y;
 44     point(){}
 45     point(double _x,double _y):
 46     x(_x),y(_y){};
 47     void input()
 48     {
 49         scanf("%lf%lf",&x,&y);
 50     }
 51     void output()
 52     {
 53         printf("%.2f %.2f\n",x,y);
 54     }
 55     bool operator==(point a)const
 56     {
 57         return dblcmp(a.x-x)==0&&dblcmp(a.y-y)==0;
 58     }
 59     bool operator<(point a)const
 60     {
 61         return dblcmp(a.x-x)==0?dblcmp(y-a.y)<0:x<a.x;
 62     }
 63     double len()
 64     {
 65         return hypot(x,y);
 66     }
 67     double len2()
 68     {
 69         return x*x+y*y;
 70     }
 71     double distance(point p)
 72     {
 73         return hypot(x-p.x,y-p.y);
 74     }
 75     point add(point p)
 76     {
 77         return point(x+p.x,y+p.y);
 78     }
 79     point sub(point p)
 80     {
 81         return point(x-p.x,y-p.y);
 82     }
 83     point mul(double b)
 84     {
 85         return point(x*b,y*b);
 86     }
 87     point div(double b)
 88     {
 89         return point(x/b,y/b);
 90     }
 91     double dot(point p)
 92     {
 93         return x*p.x+y*p.y;
 94     }
 95     double det(point p)
 96     {
 97         return x*p.y-y*p.x;
 98     }
 99     double rad(point a,point b)
100     {
101         point p=*this;
102         return fabs(atan2(fabs(a.sub(p).det(b.sub(p))),a.sub(p).dot(b.sub(p))));
103     }
104     point trunc(double r)
105     {
106         double l=len();
107         if (!dblcmp(l))return *this;
108         r/=l;
109         return point(x*r,y*r);
110     }
111     point rotleft()
112     {
113         return point(-y,x);
114     }
115     point rotright()
116     {
117         return point(y,-x);
118     }
119     point rotate(point p,double angle)//绕点p逆时针旋转angle角度
120     {
121         point v=this->sub(p);
122         double c=cos(angle),s=sin(angle);
123         return point(p.x+v.x*c-v.y*s,p.y+v.x*s+v.y*c);
124     }
125 };
126 struct line
127 {
128     point a,b;
129     line(){}
130     line(point _a,point _b)
131     {
132         a=_a;
133         b=_b;
134     }
135     bool operator==(line v)
136     {
137         return (a==v.a)&&(b==v.b);
138     }
139     //倾斜角angle
140     line(point p,double angle)
141     {
142         a=p;
143         if (dblcmp(angle-pi/2)==0)
144         {
145             b=a.add(point(0,1));
146         }
147         else
148         {
149             b=a.add(point(1,tan(angle)));
150         }
151     }
152     //ax+by+c=0
153     line(double _a,double _b,double _c)
154     {
155         if (dblcmp(_a)==0)
156         {
157             a=point(0,-_c/_b);
158             b=point(1,-_c/_b);
159         }
160         else if (dblcmp(_b)==0)
161         {
162             a=point(-_c/_a,0);
163             b=point(-_c/_a,1);
164         }
165         else
166         {
167             a=point(0,-_c/_b);
168             b=point(1,(-_c-_a)/_b);
169         }
170     }
171     void input()
172     {
173         a.input();
174         b.input();
175     }
176     void adjust()
177     {
178         if (b<a)swap(a,b);
179     }
180     double length()
181     {
182         return a.distance(b);
183     }
184     double angle()//直线倾斜角 0<=angle<180
185     {
186         double k=atan2(b.y-a.y,b.x-a.x);
187         if (dblcmp(k)<0)k+=pi;
188         if (dblcmp(k-pi)==0)k-=pi;
189         return k;
190     }
191     //点和线段关系
192     //1 在逆时针
193     //2 在顺时针
194     //3 平行
195     int relation(point p)
196     {
197         int c=dblcmp(p.sub(a).det(b.sub(a)));
198         if (c<0)return 1;
199         if (c>0)return 2;
200         return 3;
201     }
202     bool pointonseg(point p)
203     {
204         return dblcmp(p.sub(a).det(b.sub(a)))==0&&dblcmp(p.sub(a).dot(p.sub(b)))<=0;
205     }
206     bool parallel(line v)
207     {
208         return dblcmp(b.sub(a).det(v.b.sub(v.a)))==0;
209     }
210     //2 规范相交
211     //1 非规范相交
212     //0 不相交
213     int segcrossseg(line v)
214     {
215         int d1=dblcmp(b.sub(a).det(v.a.sub(a)));
216         int d2=dblcmp(b.sub(a).det(v.b.sub(a)));
217         int d3=dblcmp(v.b.sub(v.a).det(a.sub(v.a)));
218         int d4=dblcmp(v.b.sub(v.a).det(b.sub(v.a)));
219         if ((d1^d2)==-2&&(d3^d4)==-2)return 2;
220         return (d1==0&&dblcmp(v.a.sub(a).dot(v.a.sub(b)))<=0||
221                 d2==0&&dblcmp(v.b.sub(a).dot(v.b.sub(b)))<=0||
222                 d3==0&&dblcmp(a.sub(v.a).dot(a.sub(v.b)))<=0||
223                 d4==0&&dblcmp(b.sub(v.a).dot(b.sub(v.b)))<=0);
224     }
225     int linecrossseg(line v)//*this seg v line
226     {
227         int d1=dblcmp(b.sub(a).det(v.a.sub(a)));
228         int d2=dblcmp(b.sub(a).det(v.b.sub(a)));
229         if ((d1^d2)==-2)return 2;
230         return (d1==0||d2==0);
231     }
232     //0 平行
233     //1 重合
234     //2 相交
235     int linecrossline(line v)
236     {
237         if ((*this).parallel(v))
238         {
239             return v.relation(a)==3;
240         }
241         return 2;
242     }
243     point crosspoint(line v)
244     {
245         double a1=v.b.sub(v.a).det(a.sub(v.a));
246         double a2=v.b.sub(v.a).det(b.sub(v.a));
247         return point((a.x*a2-b.x*a1)/(a2-a1),(a.y*a2-b.y*a1)/(a2-a1));
248     }
249     double dispointtoline(point p)
250     {
251         return fabs(p.sub(a).det(b.sub(a)))/length();
252     }
253     double dispointtoseg(point p)
254     {
255         if (dblcmp(p.sub(b).dot(a.sub(b)))<0||dblcmp(p.sub(a).dot(b.sub(a)))<0)
256         {
257             return min(p.distance(a),p.distance(b));
258         }
259         return dispointtoline(p);
260     }
261     point lineprog(point p)
262     {
263         return a.add(b.sub(a).mul(b.sub(a).dot(p.sub(a))/b.sub(a).len2()));
264     }
265     point symmetrypoint(point p)
266     {
267         point q=lineprog(p);
268         return point(2*q.x-p.x,2*q.y-p.y);
269     }
270 };
271 
272 struct Vector:public point
273 {
274     Vector(){}
275     Vector(double a,double b)
276     {
277         x=a;    y=b;
278     }
279     Vector(point _a,point _b)   //a->b
280     {
281         double dx=_b.x-_a.x;
282         double dy=_b.y-_a.y;
283         x=dx;   y=dy;
284     }
285     Vector(line v)
286     {
287         double dx=v.b.x-v.a.x;
288         double dy=v.b.y-v.a.y;
289         x=dx;   y=dy;
290     }
291     double length()
292     {
293         return (sqrt(x*x+y*y));
294     }
295     Vector Normal()
296     {
297         double L=sqrt(x*x+y*y);
298         Vector Vans=Vector(-y/L,x/L);
299         return Vans;
300     }
301 };
302 
303 struct halfplane:public line    //半平面
304 {
305     double angle;
306     halfplane(){}
307     //表示向量 a->b逆时针(左侧)的半平面
308     halfplane(point _a,point _b)
309     {
310         a=_a;
311         b=_b;
312     }
313     halfplane(line v)
314     {
315         a=v.a;
316         b=v.b;
317     }
318     void calcangle()
319     {
320         angle=atan2(b.y-a.y,b.x-a.x);
321     }
322     bool operator<(const halfplane &b)const
323     {
324         return angle<b.angle;
325     }
326 };
327 
328 struct polygon
329 {
330     int n;
331     point p[maxp];
332     line l[maxp];
333     void input()
334     {
335         n=4;
336         for (int i=0;i<n;i++)
337         {
338             p[i].input();
339         }
340     }
341     void add(point q)
342     {
343         p[n++]=q;
344     }
345     void getline()
346     {
347         for (int i=0;i<n;i++)
348         {
349             l[i]=line(p[i],p[(i+1)%n]);
350         }
351     }
352     struct cmp
353     {
354         point p;
355         cmp(const point &p0){p=p0;}
356         bool operator()(const point &aa,const point &bb)
357         {
358             point a=aa,b=bb;
359             int d=dblcmp(a.sub(p).det(b.sub(p)));
360             if (d==0)
361             {
362                 return dblcmp(a.distance(p)-b.distance(p))<0;
363             }
364             return d>0;
365         }
366     };
367     void norm()
368     {
369         point mi=p[0];
370         for (int i=1;i<n;i++)mi=min(mi,p[i]);
371         sort(p,p+n,cmp(mi));
372     }
373     void getconvex(polygon &convex)
374     {
375         int i,j,k;
376         sort(p,p+n);
377         convex.n=n;
378         for (i=0;i<min(n,2);i++)
379         {
380             convex.p[i]=p[i];
381         }
382         if (n<=2)return;
383         int &top=convex.n;
384         top=1;
385         for (i=2;i<n;i++)
386         {
387             while (top&&convex.p[top].sub(p[i]).det(convex.p[top-1].sub(p[i]))<=0)
388                 top--;
389             convex.p[++top]=p[i];
390         }
391         int temp=top;
392         convex.p[++top]=p[n-2];
393         for (i=n-3;i>=0;i--)
394         {
395             while (top!=temp&&convex.p[top].sub(p[i]).det(convex.p[top-1].sub(p[i]))<=0)
396                 top--;
397             convex.p[++top]=p[i];
398         }
399     }
400     bool isconvex()
401     {
402         bool s[3];
403         memset(s,0,sizeof(s));
404         int i,j,k;
405         for (i=0;i<n;i++)
406         {
407             j=(i+1)%n;
408             k=(j+1)%n;
409             s[dblcmp(p[j].sub(p[i]).det(p[k].sub(p[i])))+1]=1;
410             if (s[0]&&s[2])return 0;
411         }
412         return 1;
413     }
414     //3 点上
415     //2 边上
416     //1 内部
417     //0 外部
418     int relationpoint(point q)
419     {
420         int i,j;
421         for (i=0;i<n;i++)
422         {
423             if (p[i]==q)return 3;
424         }
425         getline();
426         for (i=0;i<n;i++)
427         {
428             if (l[i].pointonseg(q))return 2;
429         }
430         int cnt=0;
431         for (i=0;i<n;i++)
432         {
433             j=(i+1)%n;
434             int k=dblcmp(q.sub(p[j]).det(p[i].sub(p[j])));
435             int u=dblcmp(p[i].y-q.y);
436             int v=dblcmp(p[j].y-q.y);
437             if (k>0&&u<0&&v>=0)cnt++;
438             if (k<0&&v<0&&u>=0)cnt--;
439         }
440         return cnt!=0;
441     }
442     //1 在多边形内长度为正
443     //2 相交或与边平行
444     //0 无任何交点
445     int relationline(line u)
446     {
447         int i,j,k=0;
448         getline();
449         for (i=0;i<n;i++)
450         {
451             if (l[i].segcrossseg(u)==2)return 1;
452             if (l[i].segcrossseg(u)==1)k=1;
453         }
454         if (!k)return 0;
455         vector<point>vp;
456         for (i=0;i<n;i++)
457         {
458             if (l[i].segcrossseg(u))
459             {
460                 if (l[i].parallel(u))
461                 {
462                     vp.pb(u.a);
463                     vp.pb(u.b);
464                     vp.pb(l[i].a);
465                     vp.pb(l[i].b);
466                     continue;
467                 }
468                 vp.pb(l[i].crosspoint(u));
469             }
470         }
471         sort(vp.begin(),vp.end());
472         int sz=vp.size();
473         for (i=0;i<sz-1;i++)
474         {
475             point mid=vp[i].add(vp[i+1]).div(2);
476             if (relationpoint(mid)==1)return 1;
477         }
478         return 2;
479     }
480     //直线u切割凸多边形左侧
481     //注意直线方向
482     void convexcut(line u,polygon &po)
483     {
484         int i,j,k;
485         int &top=po.n;
486         top=0;
487         for (i=0;i<n;i++)
488         {
489             int d1=dblcmp(p[i].sub(u.a).det(u.b.sub(u.a)));
490             int d2=dblcmp(p[(i+1)%n].sub(u.a).det(u.b.sub(u.a)));
491             if (d1>=0)po.p[top++]=p[i];
492             if (d1*d2<0)po.p[top++]=u.crosspoint(line(p[i],p[(i+1)%n]));
493         }
494     }
495     double getcircumference()
496     {
497         double sum=0;
498         int i;
499         for (i=0;i<n;i++)
500         {
501             sum+=p[i].distance(p[(i+1)%n]);
502         }
503         return sum;
504     }
505     double getarea()
506     {
507         double sum=0;
508         int i;
509         for (i=0;i<n;i++)
510         {
511             sum+=p[i].det(p[(i+1)%n]);
512         }
513         return fabs(sum)/2;
514     }
515     bool getdir()//1代表逆时针 0代表顺时针
516     {
517         double sum=0;
518         int i;
519         for (i=0;i<n;i++)
520         {
521             sum+=p[i].det(p[(i+1)%n]);
522         }
523         if (dblcmp(sum)>0)return 1;
524         return 0;
525     }
526     point getbarycentre()
527     {
528         point ret(0,0);
529         double area=0;
530         int i;
531         for (i=1;i<n-1;i++)
532         {
533             double tmp=p[i].sub(p[0]).det(p[i+1].sub(p[0]));
534             if (dblcmp(tmp)==0)continue;
535             area+=tmp;
536             ret.x+=(p[0].x+p[i].x+p[i+1].x)/3*tmp;
537             ret.y+=(p[0].y+p[i].y+p[i+1].y)/3*tmp;
538         }
539         if (dblcmp(area))ret=ret.div(area);
540         return ret;
541     }
542     double areaintersection(polygon po)
543     {
544     }
545     double areaunion(polygon po)
546     {
547         return getarea()+po.getarea()-areaintersection(po);
548     }
549     /*
550     double areacircle(circle c)
551     {
552         int i,j,k,l,m;
553         double ans=0;
554         for (i=0;i<n;i++)
555         {
556             int j=(i+1)%n;
557             if (dblcmp(p[j].sub(c.p).det(p[i].sub(c.p)))>=0)
558             {
559                 ans+=c.areatriangle(p[i],p[j]);
560             }
561             else
562             {
563                 ans-=c.areatriangle(p[i],p[j]);
564             }
565         }
566         return fabs(ans);
567     }
568     //多边形和圆关系
569     //0 一部分在圆外
570     //1 与圆某条边相切
571     //2 完全在圆内
572     int relationcircle(circle c)
573     {
574         getline();
575         int i,x=2;
576         if (relationpoint(c.p)!=1)return 0;
577         for (i=0;i<n;i++)
578         {
579             if (c.relationseg(l[i])==2)return 0;
580             if (c.relationseg(l[i])==1)x=1;
581         }
582         return x;
583     }
584     void find(int st,point tri[],circle &c)
585     {
586         if (!st)
587         {
588             c=circle(point(0,0),-2);
589         }
590         if (st==1)
591         {
592             c=circle(tri[0],0);
593         }
594         if (st==2)
595         {
596             c=circle(tri[0].add(tri[1]).div(2),tri[0].distance(tri[1])/2.0);
597         }
598         if (st==3)
599         {
600             c=circle(tri[0],tri[1],tri[2]);
601         }
602     }
603     void solve(int cur,int st,point tri[],circle &c)
604     {
605         find(st,tri,c);
606         if (st==3)return;
607         int i;
608         for (i=0;i<cur;i++)
609         {
610             if (dblcmp(p[i].distance(c.p)-c.r)>0)
611             {
612                 tri[st]=p[i];
613                 solve(i,st+1,tri,c);
614             }
615         }
616     }
617     circle mincircle()//点集最小圆覆盖
618     {
619         random_shuffle(p,p+n);
620         point tri[4];
621         circle c;
622         solve(n,0,tri,c);
623         return c;
624     }
625     int circlecover(double r)//单位圆覆盖
626     {
627         int ans=0,i,j;
628         vector<pair<double,int> >v;
629         for (i=0;i<n;i++)
630         {
631             v.clear();
632             for (j=0;j<n;j++)if (i!=j)
633             {
634                 point q=p[i].sub(p[j]);
635                 double d=q.len();
636                 if (dblcmp(d-2*r)<=0)
637                 {
638                     double arg=atan2(q.y,q.x);
639                     if (dblcmp(arg)<0)arg+=2*pi;
640                     double t=acos(d/(2*r));
641                     v.push_back(make_pair(arg-t+2*pi,-1));
642                     v.push_back(make_pair(arg+t+2*pi,1));
643                 }
644             }
645             sort(v.begin(),v.end());
646             int cur=0;
647             for (j=0;j<v.size();j++)
648             {
649                 if (v[j].second==-1)++cur;
650                 else --cur;
651                 ans=max(ans,cur);
652             }
653         }
654         return ans+1;
655     }
656     */
657     int pointinpolygon(point q)//点在凸多边形内部的判定
658     {
659         if (getdir())reverse(p,p+n);
660         if (dblcmp(q.sub(p[0]).det(p[n-1].sub(p[0])))==0)
661         {
662             if (line(p[n-1],p[0]).pointonseg(q))return n-1;
663             return -1;
664         }
665         int low=1,high=n-2,mid;
666         while (low<=high)
667         {
668             mid=(low+high)>>1;
669             if (dblcmp(q.sub(p[0]).det(p[mid].sub(p[0])))>=0&&dblcmp(q.sub(p[0]).det(p[mid+1].sub(p[0])))<0)
670             {
671                 polygon c;
672                 c.p[0]=p[mid];
673                 c.p[1]=p[mid+1];
674                 c.p[2]=p[0];
675                 c.n=3;
676                 if (c.relationpoint(q))return mid;
677                 return -1;
678             }
679             if (dblcmp(q.sub(p[0]).det(p[mid].sub(p[0])))>0)
680             {
681                 low=mid+1;
682             }
683             else
684             {
685                 high=mid-1;
686             }
687         }
688         return -1;
689     }
690 };
691 
692 struct halfplanes   //半平面交
693 {
694     int n;
695     halfplane hp[maxp];
696     point p[maxp];
697     int que[maxp];
698     int st,ed;
699     void push(halfplane tmp)
700     {
701         hp[n++]=tmp;
702     }
703     void unique()
704     {
705         int m=1,i;
706         for (i=1;i<n;i++)
707         {
708             if (dblcmp(hp[i].angle-hp[i-1].angle))hp[m++]=hp[i];
709             else if (dblcmp(hp[m-1].b.sub(hp[m-1].a).det(hp[i].a.sub(hp[m-1].a))>0))hp[m-1]=hp[i];
710         }
711         n=m;
712     }
713     bool halfplaneinsert()
714     {
715         int i;
716         for (i=0;i<n;i++)hp[i].calcangle();
717         sort(hp,hp+n);
718         unique();
719         que[st=0]=0;
720         que[ed=1]=1;
721         p[1]=hp[0].crosspoint(hp[1]);
722         for (i=2;i<n;i++)
723         {
724             while (st<ed&&dblcmp((hp[i].b.sub(hp[i].a).det(p[ed].sub(hp[i].a))))<0)ed--;
725             while (st<ed&&dblcmp((hp[i].b.sub(hp[i].a).det(p[st+1].sub(hp[i].a))))<0)st++;
726             que[++ed]=i;
727             if (hp[i].parallel(hp[que[ed-1]]))return false;
728             p[ed]=hp[i].crosspoint(hp[que[ed-1]]);
729         }
730         while (st<ed&&dblcmp(hp[que[st]].b.sub(hp[que[st]].a).det(p[ed].sub(hp[que[st]].a)))<0)ed--;
731         while (st<ed&&dblcmp(hp[que[ed]].b.sub(hp[que[ed]].a).det(p[st+1].sub(hp[que[ed]].a)))<0)st++;
732         if (st+1>=ed)return false;
733         return true;
734     }
735     void getconvex(polygon &con)
736     {
737         p[st]=hp[que[st]].crosspoint(hp[que[ed]]);
738         con.n=ed-st+1;
739         int j=st,i=0;
740         for (;j<=ed;i++,j++)
741         {
742             con.p[i]=p[j];
743         }
744     }
745 };
746 
747 point p[2000];
748 halfplanes TH;
749 int n,T;
750 
751 int main()
752 {
753     //freopen("in.txt","r",stdin);
754 
755     cin>>T;
756     while (T--)
757     {
758         cin>>n;
759         for (int i=n-1;i>=0;i--)
760             p[i].input();
761         //p[i]->p[i+1]
762 
763         TH.n=0;
764         for (int i=0;i<=n-1;i++)
765             TH.push(halfplane(p[i],p[(i+1)%n]));
766 
767         double ans=0.00;
768         if (TH.halfplaneinsert())
769         {
770             polygon Gans;
771             TH.getconvex(Gans);
772             ans=Gans.getarea();
773         }
774         printf("%.2lf\n",ans+eps);
775     }
776 
777     return 0;
778 }
View Code
posted on 2015-02-06 18:05 Pentium.Labs 阅读(189) 评论(0) 编辑收藏举报
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