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 }
时间： 2024-10-24 15:25:45