UVA 3890 Most distant points from the Sea (dichotomy + half-plane intersection)

Title Link: http://acm.hust.edu.cn/vjudge/problem/viewProblem.action?id=11358

Ideas

dichotomy + half-plane intersection

The distance between two points and the sea, by the normal vector can be obtained after the translation of the sides, half-plane intersection in the specific accuracy to determine whether there is a intersection.

Code

1#include <cmath>2#include <cstdio>3#include <cstring>4#include <algorithm>5 using namespacestd;6 7 Const DoubleEPS = 1e-7;8 9 structPt {Ten     Doublex, y; OnePt (Doublex=0,Doubley=0): X (x), Y (y) {} A }; - typedef Pt VEC; - structLine { the Pt P; Vec v; -     Doubleang; - Line () {}; -Line (Pt P,vec v):P (P), V (v) {ang=atan2 (V.Y, v.x);} +     BOOL operator< (Constline& RHS)Const{ -         returnang<Rhs.ang; +     } A }; at  -Vecoperator-(Pt a,pt B) {returnVEC (a.x-b.x,a.y-b.y); } -Vecoperator+ (VEC A,vec B) {returnVEC (a.x+b.x,a.y+b.y); } -Vecoperator* (Vec A,DoubleP) {returnVEC (a.x*p,a.y*p); } - DoubleDot (VEC A,vec B) {returna.x*b.x+a.y*b.y;} - DoubleCross (Pt a,pt B) {returna.x*b.y-a.y*b.x;} in DoubleLen (Vec A) {returnsqrt (Dot (a,a));} -VEC Normal (Vec A) {DoubleL=len (A);returnVEC (-a.y/l,a.x/m); } to  + BOOLOnleft (line l,pt P) {returnCross (L.V,P-L.P) >0; } -  the Pt lineintersection (line A,line b) { *VEC u=a.p-B.P; $     DoubleT=cross (b.v,u)/Cross (A.V,B.V);Panax Notoginseng     returna.p+a.v*T; - } the intHalfplaneintersection (line* L,intn,pt*Poly) { +Sort (l,l+n); A     intFirst,last; thePt *p=NewPt[n]; +Line *q=NewLine[n]; -q[first=last=0]=l[0]; $      for(intI=1; i<n;i++) { $          while(First<last &&!onleft (l[i],p[last-1])) last--; -          while(First<last &&!onleft (l[i],p[first)) first++; -q[++last]=L[i]; the         if(Fabs (Cross (q[last].v,q[last-1].V)) <EPS) { -last--;Wuyi             if(Onleft (q[last],l[i). P)) q[last]=L[i]; the         } -         if(first<last) p[last-1]=lineintersection (q[last-1],q[last]); Wu     } -      while(First<last &&!onleft (q[first],p[last-1])) last--; About     if(last-first<=1)return 0; $p[last]=lineintersection (Q[last],q[first]); -     intm=0; -      for(inti=first;i<=last;i++) poly[m++]=P[i]; -     returnm; A } +  the Const intN = $+Ten; - Pt P[n],poly[n]; $ Line L[n]; the VEC V[n], v2[n]; the intN; the  the intMain () { -      while(SCANF ("%d", &n) = =1&&N) { in         intm,x,y; the          for(intI=0; i<n;i++) { thescanf"%d%d",&x,&y); Aboutp[i]=Pt (x, y); the         } the          for(intI=0; i<n;i++) { thev[i]=p[(i+1)%n]-P[i]; +v2[i]=Normal (V[i]); -         } the         Doubleleft=0, right=20000;Bayi          while(right-left>EPS) { the             Doublemid=left+ (Right-left)/2; the              for(intI=0; i<n;i++) L[i]=line (p[i]+v2[i]*mid,v[i]); -m=halfplaneintersection (l,n,poly); -             if(!m) Right=mid;Elseleft=mid; the         } theprintf"%.6lf\n", left); the     } the     return 0; -}

UVA 3890 Most distant points from the Sea (dichotomy + half-plane intersection)