Convex hull convex bag

The smallest convex polygon that is included in the points given on a plane. Outputs each vertex of the convex hull counter-clockwise.

1.Graham Scanning Method (O (N*LOGN))-------Rotary Sweep technology:

2.Jarvis March Stepping Method (O (N*H)) H is the number of vertices of a convex hull--------packaging technology

Application: To find the furthest point of two-dimensional plane.

uva,109

1#include <iostream>2#include <vector>3#include <algorithm>4 5 using namespacestd;6 7 structnode8 {9     Doublex, y;Ten     //easy to find the initial point One     BOOL operator< (Constnode& a)Const{ A         returnx<a.x | | (x==a.x && y<a.y); -     } - }; the  -  -typedef vector<node> Vnode;//Convex bag -typedef vector<vnode> Vvnode;//number of convex bags +  - //cross product determines whether to turn left.  + DoubleIsleft (node& p0,node& p1,node&p2) A { at     return(p1.x-p0.x) * (P2.Y-P0.Y)-(p2.x-p0.x) * (p1.y-p0.y); - } -  - //Convex bag - intConvex_hull (Vnode P,vnode &h) { -     intn=p.size (); in     intk=0; -     //by x Ascending and then y in ascending order to sort (P.begin (), P.end ()); +      -      for(intI=0; i<n;i++){ the //wind Up *          while(k>=2&& Isleft (h[k-2],h[k-1],p[i]) <=0) $k--;Panax Notoginsengh[k++]=P[i]; -     } the     //Down Chain +      for(inti=n-2, t=k+1; i>=0; i--){ A          while(K>=t && Isleft (h[k-2],h[k-1],p[i]) <=0) thek--; +h[k++]=P[i]; -     } $     returnK; $ } - //Check if it is inside a convex polygon - intCheck (Vnode h, node p) { the     intn =h.size (); -     intI, j, C =0;Wuyi      for(i =0, j = N1; I < n; j = i++) the         if((((h[i].y <= p.y) && (P.y < h[j].y)) | | ((h[j].y <= p.y) && (P.y < H[I].Y))) && (P.x < (h[j].x-h[i].x) * (P.Y-H[I].Y)/(H[J].Y-H[I].Y) +h[i].x)) -c =!C; Wu     returnC; - } About //convex hull Area according to test instructions $ DoubleArea (Vnode p) { -     intn=p.size (); -     Doubles=0; -      A      for(intI=1; i<n;i++){ +s+= ((p[i-1].x*p[i].y-p[i].x*p[i-1].Y))/2; the     } -     returns; $ } the  the  the intMain () the { -     intN; in Vvnode Hull; the      the      while(Cin>>n && n!=-1) About     { the Vnode p (n); the          for(intI=0; i<n;i++) theCin>>p[i].x>>p[i].y; +          -Vnode H (n+1); then=Convex_hull (p,h);Bayi h.resize (n); the hull.push_back (h); the     } -      - node K; the     DoubleA=0; the      while(cin>>k.x>>k.y) { the Vvnode::iterator it; the          for(It=hull.begin (); It) -         { the             if(Check (*it,k)) the             { theA+=area (*it);94 Hull.erase (it); the                  Break; the             } the         }98     } About //output with two decimal places -Cout.precision (2);101 //fixed format, Floatfield for floating-point output102COUT.SETF (iOS::fixed, Ios::floatfield);103cout<<a<<Endl;104      the     return 0;106}

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Convex hull convex bag