poj1113--Convex bag (Andrew)

Main topic:

Given the coordinates of several points on a plane, your task is to build a circular fence, enclose all the dots, and be no less than L from all points. Find the minimum length of the fence.

It is easy to conclude that the girth of the convex hull + the circumference of the circle with the radius of L.

Let's talk about the Andrew algorithm here.

Andrew is a variant of the Graham algorithm, and Andrew is faster and more stable.

Andrew algorithm idea is to first n points according to the x-coordinate from small to large sort (x same as Y from small to large), get a sequence a1,a2,... an, will A1,A2 into the CH array, starting from A3, judging whether the point in the convex hull current direction of the left, if it is, The point is added to the CH array, otherwise the point in CH is deleted until the left side, repeating the above operation. It is worth noting that Andrew needs to do 2 of these processes, the first time to find the "convex hull", the second time to find "convex hull", the merger is the complete convex hull.

See the code specifically.

#include <iostream>#include<cstdio>#include<algorithm>#include<cmath>using namespacestd;#definePi ACOs (-1.0)structpoint{intx, y; Point (intx=0,inty=0): X (x), Y (y) {}}a[1001],ch[1001];typedef Point Vector;pointoperator-(Point A,point b) {returnPoint (a.x-b.x,a.y-b.y);}intCross (Vector A,vector b) {return(a.x*b.y-a.y*b.x);}DoubleLength (Vector a) {return(SQRT (Double) a.x*a.x+a.y*a.y));}BOOLCMP (point A,point b) {return(a.x<b.x| | (a.x==b.x&&a.y<b.y));}intn,i,j,k,l,x,y;Doublesum=0;intMain () {scanf ("%d%d",&n,&l);  for(i=1; i<=n;++i) scanf ("%d%d",&a[i].x,&a[i].y); Sort (a+1, a+n+1, CMP); intm=0;  for(i=1; i<=n;++i) {         while(m>1&&cross (ch[m]-ch[m-1],a[i]-ch[m-1]) <0) m--; ch[++m]=A[i]; } k=m;  for(i=n-1; i>=1;--i) {         while(M>k&&cross (ch[m]-ch[m-1],a[i]-ch[m-1]) <=0) m--; ch[++m]=A[i]; }     for(i=1; i<m;++i) Sum+=length (ch[i+1]-Ch[i]); printf ("%.0f\n", sum+2*pi*l); return 0;}

poj1113

poj1113--Convex bag (Andrew)