poj 1113

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凸包

至今还不知道这道题为什么凸包就是解，在网上搜结题报告也都是说求凸包，没告诉深层原因，求大神解答

#include <iostream>#include <cstdio>#include <algorithm>#include <math.h>using namespace std;const int maxn=1000+10;struct node{int x,y;};node point[maxn];int ch[maxn];int n,l;bool cmp(node a,node b){if(a.x<b.x) return true;else if(a.x==b.x) return a.y<b.y?true:false;else return false;}int cross(node a,node b,node c){return (b.x-a.x)*(c.y-b.y)-(b.y-a.y)*(c.x-b.x);}int  Andrew(){sort(point,point+n,cmp);int m=0;int i;for(i=0;i<n;i++){while(m>1&&cross(point[ch[m-1]],point[ch[m-2]],point[i])<=0) m--;ch[m++]=i;}int k=m;for(i=n-2;i>=0;i--){while(m>k&&cross(point[ch[m-1]],point[ch[m-2]],point[i])<=0) m--;ch[m++]=i;}return m;}double dis(node a,node b){return sqrt(double((b.x-a.x)*(b.x-a.x)+(b.y-a.y)*(b.y-a.y)));}int main(){while(~scanf("%d%d",&n,&l)){int i;for(i=0;i<n;i++) scanf("%d%d",&point[i].x,&point[i].y);int tot=Andrew();double out=2*acos(-1.0)*l;for(i=0;i<tot-1;i++){out+=dis(point[ch[i]],point[ch[i+1]]);}printf("%.lf\n",out);}return 0;}