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Posted on 2009-09-20 00:53 Uriel 阅读(467) 评论(0) 编辑 收藏 引用 所属分类: POJ 、 计算几何
简单凸包。。凸包周长加半径L圆的周长。。
/**//*Problem: 1113 User: Uriel Memory: 636K Time: 47MS Language: G++ Result: Accepted*/
#include<math.h> #include<stdio.h> #include <stdlib.h>
#define eps 1e-8 #define PI 3.141592653589793 #define zero(x) (((x)>0?(x):-(x))<eps)
struct point{ double x,y; };
point P[3001],convex[3001]; double res; int N,L;
//计算cross product (P1-P0)x(P2-P0) double xmult(point p1,point p2,point p0){ return (p1.x-p0.x)*(p2.y-p0.y)-(p2.x-p0.x)*(p1.y-p0.y); } //graham算法顺时针构造包含所有共线点的凸包,O(nlogn) point p1,p2; int graham_cp(const void* a,const void* b){ double ret=xmult(*((point*)a),*((point*)b),p1); return zero(ret)?(xmult(*((point*)a),*((point*)b),p2)>0?1:-1):(ret>0?1:-1); } void _graham(int n,point* p,int& s,point* ch){ int i,k=0; for (p1=p2=p[0],i=1;i<n;p2.x+=p[i].x,p2.y+=p[i].y,i++) if (p1.y-p[i].y>eps||(zero(p1.y-p[i].y)&&p1.x>p[i].x)) p1=p[k=i]; p2.x/=n,p2.y/=n; p[k]=p[0],p[0]=p1; qsort(p+1,n-1,sizeof(point),graham_cp); for (ch[0]=p[0],ch[1]=p[1],ch[2]=p[2],s=i=3;i<n;ch[s++]=p[i++]) for (;s>2&&xmult(ch[s-2],p[i],ch[s-1])<-eps;s--); }
//构造凸包接口函数,传入原始点集大小n,点集p(p原有顺序被打乱!) //返回凸包大小,凸包的点在convex中 //参数maxsize为1包含共线点,为0不包含共线点,缺省为1 //参数clockwise为1顺时针构造,为0逆时针构造,缺省为1 //在输入仅有若干共线点时算法不稳定,可能有此类情况请另行处理! //不能去掉点集中重合的点 int graham(int n,point* p,point* convex,int maxsize=1,int dir=1){ point* temp=new point[n]; int s,i; _graham(n,p,s,temp); for (convex[0]=temp[0],n=1,i=(dir?1:(s-1));dir?(i<s):i;i+=(dir?1:-1)) if (maxsize||!zero(xmult(temp[i-1],temp[i],temp[(i+1)%s]))) convex[n++]=temp[i]; delete []temp; return n; }
double Dis(int a,int b) { return sqrt((convex[a].y-convex[b].y)*(convex[a].y-convex[b].y)+(convex[a].x-convex[b].x)*(convex[a].x-convex[b].x)); }
int main() { scanf("%d %d",&N,&L); for(int i=0;i<N;i++) { scanf("%lf %lf",&P[i].x,&P[i].y); } int M=graham(N,P,convex,1,1); res=0; for(int i=0;i<M-1;i++) { // printf("*%.2f %.2f*\n",convex[i].x,convex[i].y); res+=Dis(i,i+1); } res+=Dis(0,M-1); res+=2*PI*L; printf("%.0f\n",res); // system("PAUSE"); return 0; }
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