最近&最远点对

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HDU 1589 Stars Couple（计算几何求二维平面的最近点对和最远点对)
最远点对相当于求凸包中最远的两个点（先求凸包，然后n*n枚举)
最近点对二分
#include<stdio.h>#include<string.h>#include<math.h>#include<algorithm>using namespace std;const int M=50005;typedef struct Point{double x;double y;}Point;Point p[M];Point pp[M];bool bo[M];int stack[M];//form 1 to t;double dis(Point A,Point B){return sqrt((B.x-A.x)*(B.x-A.x)+(B.y-A.y)*(B.y-A.y));}bool cmp(Point a,Point b){if(a.x<b.x)    return true;if(a.x>b.x)    return false;if(a.y<b.y)    return true;return false;}double Xdet(Point A,Point B,Point C){double x1,x2,y1,y2;x1=B.x-A.x;y1=B.y-A.y;x2=C.x-A.x;y2=C.y-A.y;return x1*y2-x2*y1;//大于0在左手边,逆时针}//把点集凸包化Gram_Scan算法(使用水平序)void Gram_Scan(Point *p,int &n)//p从1-n,把点集土包化{int i,t;sort(p+1,p+1+n,cmp);for(t=0,i=1;i<=n;i++){    if(i>1&&p[i].x==p[i-1].x&&p[i].y==p[i-1].y)      continue;    p[++t]=p[i];}n=t;t=0;memset(bo+1,true,n*sizeof(bo[0]));if(n>0){    stack[++t]=1;    bo[stack[t]]=false;}if(n>1){    stack[++t]=2;    bo[stack[t]]=false;}if(n>2){    for(i=3;i<n;i++)      if(bo[i]&&Xdet(p[stack[t-1]],p[stack[t]],p[i])>=0)      {        stack[++t]=i;        bo[i]=false;      }      else      {        while(t>=2&&Xdet(p[stack[t-1]],p[stack[t]],p[i])<0)        {          bo[stack[t]]=true;          t--;        }        stack[++t]=i;        bo[stack[t]]=false;      }   for(i=n;i>=1;i--)     if(bo[i]&&Xdet(p[stack[t-1]],p[stack[t]],p[i])>=0)     {       stack[++t]=i;       bo[i]=false;     }     else     {       while(t>=2&&Xdet(p[stack[t-1]],p[stack[t]],p[i])<0)       {         bo[stack[t]]=true;         t--;       }       stack[++t]=i;       bo[stack[t]]=false;     }     t--;}for(i=1;i<=t;i++)    pp[i]=p[stack[i]];memcpy(p+1,pp+1,t*sizeof(Point));n=t;}int n,o[M],on;int dcmp(double a,double b){    if(a-b<1e-10&&b-a<1e-10)        return 0;    if(a>b)        return 1;    return -1;}bool cmp1(const Point &a,Point &b){    return dcmp(a.x,b.x)<0;}bool cmp2(const int&a,const int&b){    return dcmp(p[a].y,p[b].y)<0;}double min(double a,double b){    return a<b?a:b;}double search(int s,int t){    int mid=(s+t)/2,i,j;    double ret=1e300;    if(s>=t)        return ret;    for(i=mid;i>=s&&!dcmp(p[i].x,p[mid].x);i--);ret=search(s,i);    for(i=mid;i<=t&&!dcmp(p[i].x,p[mid].x);i++);ret=min(ret,search(i,t));on=0;    for(i=mid;i>=s&&dcmp(p[mid].x-p[i].x,ret)<=0;i--)o[++on]=i;    for(i=mid+1;i<=t&&dcmp(p[i].x-p[mid].x,ret)<=0;i++)o[++on]=i;    sort(o+1,o+on+1,cmp2);    for(i=1;i<=on;i++)        for(j=1;j<=10;j++)            if(i+j<=on)                ret=min(ret,dis(p[o[i]],p[o[i+j]]));    return ret;}int main(){    int n,i,count=0,j;    double shortdis,longdis;    while(scanf("%d",&n),n)    {        for(i=1;i<=n;i++)            scanf("%lf%lf",&p[i].x,&p[i].y);        sort(p+1,p+n+1,cmp1);        shortdis=search(1,n);        longdis=0;        Gram_Scan(p,n);        for(i=1;i<=n-1;i++)            for(j=i+1;j<=n;j++)                if(dis(p[i],p[j])>longdis)                    longdis=dis(p[i],p[j]);        printf("Case %d:\n",++count);        printf("Distance of the nearest couple is %.3lf\n",shortdis);        printf("Distance of the most distant couple is %.3lf\n\n",longdis);    }    return 0;}
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