poj 2187【凸包求最远距离】

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http://poj.org/problem?id=2187

这里很明显不能直接暴力（50000*50000）=。=

我们要知道最远的两点一定是凸包上的顶点，所以首先构造凸包，然后枚举找出最远距离，注意这里是平方！还要注意n==2的情况，直接求距离

#include<iostream>#include<vector>#include<map>#include<stack>#include<algorithm>#include<queue>#include<list>#include<set>#include<string.h>#include<stdlib.h>#include<math.h>#include<stdio.h>#include<ctype.h>#include<iomanip>using namespace std;#define LL long long#define pi acos(-1)#define N 50010#define INF 9999999999#define eps 1e-8int n;int top;struct point{    int x,y;}p[N],stck[N],p0;int cross(point a,point b,point c){    return (b.x-a.x)*(c.y-a.y)-(b.y-a.y)*(c.x-a.x);}int dis(point a,point b){    return (a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y);}bool cmp(point a,point b){     int t=cross(p0,a,b);     return t>0 || (t==0 && dis(p0,a)<dis(p0,b));}void tubao(){    int i,j,k;    k=0;    for(i=1;i<n;i++)        if(p[i].y<p[k].y || (p[i].y==p[k].y&&p[i].x<p[k].x))            k=i;    p0=p[k];    p[k]=p[0];    p[0]=p0;    sort(p+1,p+n,cmp);    top=1;    stck[0]=p[0];    stck[1]=p[1];    for(i=2;i<n;i++)    {        while(top>0&&cross(stck[top-1],stck[top],p[i])<0)        top--;        stck[++top]=p[i];    }    top+=1;    return ;}void solve(){    int max=0;    int s;    int i,j;    for(i=0;i<top;i++)    for(j=i+1;j<top;j++)    {        s=dis(stck[i],stck[j]);        if(s>max)            max=s;    }    printf("%d\n",max);}int main(){   // freopen("a.txt","r",stdin);    while(scanf("%d",&n)!=EOF)    {        int i,j,k;        for(i=0;i<n;i++)            scanf("%d %d",&p[i].x,&p[i].y);        if(n<3)        {            printf("%d\n",dis(p[0],p[1]));            continue;        }        tubao();        solve();    }    return 0;}