Beauty Contest （凸包+旋转卡壳模板题）
Beauty Contest
题意：求凸包上最大点对的距离
AC_Code:
1 #include <iostream> 2 #include <cstdio> 3 #include <cmath> 4 #include <string> 5 #include <algorithm> 6 #include <cstring> 7 using namespace std; 8 typedef long long ll; 9 const int maxn = 5e4+10; 10 const double eps = 1e-8; 11 12 13 typedef struct Point{ 14 double x,y; 15 Point(double x=0,double y=0):x(x),y(y){} 16 }Vector; 17 18 Vector operator + (const Vector &A, const Vector &B){ return Vector(A.x+B.x,A.y+B.y); } 19 Vector operator - (const Vector &A, const Vector &B){ return Vector(A.x-B.x,A.y-B.y); } 20 Vector operator * (const Vector &A, double p){ return Vector(A.x*p,A.y*p); } 21 Vector operator / (const Vector &A, double p){ return Vector(A.x/p,A.y/p); } 22 23 bool operator <(const Point &A,const Point &B){ 24 return A.x<B.x || (A.x==B.x && A.y<B.y); 25 } 26 27 int dcmp(double x){ 28 if( fabs(x)<eps ) return 0; 29 return x<0 ? -1 : 1; 30 } 31 32 double Cross(const Vector &A, const Vector &B){ 33 return A.x*B.y-A.y*B.x; 34 } 35 36 double Dot(const Vector &A, const Vector &B){ 37 return A.x*B.x+A.y*B.y; 38 } 39 40 double Length(const Vector &A){ 41 return Dot(A,A); 42 } 43 44 double Area2(const Point &A, const Point &B, const Point &C){ 45 return Cross(B-A,C-A); 46 } 47 48 int ConvexHull(Point *p,int n,Point *ch){ 49 sort(p,p+n); 50 int m=0; 51 for(int i=0;i<n;i++){ 52 while( m>1 && dcmp(Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2]))<=0 ) m--; 53 ch[m++]=p[i]; 54 } 55 int k=m; 56 for(int i=n-2;i>=0;i--){ 57 while( m>k && dcmp(Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2]))<=0) m--; 58 ch[m++]=p[i]; 59 } 60 if( n>1 ) m--; 61 return m; 62 } 63 64 Point p[maxn],ans[maxn]; 65 66 double RotatingCaliper(int m, Point *ch){ 67 int q=1; 68 ch[m] = ch[0]; 69 double ans = 0.0; 70 for(int p=0;p<m;p++){ 71 while( fabs( Area2(ch[p],ch[p+1],ch[q+1]) ) > fabs( Area2(ch[p],ch[p+1],ch[q]) ) ) q=(q+1)%m; 72 ans = max(ans, max(Length(ch[q+1]-ch[p]), Length(ch[q+1]-ch[p+1]))); 73 ans = max(ans, max(Length(ch[q]-ch[p]), Length(ch[q]-ch[p+1]))); 74 } 75 return ans; 76 } 77 78 int main() 79 { 80 int n; 81 while( ~scanf("%d",&n) ){ 82 for(int i=0;i<n;i++){ 83 int x,y; scanf("%d%d",&x,&y); 84 p[i] = Point(x,y); 85 } 86 int cnt = ConvexHull(p,n,ans); 87 double res = RotatingCaliper(cnt,ans); 88 printf("%.0f\n",res); 89 } 90 return 0; 91 }
