Largest Triangle （凸包+旋转卡壳求最大三角形）
题意：在二维坐标中给出\(n\)个点，在这些点中挑\(3\)个点能组成的面积最大的三角形的面积
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 if( m<=2 ) return 0; 68 if( m==3 ) return fabs( Cross(ch[1]-ch[0], ch[2]-ch[0]) )*0.5; 69 double ans = 0.0; 70 int i,j,k; 71 for(i=0;i<m;i++){ 72 j=(i+1)%m; k=(j+1)%m; 73 while( fabs( Area2(ch[i],ch[j],ch[k]) ) < fabs( Area2(ch[i],ch[j],ch[(k+1)%m]) ) ) k=(k+1)%m; 74 75 while( i!=j && k!=i ){ 76 ans = max(ans, fabs( Area2(ch[i],ch[j],ch[k]) )); 77 while( fabs( Area2(ch[i],ch[j],ch[k]) ) < fabs( Area2(ch[i],ch[j],ch[(k+1)%m]) ) ) k=(k+1)%m; 78 j=(j+1)%m; 79 } 80 } 81 return ans*0.5; 82 } 83 84 int main() 85 { 86 int n; 87 while( ~scanf("%d",&n) ){ 88 for(int i=0;i<n;i++){ 89 double x,y; scanf("%lf%lf",&x,&y); 90 p[i] = Point(x,y); 91 } 92 int cnt = ConvexHull(p,n,ans); 93 double res = RotatingCaliper(cnt,ans); 94 printf("%.7f\n",res); 95 } 96 return 0; 97 }
