bzoj 1185

题目大意： 给你n个点求最小矩形覆盖。

思路：枚举凸包上的边然后，旋转卡壳找三个相应的为止把矩形的四个点求出来。

 #include<bits/stdc++.h>
 #define LL long long
 #define fi first
 #define se second
 #define mk make_pair
 #define pii pair<int,int>
 #define piii pair<int, pair<int,int>>

 using namespace std;

 const int N=1e5 + ;
 const int M=1e4 + ;
 const int inf = 0x3f3f3f3f;
 const LL INF = 0x3f3f3f3f3f3f3f3f;
 const int mod = 1e9 + ;
 const double eps = 1e-;
 const double PI = acos(-);

 int n, cnt;

 int dcmp(double x) {
     if(fabs(x) < eps) return ;
     else return x <  ? - : ;
 }

 struct Point {
     double x, y;
     Point(double x = , double y = ) : x(x), y(y) { }

 }p[N], ch[N];

 typedef Point Vector;

 Point operator + (Vector A, Vector B) {return Point(A.x + B.x, A.y + B.y);}
 Point operator - (Vector A, Vector B) {return Point(A.x - B.x, A.y - B.y);}
 Point operator * (Vector A, double p) {return Point(A.x * p, A.y * p);}
 Point operator / (Vector A, double p) {return Point(A.x / p, A.y / p);}
 bool operator < (const Vector &A, const Vector &B) {return A.y < B.y || (A.y == B.y && A.x < B.x);}
 bool operator == (const Vector &A, const Point &B) {return dcmp(A.x - B.x) ==  && dcmp(A.y - B.y) == ;}
 double Dot(Vector A, Vector B) {return A.x * B.x + A.y * B.y;}
 double Length(Vector A) {return sqrt(Dot(A, A));}
 double Angle(Vector A, Vector B) {return acos(Dot(A, B) / Length(A) / Length(B));}
 double Cross(Vector A, Vector B) {return A.x * B.y - A.y * B.x;}
 double Area2(Point A, Point B, Point C) {return Cross(B - A, C - A);}

 Vector Rotate(Vector A, double rad) {
     return Vector(A.x * cos(rad) - A.y * sin(rad), A.x * sin(rad) + A.y * cos(rad));
 }

 Point GetLineIntersection(Point P, Vector v, Point Q, Vector w) {
     Vector u = P - Q;
     double t = Cross(w, u) / Cross(v, w);
     return P + v * t;
 }

 double dis(Point A, Point B) {
     return sqrt((A.x - B.x) * (A.x - B.x) + (A.y - B.y) * (A.y - B.y));
 }
 int ConvexHull(Point *p, int n, Point *ch) {
     sort(p, p + n);
     int m = ;
     for(int i = ; i < n; i++) {
         while(m >  && dcmp(Cross(ch[m - ] - ch[m - ], p[i] - ch[m - ])) <= ) m--;
         ch[m++] = p[i];
     }

     int k = m;
     for(int i = n - ; i >= ; i--) {
         while(m > k && dcmp(Cross(ch[m - ] - ch[m - ], p[i] - ch[m - ])) <= ) m--;
         ch[m++] = p[i];
     }
     return m;
 }

 Point vec[], vec2[];

 int main() {
     scanf("%d", &n);
     for(int i = ; i < n; i++)
         scanf("%lf%lf", &p[i].x, &p[i].y);
     cnt = ConvexHull(p, n, ch);

     cnt--;
     for(int i = ; i < cnt; i++) {
         ch[cnt + i] = ch[i];
     }

     int pos1 = , pos2 = , pos3 = ;
     double ans = inf;
     for(int i = ; i < cnt; i++) {
         while(abs(Cross(ch[i] - ch[pos1 + ], ch[i + ] - ch[pos1 + ])) > abs(Cross(ch[i] - ch[pos1], ch[i + ] - ch[pos1])))
             pos1++;
         while(Dot(ch[i + ] - ch[i], ch[pos2 + ] - ch[i]) > Dot(ch[i + ] - ch[i], ch[pos2] - ch[i]))
             pos2++;
         pos3 = max(pos3, pos1);
         while(Dot(ch[i + ] - ch[i], ch[pos3 + ] - ch[i]) < Dot(ch[i + ] - ch[i], ch[pos3] - ch[i]))
             pos3++;
         Vector k1 = ch[i + ] - ch[i];
         Vector k2 = Rotate(k1, PI / );
         Point p1 = GetLineIntersection(ch[i], k1, ch[pos2], k2);
         Point p2 = GetLineIntersection(ch[i], k1, ch[pos3], k2);
         Point p3 = GetLineIntersection(ch[pos1], k1, ch[pos2], k2);
         Point p4 = GetLineIntersection(ch[pos1], k1, ch[pos3], k2);
         double ret = dis(p1, p2) * dis(p1, p3);
         if(ret < ans) {
             ans = ret;
             vec[] = p1;
             vec[] = p2;
             vec[] = p3;
             vec[] = p4;
         }
     }

     ConvexHull(vec, , vec2);
     printf("%.5f\n", ans);
     for(int i = ; i < ; i++) {
         printf("%.5f %.5f\n", vec2[i].x, vec2[i].y);
     }
     return ;
 }
 /*
 */