矩形面积 HDU

矩形面积

HDU - 5251

题意：求能覆盖凸包的最小矩形面积．

旋转卡壳～

#include <bits/stdc++.h>
using namespace std;
const double eps = 1e-8;
const int inf = 0x3f3f3f3f;
const int maxn = 4010;

struct Point{
    double x, y;
    Point(double x = 0, double y = 0): x(x), y(y){}
};
typedef Point Vector;

Vector operator - (Point a, Point b) {
    return Vector(a.x - b.x, a.y - b.y);
}
Vector operator + (Vector a, Vector b) {
    return Vector(a.x + b.x, a.y + b.y);
}
Vector operator * (Vector a, double p) {
    return Vector(a.x * p, a.y * p);
}
Vector operator / (Vector a, double p) {
    return Vector(a.x / p, a.y / p);
}
bool operator < (Point a, Point b) {
    return a.x < b.x || a.x == b.x && a.y < b.y;
}
int dcmp(double x) {
    if(fabs(x) < eps) return 0;
    return x < 0 ? -1 : 1;
}

bool operator == (Point a, Point b) {
    return dcmp(a.x - b.x) == 0 && dcmp(a.y - b.y) == 0;
}
double Dot(Vector a, Vector b) {
    return a.x * b.x + a.y * b.y;
}
double Cross(Vector a, Vector b) {
    return a.x * b.y - a.y * b.x;
}
double Length(Vector a) {
    return sqrt(Dot(a, a));
}
double Angle(Vector a) {
    return atan2(a.y, a.x);
}

int ConvexHull(Point *p, int n, Point *ch) {
    sort(p, p+n);
    int m = 0;
    for(int i = 0; i < n; i++){
        while(m > 1 && Cross(ch[m-1] - ch[m-2], p[i] - ch[m-2]) <= 0) m--;
        ch[m++] = p[i];
    }
    int k = m;
    for(int i = n-2; i >= 0; i--){
        while(m > k && Cross(ch[m-1] - ch[m-2], p[i] - ch[m-2]) <= 0) m--;
        ch[m++] = p[i];
    }
    if(n > 1) m--;
    return m;
}

double RotateCalipers(Point *p, int n){
    int up = 1, R = 1, L;
    p[n] = p[0];
    double ans = inf;
    for(int i = 0; i < n; i++) {
        while(Cross(p[i+1] - p[i], p[up] - p[i]) < Cross(p[i+1] - p[i], p[up+1] - p[i])) up = (up+1)%n;
        while(Dot(p[i+1] - p[i], p[R] - p[i]) < Dot(p[i+1] - p[i], p[R+1] - p[i])) R = (R+1)%n;
        if(i == 0) L = R;
        while(Dot(p[i+1] - p[i], p[L] - p[i]) >= Dot(p[i+1] - p[i], p[L+1] - p[i])) L = (L+1)%n;
        double len = Length(p[i+1] - p[i]);
        double area = (Cross(p[i+1] - p[i], p[up] - p[i]) / len) * (Dot(p[i+1] - p[i], p[R] - p[i]) / len - Dot(p[i+1] - p[i], p[L] - p[i]) / len);
        ans = min(ans, area);
    }
    return ans;
}
Point p[maxn], ch[maxn];
int main(){
    //freopen("in.txt", "r", stdin);
    int kase = 0;
    int t;
    scanf("%d", &t);
    while(t--){
        int n;
        scanf("%d", &n);
        n *= 4;
        for(int i = 0; i < n; i++) {
            scanf("%lf %lf", &p[i].x, &p[i].y);
        }
        int sz = ConvexHull(p, n, ch);
        double ans = RotateCalipers(ch, sz);
        printf("Case #%d:
%.0lf
", ++kase, ans);
    }
    return 0;
}