UVA 11168 (计算几何 凸包)

坑点是凸包的点只有2个的情况。

#include <cstring>
#include <cmath>
#include <iostream>
#include <algorithm>
#include <cstdio>
using namespace std;
typedef unsigned long long ll;
#define maxn 111111
#define pi acos (-1)
#define rotate Rotate

const double eps = 1e-10;
int dcmp (double x) {
    if (fabs (x) < eps)
        return 0;
    else return x < 0 ? -1 : 1;
}
struct point {
    double x, y;
    point (double _x = 0, double _y = 0) : x(_x), y(_y) {}
    point operator - (point a) const {
        return point (x-a.x, y-a.y);
    }
    point operator + (point a) const {
        return point (x+a.x, y+a.y);
    }
    bool operator < (const point &a) const {
        return x < a.x || (x == a.x && y < a.y);
    }
    bool operator == (const point &a) const {
        return dcmp (x-a.x) == 0 && dcmp (y-a.y) == 0;
    }
}p[maxn];

double cross (point a, point b) {
    return a.x*b.y-a.y*b.x;
}
double dot (point a, point b) {
    return a.x*b.x + a.y*b.y;
}
double AngleToRad (double x) {
    return x*pi/180;
}
point rotate (point a, double rad) {
    return point (a.x*cos (rad)-a.y*sin (rad), a.x*sin (rad)+a.y*cos (rad));
}

double ConvexPolygonArea (point *p, int n) {
    double area = 0;
    for (int i = 1; i < n-1; i++)
        area += cross (p[i]-p[0], p[i+1]-p[0]);
    return area/2.0;
}

int n, m, tot;
double l;
point ch[maxn];

int ConvexHull () {
    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-1]) <= 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-1]) <= 0)
            m--;
        ch[m++] = p[i];
    }
    if (n > 1)
        m--;
    return m;
}

double dis (point a, point b) {
    double xx = a.x-b.x, yy = a.y-b.y;
    return sqrt (xx*xx + yy*yy);
}

const double INF = 1e30;
int main () {
    //freopen ("in", "r", stdin);
    int t, kase = 0;
    scanf ("%d", &t);
    while (t--) {
        printf ("Case #%d: ", ++kase);
        scanf ("%d", &n);
        for (int i = 0; i < n; i++) {
            scanf ("%lf%lf", &p[i].x, &p[i].y);
        }
        if (n == 1) {
            printf ("0.000\n");
            continue;
        }
        m = ConvexHull ();
        double sum_x = 0, sum_y = 0, ans = INF;
        for (int i = 0; i < n; i++) {
            sum_x += p[i].x, sum_y += p[i].y;
        }
        if (m == 2 || m == 1) {
            printf ("0.000\n");
            continue;
        }
        for (int i = 0; i < m; i++) {
            int j = (i+1)%m;
            double a = ch[j].y-ch[i].y;
            double b = ch[i].x-ch[j].x;
            double c = ch[i].y*(ch[j].x-ch[i].x) - ch[i].x*(ch[j].y-ch[i].y);
            ans = min (ans, fabs (sum_x*a + sum_y*b + n*c) / sqrt (a*a + b*b));
        }
        printf ("%.3f\n", ans/n);
    }
    return 0;
}