vijos p1233

描述

在直角坐标系中，给出n个顶点的坐标，求这n个点所围成的图形的周长和面积。

注意：
（1）如果所有点共线则周长按直线的长度计算，面积视为0；
（2）如果部分点共线按共线后的多边形计算；
（3）所给出的n个顶点如果能围成多边形均为突多边形。

#include 

using namespace std;
const double EPS = 1e-9;

struct Point {
    double x, y;

    Point(double x = 0, double y = 0) : x(x), y(y) {}

    Point read() {
        int a, b;
        scanf("%d%d", &a, &b);
        this->x = a;
        this->y = b;
        return *this;
    }
};

typedef Point Vector;

Vector operator-(Vector a, Vector b) { return Vector(a.x - b.x, 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 Cross(Vector a, Vector b) { return a.x * b.y - a.y * b.x; }

bool operator<(const Vector &a, const Vector &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;
}

double PolygonAera(Point *p, int n) {
    double aera = 0.0;
    for (int i = 1; i < n - 1; i++)aera += Cross(p[i] - p[0], p[i + 1] - p[0]);
    return aera / 2.0;
}

double PolygonCircumference(Point *p, int n) {
    double c = Length(p[0] - p[n - 1]);
    for (int i = 1; i < n; i++)c += Length(p[i] - p[i - 1]);
    return c;
}

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;
}

int main() {
    int n;
    while (scanf("%d", &n) == 1) {
        Point s[20], ch[20];
        for (int i = 0; i < n; i++)
            s[i].read();
        int m = ConvexHull(s, n, ch);
        bool ok = false;
        for (int i = 2; i < m; i++)
            if (dcmp(Cross(ch[i] - ch[i - 1], ch[i - 1] - ch[i - 2])) != 0)
                ok = true;
        double circumference = PolygonCircumference(ch, m);
        double aera = PolygonAera(ch, m);
        if (ok)
            printf("%.2lf\n%.2lf\n", circumference, aera);
        else
            printf("%.2lf\n%.2lf\n", circumference / 2.0, 0.0);
    }
    return 0;
}