D.cpp

#include <bits/stdc++.h>

#define FOR(i,a,b) for(int i=(a),_b=(b); i<=_b; i++)
#define FORD(i,a,b) for(int i=(a),_b=(b); i>=_b; i--)
#define REP(i,a) for(int i=0,_a=(a); i<_a; i++)
#define EACH(it,a) for(__typeof(a.begin()) it = a.begin(); it != a.end(); ++it)

#define DEBUG(x) { cout << #x << " = "; cout << (x) << endl; }
#define PR(a,n) { cout << #a << " = "; FOR(_,1,n) cout << a[_] << ' '; cout << endl; }
#define PR0(a,n) { cout << #a << " = "; REP(_,n) cout << a[_] << ' '; cout << endl; }

#define sqr(x) ((x) * (x))
#define ll long long
#define SZ(X) ((int) ((X).size()))
#define double long double
using namespace std;

#define EPS 1e-6

double PI = acos(-1.0);
double DEG_to_RAD(double d) { return d * PI / 180.0; }
double RAD_to_DEG(double r) { return r * 180.0 / PI; }

inline int cmp(double a, double b) {
    return (a < b - EPS) ? -1 : ((a > b + EPS) ? 1 : 0);
}

struct Point {
    double x, y;
    Point(double x = 0.0, double y = 0.0) : x(x), y(y) {}

    Point operator + (Point a) { return Point(x+a.x, y+a.y); }
    Point operator - (Point a) { return Point(x-a.x, y-a.y); }
    Point operator * (double k) { return Point(x*k, y*k); }
    Point operator / (double k) { return Point(x/k, y/k); }

    double operator * (Point a) { return x*a.x + y*a.y; } // dot product
    double operator % (Point a) { return x*a.y - y*a.x; } // cross product

    int cmp(Point q) const { if (int t = ::cmp(x,q.x)) return t; return ::cmp(y,q.y); }

    #define Comp(x) bool operator x (Point q) const { return cmp(q) x 0; }
    Comp(>) Comp(<) Comp(==) Comp(>=) Comp(<=) Comp(!=)
    #undef Comp

    Point conj() { return Point(x, -y); }
    double norm() { return x*x + y*y; }

    // Note: There are 2 ways for implementing len():
    // 1. sqrt(norm()) --> fast, but inaccurate (produce some values that are of order X^2)
    // 2. hypot(x, y) --> slow, but much more accurate
    double len() { return sqrt(norm()); }

    Point rotate(double alpha) {
        double cosa = cos(alpha), sina = sin(alpha);
        return Point(x * cosa - y * sina, x * sina + y * cosa);
    }

    void read() {
        int t;
        scanf("%d", &t); x = t;
        scanf("%d", &t); y = t;
    }
};

int ccw(Point a, Point b, Point c) {
    return cmp((b-a)%(c-a),0);
}
// Distance from p to Line ab (closest Point --> c)
double distToLine(Point p, Point a, Point b, Point &c) {
    Point ap = p - a, ab = b - a;
    double u = (ap * ab) / ab.norm();
    c = a + (ab * u);
    return (p-c).len();
}

// Distance from p to segment ab (closest Point --> c)
double distToLineSegment(Point p, Point a, Point b, Point &c) {
    Point ap = p - a, ab = b - a;
    double u = (ap * ab) / ab.norm();
    if (u < 0.0) {
        c = Point(a.x, a.y);
        return (p - a).len();
    }
    if (u > 1.0) {
        c = Point(b.x, b.y);
        return (p - b).len();
    }
    return distToLine(p, a, b, c);
}

typedef vector<Point> Polygon;
double angle(Point a, Point o, Point b) { // min of directed angle AOB & BOA
    a = a - o; b = b - o;
    return acos((a * b) / sqrt(a.norm() * b.norm()));
}

bool in_polygon(const Polygon &P, Point pt) {
    if ((int)P.size() == 0) return false;
    double sum = 0;
    for (int i = 0; i < (int)P.size(); i++) {
        Point Pj = P[(i+1) % P.size()];
        // If allow on edge --> uncomment the following line
        // if (ccw(P[i], Pj, pt) == 0 && min(P[i], Pj) <= pt && pt <= max(P[i], Pj)) return true;
        if (ccw(pt, P[i], Pj) > 0)
            sum += angle(P[i], pt, Pj);
        else sum -= angle(P[i], pt, Pj);
    }
    return fabs(fabs(sum) - 2*PI) < EPS;
}
double signed_area(Polygon p) {
    double area = 0;
    for(int i = 0; i < p.size(); i++) {
        int j = (i+1) % p.size();
        area += p[i].x*p[j].y - p[j].x*p[i].y;
    }
    return area / 2.0;
}
double area(const Polygon &p) {
    return fabs(signed_area(p));
}


int main() {
    ios :: sync_with_stdio(false);
    int n;
    while (scanf("%d", &n) == 1) {
        double res = 1e100;
        Point O(0, 0);
        bool hasContained = false;

        double maxArea = -1, minArea = 1e100;
        int outerHeight = 0, innerHeight = 0;

        FOR(i,1,n) {
            int h1, h2; scanf("%d%d", &h1, &h2);

            int h = min(h1, h2);
            int k; scanf("%d", &k);
            Polygon P; P.resize(k);
            REP(i,k) P[i].read();

            REP(i,k) {
                int j = (i + 1) % k;
                Point tmp;

                double len = distToLineSegment(O, P[i], P[j], tmp);
                res = min(res, sqrt(len*len + h*(double) h));
            }

            double S = area(P);

            if (in_polygon(P, O)) {
                hasContained = true;
                if (minArea > S) {
                    minArea = S;
                    innerHeight = h2;
                }
            }

            if (S > maxArea) {
                maxArea = S;
                outerHeight = h1;
            }
        }
        if (!hasContained) {
            res = min(res, (double) outerHeight);
        }
        else res = min(res, (double) innerHeight);
        cout << (fixed) << setprecision(9) << res << endl;
    }
}