POJ 3525 Most Distant Point from the Sea 二分+半平面交

题目就是求多变形内部一点。 使得到任意边距离中的最小值最大。

那么我们想一下，可以发现其实求是看一个圆是否能放进这个多边形中。

那么我们就二分这个半径r，然后将多边形的每条边都往内退r距离。

求半平面交看是否存在解即可

#include <iostream>
#include <cstdio>
#include <cstring>
#include <string>
#include <algorithm>
#include <cstdlib>
#include <cmath>
#include <map>
#include <sstream>
#include <queue>
#include <vector>
#define MAXN 111111
#define MAXM 211111
#define PI acos(-1.0)
#define eps 1e-8
#define INF 1000000001
using namespace std;
int dblcmp(double d)
{
    if (fabs(d) < eps) return 0;
    return d > eps ? 1 : -1;
}
struct point
{
    double x, y;
    point(){}
    point(double _x, double _y):
    x(_x), y(_y){};
    void input()
    {
        scanf("%lf%lf",&x, &y);
    }
    double dot(point p)
    {
        return x * p.x + y * p.y;
    }
    double distance(point p)
    {
        return hypot(x - p.x, y - p.y);
    }
    point sub(point p)
    {
        return point(x - p.x, y - p.y);
    }
    double det(point p)
    {
        return x * p.y - y * p.x;
    }
    bool operator == (point a)const
    {
        return dblcmp(a.x - x) == 0 && dblcmp(a.y - y) == 0;
    }
    bool operator < (point a)const
    {
        return dblcmp(a.x - x) == 0 ? dblcmp(y - a.y) < 0 : x < a.x;
    }

}p[MAXN];
struct line
{
    point a,b;
    line(){}
    line(point _a,point _b)
    {
        a=_a;
        b=_b;
    }
    bool parallel(line v)
    {
        return dblcmp(b.sub(a).det(v.b.sub(v.a))) == 0;
    }
    point crosspoint(line v)
    {
        double a1 = v.b.sub(v.a).det(a.sub(v.a));
        double a2 = v.b.sub(v.a).det(b.sub(v.a));
        return point((a.x * a2 - b.x * a1) / (a2 - a1), (a.y * a2 - b.y * a1) / (a2 - a1));
    }
    bool operator == (line v)const
    {
    	return (a == v.a) && (b == v.b);
    }
};
struct halfplane:public line
{
	double angle;
	halfplane(){}
	//表示向量 a->b逆时针(左侧)的半平面
	halfplane(point _a, point _b)
	{
		a = _a;
		b = _b;
	}
	halfplane(line v)
	{
		a = v.a;
		b = v.b;
	}
	void calcangle()
	{
		angle = atan2(b.y - a.y, b.x - a.x);
	}
	bool operator <(const halfplane &b)const
	{
		return angle < b.angle;
	}
};
struct polygon
{
    int n;
    point p[MAXN];
    line l[MAXN];
    double area;
    void getline()
    {
        for (int i = 0; i < n; i++)
        {
            l[i] = line(p[i], p[(i + 1) % n]);
        }
    }
    void getarea()
    {
        area = 0;
        int a = 1, b = 2;
        while(b <= n - 1)
        {
            area += p[a].sub(p[0]).det(p[b].sub(p[0]));
            a++;
            b++;
        }
        area = fabs(area) / 2;
    }
}convex;
struct halfplanes
{
	int n;
	halfplane hp[MAXN];
	point p[MAXN];
	int que[MAXN];
	int st, ed;
	void push(halfplane tmp)
	{
		hp[n++] = tmp;
	}
	void unique()
	{
		int m = 1, i;
		for (i = 1; i < n;i++)
		{
			if (dblcmp(hp[i].angle - hp[i - 1].angle))hp[m++] = hp[i];
			else if (dblcmp(hp[m - 1].b.sub(hp[m - 1].a).det(hp[i].a.sub(hp[m - 1].a)) > 0))hp[m - 1] = hp[i];
		}
		n = m;
	}
	bool halfplaneinsert()
	{
		int i;
		for (i = 0; i < n; i++) hp[i].calcangle();
		sort(hp, hp + n);
		unique();
		que[st = 0] = 0;
		que[ed = 1] = 1;
		p[1] = hp[0].crosspoint(hp[1]);
		for (i = 2; i < n; i++)
		{
			while (st < ed && dblcmp((hp[i].b.sub(hp[i].a).det(p[ed].sub(hp[i].a)))) < 0) ed--;
			while (st < ed && dblcmp((hp[i].b.sub(hp[i].a).det(p[st + 1].sub(hp[i].a)))) < 0) st++;
			que[++ed] = i;
			if (hp[i].parallel(hp[que[ed - 1]])) return false;
			p[ed] = hp[i].crosspoint(hp[que[ed - 1]]);
		}
		while (st < ed && dblcmp(hp[que[st]].b.sub(hp[que[st]].a).det(p[ed].sub(hp[que[st]].a))) < 0) ed--;
		while (st < ed && dblcmp(hp[que[ed]].b.sub(hp[que[ed]].a).det(p[st + 1].sub(hp[que[ed]].a))) < 0) st++;
		if (st + 1 >= ed)return false;
		return true;
	}
	void getconvex(polygon &con)
	{
		p[st] = hp[que[st]].crosspoint(hp[que[ed]]);
		con.n = ed - st + 1;
		int j = st, i = 0;
		for (; j <= ed; i++, j++)
		{
			con.p[i] = p[j];
		}
	}
}h;
int T;
int n;
line getmove(point a, point b, double mid)
{
    double x = a.x - b.x;
    double y = a.y - b.y;
    double L = a.distance(b);
    point ta = point(mid * y / L + a.x, a.y - mid * x / L);
    point tb = point(mid * y / L + b.x, b.y - mid * x / L);
    return line(ta, tb);
}
bool check(double mid)
{
    h.n = 0;
    for(int i = 0; i < n; i++)
    {
        line tmp = getmove(p[i], p[(i + 1) % n], mid);
        h.push(halfplane(tmp));
    }
    return h.halfplaneinsert();
}
int main()
{
    int cas = 0;
    while(scanf("%d", &n) != EOF && n)
    {
        for(int i = 0; i < n; i++) p[i].input();
        double low = 0, high = INF;
        for(int i = 0; i < 100; i++)
        {
            double mid = (low + high) / 2;
            if(check(mid)) low = mid;
            else high = mid;
        }
        printf("%.6f\n", low);
    }
    return 0;
}