LA 3890 Most Distant Point from the Sea(半平面交) Most Distant Point from the Sea

【题目链接】Most Distant Point from the Sea

【题目类型】半平面交

&题解：

蓝书279 二分答案,判断平移后的直线的半平面交是否为空.
模板是照着敲的,还有一些地方不是很懂, 应该还要慢慢体会吧

&代码：

#include <cstdio>
#include <cmath>
#include <algorithm>
#include <vector>
using namespace std;

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

typedef Point Vector;

Vector operator + (const Vector& A, const Vector& B) {return Vector(A.x + B.x, A.y + B.y);}
Vector operator - (const Vector& A, const Vector& B) {return Vector(A.x - B.x, A.y - B.y);}
Vector operator * (const Vector& A, double p) {return Vector(A.x * p, A.y * p);}
double Dot(const Vector& A, const Vector& B) {return A.x * B.x + A.y * B.y;}
double Cross(const Vector& A, const Vector& B) {return A.x * B.y - A.y * B.x;}
double Length(const Vector& A) {return sqrt(Dot(A, A));}
Vector Normal(const Vector& A) {double l = Length(A); return Vector(-A.y / l, A.x / l);}

double PolygonArea(vector<Point> p) {
	int n = p.size();
	double s = 0;
	for(int i = 1; i < n - 1; i++) {
		s += Cross(p[i] - p[0], p[i + 1] - p[0]);
	}
	return s / 2;
}

struct Line {
	Point p, v;
	double ang;
	Line() {}
	Line(Point p, Vector v): p(p), v(v) {ang = atan2(v.y, v.x);}
	bool operator < (const Line& l) const {
		return ang < l.ang;
	}
};

bool OnLeft(const Line& L, const Point& p) {
	return Cross(L.v, p - L.p) > 0;
}

Point GetLineIntersection(const Line& a, const Line& b) {
	Vector u = a.p - b.p;
	double t = Cross(b.v, u) / Cross(a.v, b.v);
	return a.p + a.v * t;
}

const double eps = 1e-6;
vector<Point> HalfplaneIntersection(vector<Line> L) {
	int n = L.size();
	sort(L.begin(), L.end());
	int first, last;
	vector<Point> p(n), ans;
	vector<Line> que(n);
	que[first = last = 0] = L[0];
	for(int i = 1; i < n; i++) {
		while(first < last && !OnLeft(L[i], p[last - 1])) last--;
		while(first < last && !OnLeft(L[i], p[first])) first++;
		que[++last] = L[i];
		if(fabs(Cross(que[last].v, que[last - 1].v)) < eps) {
			last--;
			if(OnLeft(que[last], L[i].p)) que[last] = L[i];
		}
		if(first < last) p[last - 1] = GetLineIntersection(que[last - 1], que[last]);
	}
	while(first < last && !OnLeft(que[first], p[last - 1])) last--;
	if(last - first <= 1) return ans;
	p[last] = GetLineIntersection(que[last], que[first]);
	for(int i = first; i <= last; i++)
		ans.push_back(p[i]);
	return ans;
}

int main() {
	//("E:1.in", "r", stdin);
	int n;
	while(scanf("%d", &n) == 1 && n) {
		vector<Vector> p, v, nor;
		int m, x, y;
		for(int i = 0; i < n; i++) {
			scanf("%d%d", &x, &y);
			p.push_back(Point(x, y));
		}
		if(PolygonArea(p) < 0) reverse(p.begin(), p.end());
		for(int i = 0; i < n; i++) {
			v.push_back(p[(i + 1) % n] - p[i]);
			nor.push_back(Normal(v[i]));
		}
		double left = 0, right = 20000;
		while(right - left > 1e-6) {
			vector<Line> L;
			double mid = left + (right - left) / 2;
			for(int i = 0; i < n; i++)
				L.push_back(Line(p[i] + nor[i]*mid, v[i]));
			vector<Point> poly = HalfplaneIntersection(L);
			if(poly.empty()) right = mid;
			else left = mid;
		}
		printf("%f
", left);
	}
	return 0;
}