【BZOJ 1038】【ZJOI 2008】瞭望塔

#include<cmath>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int N = 303;

struct Point {
	double x, y;
	Point(double _x = 0, double _y = 0) : x(_x), y(_y) {}
} t[N], p[N];
struct Line {
	Point p, v; double ang;
	Line(Point _p = Point(0, 0), Point _v = Point(0, 0), double _ang = 0) : p(_p), v(_v), ang(_ang) {}
	bool operator < (const Line &x) const {
		return ang < x.ang;
	}
} l[N], q[N];

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

int dcmp(double x) {return fabs(x) < 1e-8 ? 0 : (x < 0 ? -1 : 1);}
double Dot(Point a, Point b) {return a.x * b.x + a.y * b.y;}
double Cross(Point a, Point b) {return a.x * b.y - a.y * b.x;}
double sqr(double x) {return x * x;}
double dis(Point a, Point b) {return sqrt(sqr(a.x - b.x) + sqr(a.y - b.y));}

bool onleft(Point a, Line b) {return dcmp(Cross(a - b.p, b.v)) < 0;}
Point intersection(Line a, Line b) {
	Point u; double t;
	u = a.p - b.p;
	t = Cross(b.v, u) / Cross(a.v, b.v);
	return a.p + (a.v * t);
}

int n, head = 1, tail = 2;
double ans;

void mkhalf() {
	q[1] = l[1]; q[2] = l[2];
	p[1] = intersection(q[1], q[2]);
	for(int i = 3; i < n; ++i) {
		while (head < tail && !onleft(p[tail - 1], l[i])) --tail;
		while (head < tail && !onleft(p[head], l[i])) ++head;
		q[++tail] = l[i];
		if (dcmp(Cross(q[tail].v, q[tail - 1].v) == 0)) {
			--tail;
			if (onleft(l[i].p, q[tail])) q[tail] = l[i];
		}
		if (head < tail) p[tail - 1] = intersection(q[tail - 1], q[tail]);
	}
//	while (head < tail + 1 && !onleft(p[tail - 1], q[head])) --tail;
}

double cal(int num) {
	Point j;
	double x = t[num].x, y = t[num].y;
	if (x <= p[head].x) {
		j = intersection(q[head], Line(t[num], Point(0, 1)));
		return j.y - y;
	}
	if (x >= p[tail - 1].x) {
		j = intersection(q[tail], Line(t[num], Point(0, 1)));
		return j.y - y;
	}
	int left = head, right = tail - 1, mid;
	while (left < right) {
		mid = (left + right + 1) >> 1;
		if (p[mid].x > x) right = mid - 1;
		else left = mid;
	}
	j = intersection(q[left + 1], Line(t[num], Point(0, 1)));
	return j.y - y;
}

double cal2(int num) {
	Point j;
	double x = p[num].x, y = p[num].y;
	int left = 1, right = n, mid;
	while (left < right) {
		mid = (left + right + 1) >> 1;
		if (t[mid].x > x) right = mid - 1;
		else left = mid;
	}
	j = intersection(Line(t[left], t[left + 1] - t[left]), Line(p[num], Point(0, -1)));
	return y - j.y;
}

int main() {
	scanf("%d", &n);
	for(int i = 1; i <= n; ++i) scanf("%lf", &t[i].x);
	for(int i = 1; i <= n; ++i) scanf("%lf", &t[i].y);
	
	for(int i = 1; i < n; ++i) l[i] = Line(t[i], t[i + 1] - t[i]), l[i].ang = atan2(l[i].v.y, l[i].v.x);
	sort(l + 1, l + n);
	mkhalf();
	
	ans = cal(1);
	for(int i = 2; i <= n; ++i)
		ans = min(ans, cal(i));
	for(int i = head; i < tail; ++i)
		if (t[1].x <= p[i].x && p[i].x <= t[n].x)
			ans = min(ans, cal2(i));
	
//	for(int i = head; i < tail; ++i) printf("%.2lf %.2lf\n", p[i].x, p[i].y);
	
	printf("%.3lf\n", ans + 1e-8);
	return 0;
}