POJ 1912 A highway and the seven dwarfs (凸包&O(logN)判断直线是否与凸包相交)

/*2672ms,4624KB*/

#include<cstdio>
#include<cmath>
#include<algorithm>
using namespace std;
const double pi = acos(-1.0);
const double eps = 1e-10; ///这题不卡精度
const int mx = 100005;

struct P
{
	double x, y;
	P(double x = 0.0, double y = 0.0): x(x), y(y) {}
	bool read()
	{
		return ~scanf("%lf%lf", &x, &y);
	}
	///由于比较的是原始输入数据，所以不用eps
	bool operator < (const P& p) const ///加cosnt和引用以便sort调用，其他函数不加
	{
		return x < p.x || x == p.x && y < p.y;
	}
	P operator + (P p)
	{
		return P(x + p.x, y + p.y);
	}
	P operator - (P p)
	{
		return P(x - p.x, y - p.y);
	}
	P operator * (double d)
	{
		return P(x * d, y * d);
	}
	P operator / (double d)
	{
		return P(x / d, y / d);
	}
	double dot(P p)
	{
		return x * p.x + y * p.y;
	}
	double det(P p)
	{
		return x * p.y - y * p.x;
	}
	///根据凸包构造之后的点的顺序，规定角度范围为(-pi/2, 3/(2pi)]
	double getA()
	{
		double A = atan2(y, x);
		if (A < -pi / 2.0 + eps) A += pi * 2;
		return A;
	}
} p[mx], ans[mx], q1, q2;
int n, len;
double A[mx];

///求凸包
void convex_hull()
{
	sort(p, p + n);
	len = 0;
	int i;
	for (i = 0; i < n; ++i)
	{
		while (len >= 2 && (ans[len - 1] - ans[len - 2]).det(p[i] - ans[len - 1]) < eps)
			--len;
		ans[len++] = p[i];
	}
	int tmp = len;
	for (i = n - 2; i >= 0; --i)
	{
		while (len > tmp && (ans[len - 1] - ans[len - 2]).det(p[i] - ans[len - 1]) < eps)
			--len;
		ans[len++] = p[i];
	}
	--len;
	ans[len] = ans[0];///这句话直接写在凸包里
	for (i = 0; i < len; ++i)
		A[i] = (ans[i + 1] - ans[i]).getA();
}

inline bool dcmp(double a, double b)
{
	return a + eps < b;
}

///二分找第一个角度大于x的边
inline int Find(double angle)
{
	return upper_bound(A, A + len, angle, dcmp) - A;
}

inline bool judge(P q1, P q2)
{
	int i = Find((q2 - q1).getA());
	int j = Find((q1 - q2).getA()); ///直线两侧各找一点，若两点在直线两侧，则直线必过凸包
	if ((q2 - q1).det(ans[i] - q1) * (q2 - q1).det(ans[j] - q1) > -eps) return true;
	else return false;
}

int main()
{
	scanf("%d", &n);
	for (int i = 0; i < n; ++i) p[i].read();
	if (n > 1) convex_hull();
	while (q1.read())
	{
		q2.read();
		puts(n <= 1 || judge(q1, q2) ? "GOOD" : "BAD");
	}
	return 0;
}