Submission #119716

#	Time	Username	Problem	Language	Result	Execution time	Memory
119716		tutis	2circles (balkan11_2circles)	C++17	100 / 100	589 ms	10492 KiB

twocircles

/*input
6
0 0
8 0
8 6
4 8
2 8
0 4

*/
#pragma GCC optimize ("O3")
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
struct point
{
	ld x, y;
	point() {}
	point(ld x, ld y): x(x), y(y) {}
	ld r()
	{
		return sqrtl(x * x + y * y);
	}
};
point operator+(const point &a, const point &b)
{
	return point(a.x + b.x, a.y + b.y);
}
point operator-(const point &a, const point &b)
{
	return point(a.x - b.x, a.y - b.y);
}
point operator*(const point &a, const point &b)
{
	return point(a.x * b.x - a.y * b.y, a.x * b.y + a.y * b.x);
}
point operator*(point a, ld k)
{
	return point(a.x * k, a.y * k);
}
ld dot(const point &a, const point &b)
{
	return a.x * b.x + a.y * b.y;
}
ld cross(const point &a, const point &b)
{
	return a.x * b.y - a.y * b.x;
}
point x(const point &a, point b, const point &c, point d)
{
	b = b - a;
	d = d - c;
	ld y = cross(a - c, b) / cross(d, b);
	return c + d * y;
}
ld y(const point &a, point b, const point &c, point d)
{
	b = b - a;
	d = d - c;
	return cross(a - c, b) / cross(d, b);
}
struct line
{
	point a, b;
};
point x(const line &a, const line &b)
{
	return x(a.a, a.b, b.a, b.b);
}
ld y(const line &a, const line &b)
{
	return y(a.a, a.b, b.a, b.b);
}
int n;
point A[505050];
bool nereik(const line &a, const line &b, const line &c)
{
	return y(a, b) >= y(c, b);
}
void taisom(list<line> &a)
{
	if (a.size() <= 2)
	{
		a = {};
		return;
	}
	int dar = a.size() + 10;
	for (auto ii = a.begin(); dar > 0;)
	{
		if (a.size() <= 2)
		{
			a = {};
			return;
		}
		auto jj = ii; jj++;
		if (jj == a.end())jj = a.begin();
		auto kk = jj; kk++;
		if (kk == a.end())kk = a.begin();
		auto zz = ii;
		if (zz != a.begin())
			zz--;
		else
			zz = (--a.end());

		if (abs(cross(zz->b - zz->a, jj->b - jj->a)) > 0.5)
		{
			if (nereik(*zz, *ii, *jj))
			{
				a.erase(ii);
				dar = a.size() + 10;
				ii = zz;
				continue;
			}
		}
		else
		{
			if (cross(jj->a - zz->a, zz->b - zz->a) > 0)
			{
				a = {};
				return;
			}
		}
		if (abs(cross(ii->b - ii->a, kk->b - kk->a)) > 0.5)
		{
			if (nereik(*ii, *jj, *kk))
			{
				a.erase(jj);
				dar = a.size() + 10;
				continue;
			}
		}
		else
		{
			if (cross(kk->a - ii->a, ii->b - ii->a) > 0)
			{
				a = {};
				return;
			}
		}
		ii++;
		dar--;
		if (ii == a.end())
			ii = a.begin();
	}
}
vector<point>x(vector<line>a)
{
	vector<point>ret;
	for (int i = 0; i < (int)a.size(); i++)
	{
		ret.push_back(x(a[i], a[(i + 1) % a.size()]));
	}
	return ret;
}
ld maxi(vector<point> a, ld r)
{
	int n = a.size();
	if (n <= 2)
		return false;
	a.push_back(a[0]);
	int j = 1;
	for (int i = 0; i < n; i++)
	{
		while (true)
		{
			if ((a[j] - a[i]).r() >= r)
				return true;
			if ((a[j] - a[i + 1]).r() >= r)
				return true;
			int j_ = (j + 1) % n;
			if (abs(cross(a[j_] - a[i], a[i] - a[i + 1])) >=
			        abs(cross(a[j] - a[i], a[i] - a[i + 1])))
				j = j_;
			else
				break;
		}
		if ((a[j] - a[i]).r() >= r)
			return true;
		if ((a[j] - a[i + 1]).r() >= r)
			return true;
	}
	return false;
}
bool ok(ld r)
{
	list<line>tieses;
	for (int i = 0; i < n; i++)
	{
		point v = (A[i + 1] - A[i]) * point(0, 1);
		v = v * (r / v.r());
		tieses.push_back(line());
		tieses.back().a = A[i] + v;
		tieses.back().b = A[i + 1] + v;
	}
	taisom(tieses);
	vector<line>z(tieses.begin(), tieses.end());
	return maxi(x(z), 2 * r);
}
int main()
{
	ios_base::sync_with_stdio(false);
	cin >> n;
	for (int i = 0; i < n; i++)
		cin >> A[i].x >> A[i].y;
	A[n] = A[0];
	ld lo = 0;
	ld hi = 4e7;
	for (int t = 0; t < 40; t++)
	{
		ld r = (lo + hi) / 2;
		if (ok(r))
			lo = r;
		else
			hi = r;
	}
	ld r = (lo + hi) / 2;
	cout << fixed << setprecision(15) << r << "\n";
}

• Subtask 1: 100 / 100