Submission #119710

#	Time	Username	Problem	Language	Result	Execution time	Memory
119710		tutis	2circles (balkan11_2circles)	C++17	40 / 100	4096 ms	10860 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)
{
	int kiek = (int)a.size() * 5 + 7;
	auto ii = a.begin();
	while (kiek--)
	{
		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();
		if (abs(cross(ii->b - ii->a, kk->b - kk->a)) > 1e-6)
		{
			if (nereik(*ii, *jj, *kk))
			{
				a.erase(jj);
				continue;
			}
		}
		else
		{
			if (cross(kk->a - ii->a, ii->b - ii->a) > 0)
			{
				a = {};
				return;
			}
		}
		ii++;
		if (ii == a.end())
			ii = a.begin();
	}
}
vector<point>x(list<line>a)
{
	vector<point>ret;
	for (auto it = a.begin(); it != a.end(); it++)
	{
		auto it1 = it;
		it1++;
		if (it1 == a.end())
			it1 = a.begin();
		ret.push_back(x(*it, *it1));
	}
	return ret;
}
ld maxi(const vector<point> &a)
{
	ld ret = 0;
	for (int i = 0; i < (int)a.size(); i++)
	{
		for (int j = 0; j < i; j++)
		{
			ret = max(ret, (a[i] - a[j]).r());
		}
	}
	return ret;
}
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);
	ld rr = maxi(x(tieses));
	return rr >= 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 = 1ll << 30;
	for (int t = 0; t < 50; 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: 40 / 100