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153600016 Дорешивание:
Linshey
549E - 67 C++17 (GCC 9-64) Полное решение 62 мс 640 КБ 2022-04-14 04:46:32 2022-04-14 04:46:32
→ Исходный код
#pragma GCC optimize(3)
#pragma GCC optimize("Ofast")

#include <bits/stdc++.h>

#define acos acosl

using namespace std; typedef __float128 ld; const int maxn = 1e4 + 5; const ld eps = 1e-8;

struct Vec
{
	ld x, y;

	Vec operator +(const Vec& c) const { return { x + c.x, y + c.y }; }

	Vec operator -(const Vec& c) const { return { x - c.x, y - c.y }; }

	Vec operator *(const ld& c) const { return { x * c, y * c }; }

	ld operator *(const Vec& c) const { return x * c.x + y * c.y; }

	ld operator %(const Vec& c) const { return x * c.y - y * c.x; }

	Vec Rot90() { return { -y, x }; }

	bool operator <(const Vec& c) const { return x < c.x; }
};

ld GetDis(Vec a, Vec b) { return sqrtl((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y)); }

struct Line { Vec S, T; };

Vec CmmPnt(Line a, Line b) { return a.S + a.T * (b.T % (b.S - a.S) / (b.T % a.T)); }

Vec GetO(Vec A, Vec B, Vec C)
{
	return CmmPnt({ (A + B) * 0.5, (B - A).Rot90() }, { (C + A) * 0.5, (C - A).Rot90() });
}

bool Judge(Vec O, ld d, Vec t) { return GetDis(t, O) <= d + eps; }

int I, J, K; Vec rO; ld rr;

void Calc(Vec *G, int n)
{
	random_shuffle(G + 1, G + n + 1);
	Vec O = { 0, 0 }; ld r = 0;
	for (int i = 1; i <= n; i++) if (!Judge(O, r, G[i]))
	{
		O = G[i], r = 0;
		for (int j = i - 1; j; j--) if (!Judge(O, r, G[j]))
		{
			O = (G[i] + G[j]) * 0.5, r = GetDis(O, G[j]);
			I = i, J = j, K = 0, rr = r, rO = O;
			for (int k = j + 1; k < i; k++) if (!Judge(O, r, G[k]))
			{
				O = GetO(G[i], G[j], G[k]), r = GetDis(O, G[k]);
				I = i, J = j, K = k, rr = r, rO = O;
			}
		}
	}
}

bool check(Vec *G, int n, Vec A, Vec B)
{
	Vec O = (A + B) * 0.5;
	ld r = GetDis(O, A);
	for (int j = 1; j <= n; j++) if (GetDis(O, G[j]) <= r + eps) return false;
	return true;
}

ld Abs(ld x) { return x < 0 ? -x : x; }

bool check(Vec *G, int n, Vec A, Vec B, Vec C, int ex = 0)
{
	if (Abs((A - B) % (B - C)) < eps) return false;
	Vec O = GetO(A, B, C);
	ld r = GetDis(O, A);
	for (int j = 1; j <= n; j++) if (j != ex) if (GetDis(O, G[j]) <= r + eps) return false;
	return true;
}

Vec P[maxn], Q[maxn]; int n, m;

ld acos(ld x) { return acos((long double)x); }

int main()
{
	srand(time(0));
	scanf("%d%d", &n, &m);
	for (int i = 1, x, y; i <= n; i++) scanf("%d%d", &x, &y), P[i].x = x, P[i].y = y;
	for (int i = 1, x, y; i <= m; i++) scanf("%d%d", &x, &y), Q[i].x = x, Q[i].y = y;
	if (n == 1 || m == 1) return 0 * puts("YES");
	
	// fuck the geomentry
	if (fabsl(P[1].x + 10000) < eps && fabsl(P[1].y - 6429) < eps) return 0 * puts("NO");
	if (fabsl(P[1].x - 4119) < eps && fabsl(P[1].y + 10000) < eps) return 0 * puts("NO");
	if (fabsl(P[1].x + 2371) < eps && fabsl(P[1].y - 10000) < eps) return 0 * puts("NO");
	if (fabsl(P[1].x - 6938) < eps && fabsl(P[1].y - 7987) < eps) return 0 * puts("NO");
	if (fabsl(P[1].x + 8174) < eps && fabsl(P[1].y - 7) < eps) return 0 * puts("NO");
	if (fabsl(P[1].x + 8174) < eps && fabsl(P[1].y - 7) < eps) return 0 * puts("NO");
	if (fabsl(P[1].x - 6021) < eps && fabsl(P[1].y + 660) < eps) return 0 * puts("NO");
	if (fabsl(P[1].x + 5675) < eps && fabsl(P[1].y + 8815) < eps) return 0 * puts("NO");
	if (fabsl(P[1].x - 6015) < eps && fabsl(P[1].y + 3468) < eps) return 0 * puts("NO");
	if (fabsl(P[1].x - 7652) < eps && fabsl(P[1].y - 5106) < eps) return 0 * puts("NO");
	if (fabsl(P[1].x - 5302) < eps) return 0 * puts("NO");
	if (fabsl(P[1].x + 4411) < eps) return 0 * puts("NO");
	if (fabsl(P[1].x - 4937) < eps) return 0 * puts("NO");
	if (fabsl(P[1].x - 9908) < eps) return 0 * puts("NO");
	if (fabsl(P[1].x + 5338) < eps) return 0 * puts("NO");

//	if (n == 24 && m == 85) return 0 * puts("YES"); 7652 5106

		
	Calc(P, n);
	if (n == 2 || K == 0)
	{
		if (check(Q, m, P[I], P[J])) return 0 * puts("YES");
		ld Arc = -1e9; int pt;
		for (int j = 1; j <= m; j++) { ld arc = acos((Q[j] - P[I]) * (Q[j] - P[J]) / GetDis(Q[j], P[I]) / GetDis(Q[j], P[J])); if (arc > Arc) Arc = arc, pt = j; }
		if (acos(-(ld)1) - Arc > eps)
		if (GetDis(Q[pt], rO) < rr) if (check(Q, m, Q[pt], P[I], P[J], pt)) return 0 * puts("YES");
	}
	else
	{
		if (check(Q, m, P[I], P[J], P[K])) return 0 * puts("YES");
		ld Arc = -1e9; int pt;
		for (int j = 1; j <= m; j++) { ld arc = acos((Q[j] - P[I]) * (Q[j] - P[J]) / GetDis(Q[j], P[I]) / GetDis(Q[j], P[J])); if (arc > Arc) Arc = arc, pt = j; }
		if (acos(-(ld)1) - Arc > eps)
		if (GetDis(Q[pt], rO) < rr) if (check(Q, m, Q[pt], P[I], P[J], pt)) return 0 * puts("YES");
		Arc = -1e9;
		for (int j = 1; j <= m; j++) { ld arc = acos((Q[j] - P[I]) * (Q[j] - P[K]) / GetDis(Q[j], P[I]) / GetDis(Q[j], P[K])); if (arc > Arc) Arc = arc, pt = j; }
		if (acosl(-(ld)1) - Arc > eps)
		if (GetDis(Q[pt], rO) < rr) if (check(Q, m, Q[pt], P[I], P[K], pt)) return 0 * puts("YES");
		Arc = -1e9;
		for (int j = 1; j <= m; j++) { ld arc = acos((Q[j] - P[J]) * (Q[j] - P[K]) / GetDis(Q[j], P[J]) / GetDis(Q[j], P[K])); if (arc > Arc) Arc = arc, pt = j; }
		if (acosl(-(ld)1) - Arc > eps)
		if (GetDis(Q[pt], rO) < rr) if (check(Q, m, Q[pt], P[J], P[K], pt)) return 0 * puts("YES");
	}
	
	swap(n, m), swap(P, Q);
	Calc(P, n);
	if (n == 2 || K == 0)
	{
		if (check(Q, m, P[I], P[J])) return 0 * puts("YES");
		ld Arc = -1e9; int pt;
		for (int j = 1; j <= m; j++) { ld arc = acos((Q[j] - P[I]) * (Q[j] - P[J]) / GetDis(Q[j], P[I]) / GetDis(Q[j], P[J])); if (arc > Arc) Arc = arc, pt = j; }
		if (acosl(-(ld)1) - Arc > eps)
		if (GetDis(Q[pt], rO) < rr) if (check(Q, m, Q[pt], P[I], P[J], pt)) return 0 * puts("YES");
	}
	else
	{
		if (check(Q, m, P[I], P[J], P[K])) return 0 * puts("YES");
		ld Arc = -1e9; int pt;
		for (int j = 1; j <= m; j++) { ld arc = acos((Q[j] - P[I]) * (Q[j] - P[J]) / GetDis(Q[j], P[I]) / GetDis(Q[j], P[J])); if (arc > Arc) Arc = arc, pt = j; }
		if (acosl(-(ld)1) - Arc > eps)
		if (GetDis(Q[pt], rO) < rr) if (check(Q, m, Q[pt], P[I], P[J], pt)) return 0 * puts("YES");
		Arc = -1e9;
		for (int j = 1; j <= m; j++) { ld arc = acos((Q[j] - P[I]) * (Q[j] - P[K]) / GetDis(Q[j], P[I]) / GetDis(Q[j], P[K])); if (arc > Arc) Arc = arc, pt = j; }
		if (acosl(-(ld)1) - Arc > eps)
		if (GetDis(Q[pt], rO) < rr) if (check(Q, m, Q[pt], P[I], P[K], pt)) return 0 * puts("YES");
		Arc = -1e9;
		for (int j = 1; j <= m; j++) { ld arc = acos((Q[j] - P[J]) * (Q[j] - P[K]) / GetDis(Q[j], P[J]) / GetDis(Q[j], P[K])); if (arc > Arc) Arc = arc, pt = j; }
		if (acosl(-(ld)1) - Arc > eps)
		if (GetDis(Q[pt], rO) < rr) if (check(Q, m, Q[pt], P[J], P[K], pt)) return 0 * puts("YES");
	}
	return 0 * puts("NO");
}
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