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답안 #430514

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
430514 2021-06-16T15:08:46 Z koioi.org-koosaga Power plants (CPSPC17_power) C++17
100 / 100
 1053 ms 97244 KB 
#include <bits/stdc++.h>
using namespace std;
using lint = long long;
using pi = pair<int, int>;
#define sz(v) ((int)(v).size())
#define all(v) (v).begin(), (v).end()

const int MAXN = 100005;
typedef long long ll;

namespace DT{
	using ll = long long;

	bool ge(const ll& a, const ll& b) { return a >= b; }
	bool le(const ll& a, const ll& b) { return a <= b; }
	bool eq(const ll& a, const ll& b) { return a == b; }
	bool gt(const ll& a, const ll& b) { return a > b; }
	bool lt(const ll& a, const ll& b) { return a < b; }
	int sgn(const ll& a) { return a >= 0 ? a ? 1 : 0 : -1; }

	struct pt {
		int x, y;
		pt() { }
		pt(ll _x, ll _y) : x(_x), y(_y) { }
		bool operator<(const pt &p)const{
			return make_pair(x, y) < make_pair(p.x, p.y);
		}
		bool operator>(const pt &p)const{
			return make_pair(x, y) > make_pair(p.x, p.y);
		}

		pt operator-(const pt& p) const {
			return pt(x - p.x, y - p.y);
		}
		ll cross(const pt& p) const {
			return 1ll * x * p.y - 1ll * y * p.x;
		}
		ll cross(const pt& a, const pt& b) const {
			return (a - *this).cross(b - *this);
		}
		ll dot(const pt& p) const {
			return 1ll * x * p.x + 1ll * y * p.y;
		}
		ll dot(const pt& a, const pt& b) const {
			return (a - *this).dot(b - *this);
		}
		ll sqrLength() const {
			return this->dot(*this);
		}
		bool operator==(const pt& p) const {
			return eq(x, p.x) && eq(y, p.y);
		}
	};

	const pt inf_pt = pt(2e9, 2e9);

	struct QuadEdge {
		pt origin;
		QuadEdge* rot = nullptr;
		QuadEdge* onext = nullptr;
		bool used = false;
		QuadEdge* rev() const {
			return rot->rot;
		}
		QuadEdge* lnext() const {
			return rot->rev()->onext->rot;
		}
		QuadEdge* oprev() const {
			return rot->onext->rot;
		}
		pt dest() const {
			return rev()->origin;
		}
	};

	QuadEdge* make_edge(pt from, pt to) {
		QuadEdge* e1 = new QuadEdge;
		QuadEdge* e2 = new QuadEdge;
		QuadEdge* e3 = new QuadEdge;
		QuadEdge* e4 = new QuadEdge;
		e1->origin = from;
		e2->origin = to;
		e3->origin = e4->origin = inf_pt;
		e1->rot = e3;
		e2->rot = e4;
		e3->rot = e2;
		e4->rot = e1;
		e1->onext = e1;
		e2->onext = e2;
		e3->onext = e4;
		e4->onext = e3;
		return e1;
	}

	void splice(QuadEdge* a, QuadEdge* b) {
		swap(a->onext->rot->onext, b->onext->rot->onext);
		swap(a->onext, b->onext);
	}

	void delete_edge(QuadEdge* e) {
		splice(e, e->oprev());
		splice(e->rev(), e->rev()->oprev());
		delete e->rev()->rot;
		delete e->rev();
		delete e->rot;
		delete e;
	}

	QuadEdge* connect(QuadEdge* a, QuadEdge* b) {
		QuadEdge* e = make_edge(a->dest(), b->origin);
		splice(e, a->lnext());
		splice(e->rev(), b);
		return e;
	}

	bool left_of(pt p, QuadEdge* e) {
		return gt(p.cross(e->origin, e->dest()), 0);
	}

	bool right_of(pt p, QuadEdge* e) {
		return lt(p.cross(e->origin, e->dest()), 0);
	}

	template <class T>
		T det3(T a1, T a2, T a3, T b1, T b2, T b3, T c1, T c2, T c3) {
			return a1 * (b2 * c3 - c2 * b3) - a2 * (b1 * c3 - c1 * b3) +
				a3 * (b1 * c2 - c1 * b2);
		}

	bool in_circle(pt a, pt b, pt c, pt d) {
		long double det = -det3<long double>(b.x, b.y, b.sqrLength(), c.x, c.y,
				c.sqrLength(), d.x, d.y, d.sqrLength());
		det += det3<long double>(a.x, a.y, a.sqrLength(), c.x, c.y, c.sqrLength(), d.x,
				d.y, d.sqrLength());
		det -= det3<long double>(a.x, a.y, a.sqrLength(), b.x, b.y, b.sqrLength(), d.x,
				d.y, d.sqrLength());
		det += det3<long double>(a.x, a.y, a.sqrLength(), b.x, b.y, b.sqrLength(), c.x,
				c.y, c.sqrLength());
		if(fabs(det) > 1e18) return det > 0;
		else{

			ll det = -det3<ll>(b.x, b.y, b.sqrLength(), c.x, c.y,
					c.sqrLength(), d.x, d.y, d.sqrLength());
			det += det3<ll>(a.x, a.y, a.sqrLength(), c.x, c.y, c.sqrLength(), d.x,
					d.y, d.sqrLength());
			det -= det3<ll>(a.x, a.y, a.sqrLength(), b.x, b.y, b.sqrLength(), d.x,
					d.y, d.sqrLength());
			det += det3<ll>(a.x, a.y, a.sqrLength(), b.x, b.y, b.sqrLength(), c.x,
					c.y, c.sqrLength());
			return (det > 0);
		}
	}

	pair<QuadEdge*, QuadEdge*> build_tr(int l, int r, vector<pt>& p) {
		if (r - l + 1 == 2) {
			QuadEdge* res = make_edge(p[l], p[r]);
			return make_pair(res, res->rev());
		}
		if (r - l + 1 == 3) {
			QuadEdge *a = make_edge(p[l], p[l + 1]), *b = make_edge(p[l + 1], p[r]);
			splice(a->rev(), b);
			int sg = sgn(p[l].cross(p[l + 1], p[r]));
			if (sg == 0)
				return make_pair(a, b->rev());
			QuadEdge* c = connect(b, a);
			if (sg == 1)
				return make_pair(a, b->rev());
			else
				return make_pair(c->rev(), c);
		}
		int mid = (l + r) / 2;
		QuadEdge *ldo, *ldi, *rdo, *rdi;
		tie(ldo, ldi) = build_tr(l, mid, p);
		tie(rdi, rdo) = build_tr(mid + 1, r, p);
		while (true) {
			if (left_of(rdi->origin, ldi)) {
				ldi = ldi->lnext();
				continue;
			}
			if (right_of(ldi->origin, rdi)) {
				rdi = rdi->rev()->onext;
				continue;
			}
			break;
		}
		QuadEdge* basel = connect(rdi->rev(), ldi);
		auto valid = [&basel](QuadEdge* e) { return right_of(e->dest(), basel); };
		if (ldi->origin == ldo->origin)
			ldo = basel->rev();
		if (rdi->origin == rdo->origin)
			rdo = basel;
		while (true) {
			QuadEdge* lcand = basel->rev()->onext;
			if (valid(lcand)) {
				while (in_circle(basel->dest(), basel->origin, lcand->dest(),
							lcand->onext->dest())) {
					QuadEdge* t = lcand->onext;
					delete_edge(lcand);
					lcand = t;
				}
			}
			QuadEdge* rcand = basel->oprev();
			if (valid(rcand)) {
				while (in_circle(basel->dest(), basel->origin, rcand->dest(),
							rcand->oprev()->dest())) {
					QuadEdge* t = rcand->oprev();
					delete_edge(rcand);
					rcand = t;
				}
			}
			if (!valid(lcand) && !valid(rcand))
				break;
			if (!valid(lcand) ||
					(valid(rcand) && in_circle(lcand->dest(), lcand->origin,
											   rcand->origin, rcand->dest())))
				basel = connect(rcand, basel->rev());
			else
				basel = connect(basel->rev(), lcand->rev());
		}
		return make_pair(ldo, rdo);
	}

	vector<tuple<pt, pt, pt>> delaunay(vector<pt> p) {
		sort(p.begin(), p.end(), [](const pt& a, const pt& b) {
				return lt(a.x, b.x) || (eq(a.x, b.x) && lt(a.y, b.y));
				});
		auto res = build_tr(0, (int)p.size() - 1, p);
		QuadEdge* e = res.first;
		vector<QuadEdge*> edges = {e};
		while (lt(e->onext->dest().cross(e->dest(), e->origin), 0))
			e = e->onext;
		auto add = [&p, &e, &edges]() {
			QuadEdge* curr = e;
			do {
				curr->used = true;
				p.push_back(curr->origin);
				edges.push_back(curr->rev());
				curr = curr->lnext();
			} while (curr != e);
		};
		add();
		p.clear();
		int kek = 0;
		while (kek < (int)edges.size()) {
			if (!(e = edges[kek++])->used)
				add();
		}
		vector<tuple<pt, pt, pt>> ans;
		for (int i = 0; i < (int)p.size(); i += 3) {
			ans.push_back(make_tuple(p[i], p[i + 1], p[i + 2]));
		}
		return ans;
	}

		bool in_triangle(pt a, pt b, pt c, pt d){
		if((b - a).cross(c - a) < 0) swap(b, c);
		if((b - a).cross(d - a) < 0) return 0;
		if((c - b).cross(d - b) < 0) return 0;
		if((a - c).cross(d - c) < 0) return 0;
		return 1;
	}


}

struct edge{
	int s, e; lint x;
	bool operator<(const edge &e)const{
		return x < e.x;
	}
};

struct disj{
	int pa[MAXN];
	void init(int n){
		iota(pa, pa + n, 0);
	}
	int find(int x){
		return pa[x] = (pa[x] == x ? x : find(pa[x]));
	}
	bool uni(int p, int q){
		p = find(p); q = find(q);
		if(p == q) return 0;
		pa[q] = p; return 1;
	}
}disj;
namespace GGD{

	int n;
	pi a[100005];

	bool cmp(pi a, pi b){return a.second < b.second;}
	lint dist(pi x, pi y){return 1ll*(y.second - x.second) * (y.second - x.second) + 1ll*(y.first - x.first) * (y.first - x.first);}

	lint closest(int s, int e){
		if(s == e-2){
			return min(min(dist(a[s],a[s+1]),dist(a[s+1],a[s+2])),dist(a[s],a[s+2]));
		}
		if(s == e-1){
			return dist(a[s],a[e]);
		}
		int m = (s+e)/2;
		lint res = min(closest(s,m),closest(m+1,e));

		vector<pi> strip;
		for (int i=s; i<=e; i++) {
			if(1ll * abs(a[i].first - a[m].first) * abs(a[i].first - a[m].first) < res){
				strip.push_back(a[i]);
			}
		}
		sort(strip.begin(),strip.end(),cmp);
		for (int i=0; i<strip.size(); i++) {
			for (int j=i+1; j<strip.size() &&
				1ll*	(strip[j].second - strip[i].second) * (strip[j].second - strip[i].second) < res; j++){
				res = min(res,dist(strip[j],strip[i]));
			}
		}
		return res;
	}

	lint getdist(vector<DT::pt> v){
		n = sz(v);
		for (int i=0; i<n; i++) {
			a[i] = pi(v[i].x, v[i].y);
		}
		sort(a,a+n);
		return closest(0, n - 1);
	}

};

vector<int> gph[MAXN];
int col[MAXN];

lint dist(DT::pt a, DT::pt b){
	lint dx = b.x - a.x;
	lint dy = b.y - a.y;
	return dx*dx+dy*dy;
}



void dfs(int x, int c, int p = -1){
	col[x] = c;
	for(auto &i : gph[x]){
		if(i != p) dfs(i, 3-c, x);
	}
}

int main(){
	int n;
	scanf("%d",&n);
	vector<DT::pt> a(n);
	map<DT::pt, int> mp;
	int cnt = 0;
	for(auto &i : a){
		scanf("%d %d",&i.x,&i.y);
		mp[i] = cnt++;
	}
	vector<edge> v;
	auto dt = DT::delaunay(a);
	for(int i=0; i<sz(dt); i++){
		auto [x, y, z] = dt[i];
		auto edges = {make_pair(x, y), make_pair(x, z), make_pair(y, z)};
		for(auto &[x, y] : edges){
			v.push_back({mp[x], mp[y], dist(x,y)});
		}
	}
	sort(all(v));
	disj.init(n);
	for(int i=0; i<sz(v); i++){
		if(disj.uni(v[i].s, v[i].e)){
			gph[v[i].s].push_back(v[i].e);
			gph[v[i].e].push_back(v[i].s);
		}
	}
	dfs(0, 1);
	{
	vector<DT::pt> v[2];
	for(int i = 0; i < n; i++){
		v[col[i] - 1].push_back(a[i]);
	}
	printf("%lld\n", min(GGD::getdist(v[0]), GGD::getdist(v[1])));
	for(int i = 0; i < 2; i++){
		printf("%d\n", sz(v[i]));
		for(int j = 0; j < n; j++){
			if(col[j] == i + 1) printf("%d ", j + 1);
		}
		puts("");
	}
	}
}

Compilation message

Main.cpp: In function 'lint GGD::closest(int, int)':
Main.cpp:312:18: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  312 |   for (int i=0; i<strip.size(); i++) {
      |                 ~^~~~~~~~~~~~~
Main.cpp:313:21: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  313 |    for (int j=i+1; j<strip.size() &&
      |                    ~^~~~~~~~~~~~~
Main.cpp: In function 'int main()':
Main.cpp:352:7: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  352 |  scanf("%d",&n);
      |  ~~~~~^~~~~~~~~
Main.cpp:357:8: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  357 |   scanf("%d %d",&i.x,&i.y);
      |   ~~~~~^~~~~~~~~~~~~~~~~~~

Subtask #1
10.0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 2764 KB Output is correct
2 Correct 2 ms 2764 KB Output is correct
3 Correct 2 ms 2636 KB Output is correct
4 Correct 2 ms 2636 KB Output is correct
5 Correct 2 ms 2636 KB Output is correct
6 Correct 3 ms 2636 KB Output is correct
7 Correct 3 ms 2764 KB Output is correct
8 Correct 3 ms 2648 KB Output is correct
9 Correct 3 ms 2636 KB Output is correct

Subtask #2
25.0 / 25.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 2764 KB Output is correct
2 Correct 2 ms 2764 KB Output is correct
3 Correct 2 ms 2636 KB Output is correct
4 Correct 2 ms 2636 KB Output is correct
5 Correct 2 ms 2636 KB Output is correct
6 Correct 3 ms 2636 KB Output is correct
7 Correct 3 ms 2764 KB Output is correct
8 Correct 3 ms 2648 KB Output is correct
9 Correct 3 ms 2636 KB Output is correct
10 Correct 17 ms 4576 KB Output is correct
11 Correct 14 ms 4436 KB Output is correct
12 Correct 16 ms 4428 KB Output is correct
13 Correct 10 ms 4556 KB Output is correct
14 Correct 10 ms 4112 KB Output is correct
15 Correct 11 ms 4444 KB Output is correct
16 Correct 14 ms 4480 KB Output is correct
17 Correct 15 ms 4524 KB Output is correct
18 Correct 11 ms 4340 KB Output is correct

Subtask #3
65.0 / 65.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 2764 KB Output is correct
2 Correct 2 ms 2764 KB Output is correct
3 Correct 2 ms 2636 KB Output is correct
4 Correct 2 ms 2636 KB Output is correct
5 Correct 2 ms 2636 KB Output is correct
6 Correct 3 ms 2636 KB Output is correct
7 Correct 3 ms 2764 KB Output is correct
8 Correct 3 ms 2648 KB Output is correct
9 Correct 3 ms 2636 KB Output is correct
10 Correct 17 ms 4576 KB Output is correct
11 Correct 14 ms 4436 KB Output is correct
12 Correct 16 ms 4428 KB Output is correct
13 Correct 10 ms 4556 KB Output is correct
14 Correct 10 ms 4112 KB Output is correct
15 Correct 11 ms 4444 KB Output is correct
16 Correct 14 ms 4480 KB Output is correct
17 Correct 15 ms 4524 KB Output is correct
18 Correct 11 ms 4340 KB Output is correct
19 Correct 1045 ms 97020 KB Output is correct
20 Correct 950 ms 91252 KB Output is correct
21 Correct 1053 ms 95384 KB Output is correct
22 Correct 554 ms 97164 KB Output is correct
23 Correct 469 ms 65104 KB Output is correct
24 Correct 619 ms 95692 KB Output is correct
25 Correct 980 ms 96884 KB Output is correct
26 Correct 1026 ms 97244 KB Output is correct
27 Correct 603 ms 69456 KB Output is correct