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답안 #107474

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
107474 2019-04-24T17:03:15 Z gs14004 경계 (BOI14_demarcation) C++17
50 / 100
 254 ms 25132 KB 
#include <bits/stdc++.h>
using namespace std;
using lint = long long;
using pi = pair<int, int>;
const int MAXN = 100005;
const int oo = 1.05e9;

int n;
vector<pi> a;

lint ccw(pi a, pi b, pi c){
	int dx1 = b.first - a.first;
	int dy1 = b.second - a.second;
	int dx2 = c.first - a.first;
	int dy2 = c.second - a.second;
	return 1ll * dx1 * dy2 - 1ll * dy1 * dx2;
}

void normalize(vector<pi> &v){
	int minx = oo, miny = oo;
	for(auto &i : v){
		minx = min(minx, i.first);
		miny = min(miny, i.second);
	}
	for(auto &i : v){
		i.first -= minx;
		i.second -= miny;
	}
	rotate(v.begin(), min_element(v.begin(), v.end()), v.end());
}

void reflect(vector<pi> &v){
	for(auto &i : v){
		i.first = -i.first;
	}
	normalize(v);
}

void turn(vector<pi> &v){
	for(auto &i : v){
		i = pi(-i.second, i.first);
	}
	normalize(v);
}

lint get_area(vector<pi> &v){
	lint ret = 0;
	for(int i=2; i<v.size(); i++){
		ret += ccw(v[0], v[i-1], v[i]);
	}
	return ret;
}

bool hapdong(vector<pi> &v1, vector<pi> &v2){
	normalize(v1);
	normalize(v2);
	for(int i=0; i<4; i++){
		turn(v2);
		if(v1 == v2) return 1;
	}
	reflect(v2);
	for(int i=0; i<4; i++){
		turn(v2);
		if(v1 == v2) return 1;
	}
	reverse(v2.begin(), v2.end());
	normalize(v2);
	for(int i=0; i<4; i++){
		turn(v2);
		if(v1 == v2) return 1;
	}
	reflect(v2);
	for(int i=0; i<4; i++){
		turn(v2);
		if(v1 == v2) return 1;
	}
	return 0;
}

bool mid(int s, int x, int e){
	return 1ll * (e-x) * (x-s) >= 0;
}

bool smid(int s, int x, int e){
	return 1ll * (e-x) * (x-s) > 0;
}

void cut_polygon(vector<pi> &in, vector<pi> &out1, vector<pi> &out2, int sx, int ex, int y){
	if(get_area(in) < 0) reverse(in.begin(), in.end());
	int p = min_element(in.begin(), in.end(), [&](const pi &a, const pi &b){
		return a.second < b.second;
	}) - in.begin();
	if(in[p].second >= y){
		out2 = in;
		return;
	}
	int cpos = 0;
	for(int i=0; i<in.size(); i++){
		pi p1 = in[p%in.size()];
		pi p2 = in[(p+1)%in.size()];
		p++;
		if(p1.second != p2.second && smid(p1.second, y, p2.second) && mid(sx, p1.first, ex)){
			if(cpos == 0) out1.push_back(p1);
			else out2.push_back(p1);
			out1.push_back(pi(p1.first, y));
			out2.push_back(pi(p1.first, y));
			cpos ^= 1;
		}
		else if(p1.second == y && p2.second == y && (mid(sx, p1.first, ex) || mid(sx, p2.first, ex))){
			if(sx != -oo && ex != oo && smid(sx, p1.first, ex) && smid(sx, p2.first, ex)){
				out1 = in;
				out2.clear();
				return;
			}
			if(cpos == 0) out1.push_back(p1);
			else out2.push_back(p1);
			cpos ^= 1;
		}
		else{
			if(cpos == 0) out1.push_back(p1);
			else out2.push_back(p1);
		}
	}
}

int rsx = -1, rsy = -1, rex = -1, rey = -1;
 
bool non_enclosing(int sx, int ex, int y){
	for(int i=0; i<n; i++){
		pi p1 = a[i];
		pi p2 = a[(i+1)%n];
		if(p1.second != y || p2.second != y) continue;
		if(p1.first > p2.first) swap(p1, p2);
		if(smid(sx, p1.first, ex) && smid(sx, p2.first, ex)) return 0;
	}
	return 1;
}

void save_results(int sx, int ex, int y){
	for(int i=0; i<n; i++){
		pi p1 = a[i];
		pi p2 = a[(i+1)%n];
		if(p1.second != y || p2.second != y) continue;
		if(p1.first > p2.first) swap(p1, p2);
		if(p1.first <= sx) sx = max(sx, p2.first);
		if(p2.first >= ex) ex = min(ex, p1.first);
	}
	rsx = sx;
	rex = ex;
	rsy = y;
	rey = y;
}

struct rect{
	int sx, ex, sy, ey;
};

struct block{
	int pos, s, e;
	bool operator<(const block &b)const{
		return pi(s, e) < pi(b.s, b.e);
	}
};

struct swp{
	int yc, xs, xe, act;
	bool operator<(const swp &b)const{
		return pi(yc, -act) < pi(b.yc, -b.act);
	}
};

struct disj{
	int pa[MAXN];
	void init(){
		iota(pa, pa + MAXN, 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;

struct event1{
	int x, y, idx, mode;
	bool operator<(const event1 &sg)const{
		return pi(x, y) < pi(sg.x, sg.y);
	}
};

bool insec_by_edge(rect x, rect y){
	x.sx = max(x.sx, y.sx);
	x.ex = min(x.ex, y.ex);
	x.sy = max(x.sy, y.sy);
	x.ey = min(x.ey, y.ey);
	if(x.sx > x.ex || x.sy > x.ey) return 0;
	if(x.sx < x.ex && x.sy < x.ey) assert(0);
	if(pi(x.sx, x.sy) == pi(x.ex, x.ey)) return 0;
	return 1;
}

lint area[MAXN];
lint sum[MAXN], msz[MAXN];
vector<int> gph[MAXN];

void build_tree(vector<rect> v){
	vector<event1> xl, yl;
	for(int i=0; i<v.size(); i++){
		xl.push_back({v[i].sx, v[i].sy, i, +1});
		xl.push_back({v[i].sx, v[i].ey, i, -1});
		xl.push_back({v[i].ex, v[i].sy, i, +1});
		xl.push_back({v[i].ex, v[i].ey, i, -1});

		yl.push_back({v[i].sy, v[i].sx, i, +1});
		yl.push_back({v[i].sy, v[i].ex, i, -1});
		yl.push_back({v[i].ey, v[i].sx, i, +1});
		yl.push_back({v[i].ey, v[i].ex, i, -1});
	}
	disj.init();
	auto proc = [&](vector<event1> v){
		sort(v.begin(), v.end());
		set<int> s;
		for(int i=0; i<v.size(); ){
			int e = i;
			while(e < v.size() && pi(v[i].x, v[i].y) == pi(v[e].x, v[e].y)) e++;
			for(int j=i; j<e; j++){
				if(v[j].mode == +1) s.insert(v[j].idx);
				else s.erase(v[j].idx);
			}
			if(s.size() > 1){
				assert(s.size() == 2);
				if(disj.uni(*s.rbegin(), *s.begin())){
					int x = *s.rbegin();
					int y = *s.begin();
					gph[x].push_back(y);
					gph[y].push_back(x);
				}
			}
			i = e;
		}
	};
	proc(xl); proc(yl);
}

void dfs(int x, int p){
	sum[x] = area[x];
	msz[x] = 0;
	for(auto &i : gph[x]){
		if(i != p){
			dfs(i, x);
			sum[x] += sum[i];
			msz[x] = max(msz[x], sum[i]);
		}
	}
}

void solve(){
	vector<swp> event;
	set<block> s;
	vector<rect> rect_list;
	for(int i=0; i<n; i++){
		pi p1 = a[i];
		pi p2 = a[(i+1)%n];
		if(p1.first == p2.first) continue;
		if(p1.first < p2.first){
			event.push_back({p1.second, p1.first, p2.first, +1});
		}
		else{
			event.push_back({p1.second, p2.first, p1.first, -1});
		}
	}
	sort(event.begin(), event.end());
	auto rect_close = [&](block b, int pos){
		if(b.pos < pos){
			rect_list.push_back({b.s, b.e, b.pos, pos});
		}
	};
	for(int i=0; i<event.size(); ){
		int e = i;
		while(e < event.size() && event[e].yc == event[i].yc){
			if(event[e].act == 1){
				auto lbnd = s.lower_bound({-1, event[e].xs, event[e].xe});
				int curs = event[e].xs;
				int cure = event[e].xe;
				if(lbnd != s.begin() && prev(lbnd)->e == event[e].xs){
					curs = prev(lbnd)->s;
					rect_close(*prev(lbnd), event[e].yc);
					s.erase(prev(lbnd));
				}
				if(lbnd != s.end() && lbnd->s == event[e].xe){
					cure = lbnd->e;
					rect_close(*lbnd, event[e].yc);
					s.erase(lbnd);
				}
				s.insert({event[e].yc, curs, cure});
			}
			else{
				auto lbnd = --s.lower_bound({-1, event[e].xe + 1, -1});
				if(pi(lbnd->s, lbnd->e) == pi(event[e].xs, event[e].xe)){
					rect_close(*lbnd, event[e].yc);
					s.erase(lbnd);
				}
				else if(lbnd->s == event[e].xs){
					rect_close(*lbnd, event[e].yc);
					s.erase(lbnd);
					s.insert({event[e].yc, event[e].xe, lbnd->e});
				}
				else if(lbnd->e == event[e].xe){
					rect_close(*lbnd, event[e].yc);
					s.erase(lbnd);
					s.insert({event[e].yc, lbnd->s, event[e].xs});
				}
				else{
					rect_close(*lbnd, event[e].yc);
					block nxt1 = {event[e].yc, lbnd->s, event[e].xs};
					block nxt2 = {event[e].yc, event[e].xe, lbnd->e};
					s.erase(lbnd);
					s.insert(nxt1);
					s.insert(nxt2);
				}
			}
			e++;
		}
		i = e;
	}
	for(int i=0; i<rect_list.size(); i++){
		gph[i].clear();
		area[i] = 1ll * (rect_list[i].ex - rect_list[i].sx) * (rect_list[i].ey - rect_list[i].sy);
	}
	build_tree(rect_list);
	dfs(0, -1);
	if(sum[0] % 2) return;
	for(int i=0; i<rect_list.size(); i++){
		lint mxvi = max(msz[i], sum[0] - sum[i]);
		if(mxvi <= sum[0] / 2){
			lint lower_line = 0;
			lint thres = sum[0] / 2;
			for(auto &j : gph[i]){
				if(rect_list[j].sy < rect_list[i].sy){
					dfs(j, i);
					lower_line += sum[j];
				}
			}
			thres -= lower_line;
			if(thres % (rect_list[i].ex - rect_list[i].sx) == 0){
				lint mok = thres / (rect_list[i].ex - rect_list[i].sx);
				mok += rect_list[i].sy;
				vector<pi> v1, v2;
				cut_polygon(a, v1, v2, rect_list[i].sx, rect_list[i].ex, mok);
				if(hapdong(v1, v2)){
					save_results(rect_list[i].sx, rect_list[i].ex, mok);
				}
			}
			break;
		}
	}
}

int main(){
	scanf("%d",&n);
	a.resize(n);
	for(int i=0; i<n; i++){
		scanf("%d %d",&a[i].first, &a[i].second);
	}
	for(int i=0; i<2; i++){
		auto area = get_area(a);
		if(area < 0) reverse(a.begin(), a.end());
		solve();
		if(i == 1) swap(rsx, rsy), swap(rex, rey);
		if(rsx != -1){
			printf("%d %d %d %d",rsx, rsy, rex, rey);
			return 0;
		}
		for(int i=0; i<n; i++){
			swap(a[i].first, a[i].second);
		}
	}
	puts("NO");
}

Compilation message

demarcation.cpp: In function 'lint get_area(std::vector<std::pair<int, int> >&)':
demarcation.cpp:48:16: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for(int i=2; i<v.size(); i++){
               ~^~~~~~~~~
demarcation.cpp: In function 'void cut_polygon(std::vector<std::pair<int, int> >&, std::vector<std::pair<int, int> >&, std::vector<std::pair<int, int> >&, int, int, int)':
demarcation.cpp:98:16: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for(int i=0; i<in.size(); i++){
               ~^~~~~~~~~~
demarcation.cpp: In function 'void build_tree(std::vector<rect>)':
demarcation.cpp:212:16: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for(int i=0; i<v.size(); i++){
               ~^~~~~~~~~
demarcation.cpp: In lambda function:
demarcation.cpp:227:17: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   for(int i=0; i<v.size(); ){
                ~^~~~~~~~~
demarcation.cpp:229:12: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
    while(e < v.size() && pi(v[i].x, v[i].y) == pi(v[e].x, v[e].y)) e++;
          ~~^~~~~~~~~~
demarcation.cpp: In function 'void solve()':
demarcation.cpp:282:16: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for(int i=0; i<event.size(); ){
               ~^~~~~~~~~~~~~
demarcation.cpp:284:11: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   while(e < event.size() && event[e].yc == event[i].yc){
         ~~^~~~~~~~~~~~~~
demarcation.cpp:330:16: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for(int i=0; i<rect_list.size(); i++){
               ~^~~~~~~~~~~~~~~~~
demarcation.cpp:337:16: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for(int i=0; i<rect_list.size(); i++){
               ~^~~~~~~~~~~~~~~~~
demarcation.cpp: In function 'int main()':
demarcation.cpp:364:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  scanf("%d",&n);
  ~~~~~^~~~~~~~~
demarcation.cpp:367:8: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
   scanf("%d %d",&a[i].first, &a[i].second);
   ~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Subtask #1
12.0 / 12.0

# 결과 실행 시간 메모리 Grader output
1 Correct 24 ms 5516 KB Output is correct
2 Correct 5 ms 3072 KB Output is correct
3 Correct 6 ms 3072 KB Output is correct
4 Correct 18 ms 4468 KB Output is correct
5 Correct 5 ms 3044 KB Output is correct
6 Correct 4 ms 3072 KB Output is correct
7 Correct 5 ms 3072 KB Output is correct
8 Correct 5 ms 3072 KB Output is correct
9 Correct 93 ms 15476 KB Output is correct
10 Correct 5 ms 3072 KB Output is correct
11 Correct 6 ms 3200 KB Output is correct
12 Correct 5 ms 3072 KB Output is correct
13 Correct 5 ms 3072 KB Output is correct

Subtask #2
15.0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Correct 5 ms 3072 KB Output is correct
2 Correct 5 ms 3072 KB Output is correct
3 Correct 5 ms 3072 KB Output is correct
4 Correct 5 ms 3072 KB Output is correct
5 Correct 5 ms 3072 KB Output is correct
6 Correct 5 ms 3072 KB Output is correct
7 Correct 5 ms 3072 KB Output is correct
8 Correct 4 ms 3072 KB Output is correct
9 Correct 5 ms 3072 KB Output is correct
10 Correct 4 ms 3072 KB Output is correct
11 Correct 4 ms 3072 KB Output is correct
12 Correct 4 ms 3072 KB Output is correct
13 Correct 4 ms 3072 KB Output is correct
14 Correct 5 ms 3120 KB Output is correct
15 Correct 5 ms 3072 KB Output is correct
16 Correct 5 ms 3072 KB Output is correct
17 Correct 5 ms 3072 KB Output is correct
18 Correct 6 ms 3072 KB Output is correct
19 Correct 4 ms 3200 KB Output is correct
20 Correct 4 ms 3072 KB Output is correct
21 Correct 5 ms 3200 KB Output is correct
22 Correct 5 ms 3072 KB Output is correct
23 Correct 6 ms 3072 KB Output is correct
24 Correct 5 ms 3072 KB Output is correct
25 Correct 5 ms 3072 KB Output is correct
26 Correct 4 ms 3072 KB Output is correct
27 Correct 5 ms 3072 KB Output is correct
28 Correct 5 ms 3072 KB Output is correct
29 Correct 4 ms 3072 KB Output is correct
30 Correct 4 ms 3072 KB Output is correct

Subtask #3
23.0 / 23.0

# 결과 실행 시간 메모리 Grader output
1 Correct 5 ms 3072 KB Output is correct
2 Correct 5 ms 3072 KB Output is correct
3 Correct 5 ms 3072 KB Output is correct
4 Correct 5 ms 3072 KB Output is correct
5 Correct 5 ms 3072 KB Output is correct
6 Correct 5 ms 3072 KB Output is correct
7 Correct 6 ms 3072 KB Output is correct
8 Correct 6 ms 3200 KB Output is correct
9 Correct 5 ms 3072 KB Output is correct
10 Correct 6 ms 3072 KB Output is correct
11 Correct 6 ms 3072 KB Output is correct
12 Correct 6 ms 3072 KB Output is correct
13 Correct 7 ms 3072 KB Output is correct
14 Correct 5 ms 3072 KB Output is correct
15 Correct 4 ms 3072 KB Output is correct
16 Correct 5 ms 3072 KB Output is correct
17 Correct 6 ms 3072 KB Output is correct
18 Correct 5 ms 3072 KB Output is correct
19 Correct 6 ms 3200 KB Output is correct
20 Correct 5 ms 3072 KB Output is correct
21 Correct 5 ms 3072 KB Output is correct
22 Correct 5 ms 3072 KB Output is correct
23 Correct 6 ms 3072 KB Output is correct
24 Correct 5 ms 3072 KB Output is correct
25 Correct 4 ms 3072 KB Output is correct
26 Correct 6 ms 3072 KB Output is correct
27 Correct 5 ms 3044 KB Output is correct
28 Correct 5 ms 3072 KB Output is correct
29 Correct 6 ms 3072 KB Output is correct
30 Correct 5 ms 3072 KB Output is correct
31 Correct 4 ms 3072 KB Output is correct
32 Correct 6 ms 3328 KB Output is correct
33 Correct 6 ms 3328 KB Output is correct
34 Correct 7 ms 3440 KB Output is correct
35 Correct 6 ms 3320 KB Output is correct
36 Correct 8 ms 3328 KB Output is correct
37 Correct 6 ms 3328 KB Output is correct
38 Correct 9 ms 3436 KB Output is correct
39 Correct 5 ms 3196 KB Output is correct

Subtask #4
0 / 50.0

# 결과 실행 시간 메모리 Grader output
1 Correct 23 ms 5516 KB Output is correct
2 Correct 5 ms 3072 KB Output is correct
3 Correct 5 ms 3072 KB Output is correct
4 Correct 14 ms 4468 KB Output is correct
5 Correct 5 ms 3072 KB Output is correct
6 Correct 5 ms 3072 KB Output is correct
7 Correct 5 ms 3072 KB Output is correct
8 Correct 5 ms 3072 KB Output is correct
9 Correct 88 ms 15296 KB Output is correct
10 Correct 5 ms 3072 KB Output is correct
11 Correct 5 ms 3200 KB Output is correct
12 Correct 4 ms 3072 KB Output is correct
13 Correct 5 ms 3072 KB Output is correct
14 Correct 27 ms 3072 KB Output is correct
15 Correct 5 ms 3072 KB Output is correct
16 Correct 5 ms 3200 KB Output is correct
17 Correct 5 ms 3072 KB Output is correct
18 Correct 5 ms 3072 KB Output is correct
19 Correct 5 ms 3072 KB Output is correct
20 Correct 5 ms 3072 KB Output is correct
21 Correct 5 ms 3072 KB Output is correct
22 Correct 5 ms 3200 KB Output is correct
23 Correct 5 ms 3072 KB Output is correct
24 Correct 5 ms 3072 KB Output is correct
25 Correct 5 ms 3116 KB Output is correct
26 Correct 6 ms 3072 KB Output is correct
27 Correct 4 ms 3072 KB Output is correct
28 Correct 5 ms 3072 KB Output is correct
29 Correct 5 ms 3072 KB Output is correct
30 Correct 5 ms 3072 KB Output is correct
31 Correct 4 ms 3072 KB Output is correct
32 Correct 5 ms 3200 KB Output is correct
33 Correct 5 ms 3116 KB Output is correct
34 Correct 5 ms 3072 KB Output is correct
35 Correct 7 ms 3328 KB Output is correct
36 Correct 6 ms 3440 KB Output is correct
37 Correct 7 ms 3440 KB Output is correct
38 Correct 6 ms 3320 KB Output is correct
39 Correct 7 ms 3328 KB Output is correct
40 Correct 6 ms 3328 KB Output is correct
41 Correct 8 ms 3436 KB Output is correct
42 Correct 8 ms 3200 KB Output is correct
43 Correct 11 ms 3768 KB Output is correct
44 Correct 65 ms 9584 KB Output is correct
45 Correct 44 ms 8008 KB Output is correct
46 Correct 44 ms 8520 KB Output is correct
47 Correct 42 ms 7380 KB Output is correct
48 Correct 46 ms 8580 KB Output is correct
49 Correct 76 ms 12008 KB Output is correct
50 Correct 104 ms 14928 KB Output is correct
51 Correct 211 ms 25132 KB Output is correct
52 Correct 137 ms 19600 KB Output is correct
53 Correct 254 ms 24316 KB Output is correct
54 Incorrect 199 ms 23004 KB Output isn't correct
55 Halted 0 ms 0 KB -