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답안 #107485

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
107485 2019-04-24T18:10:29 Z gs14004 경계 (BOI14_demarcation) C++17
50 / 100
 243 ms 23176 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;

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(sx < p1.first && p2.first < ex) return;
		if(p1.first <= sx && sx <= p2.first) sx = p2.first;
		if(p1.first <= ex && ex <= p2.first) ex = p1.first;
	}
	assert(sx < ex);
	rsx = sx;
	rex = ex;
	rsy = y;
	rey = y;
}

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

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

struct event2{
	int pos, s, e;
	bool operator<(const event2 &b)const{
		return pi(s, e) < pi(b.s, b.e);
	}
};

struct event3{
	int yc, xs, xe, act;
	bool operator<(const event3 &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;

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<event3> event;
	set<event2> 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 = [&](event2 b, int pos){
		if(b.pos < pos){
			rect_list.push_back({b.s, b.e, b.pos, pos});
		}
	};
	for(auto &i : event){
		if(i.act == 1){
			auto lbnd = s.lower_bound({-1, i.xs, i.xe});
			int curs = i.xs, cure = i.xe;
			if(lbnd != s.begin() && prev(lbnd)->e == i.xs){
				curs = prev(lbnd)->s;
				rect_close(*prev(lbnd), i.yc);
				s.erase(prev(lbnd));
			}
			if(lbnd != s.end() && lbnd->s == i.xe){
				cure = lbnd->e;
				rect_close(*lbnd, i.yc);
				s.erase(lbnd);
			}
			s.insert({i.yc, curs, cure});
		}
		else{
			auto lbnd = --s.lower_bound({-1, i.xe + 1, -1});
			if(pi(lbnd->s, lbnd->e) == pi(i.xs, i.xe)){
				rect_close(*lbnd, i.yc);
				s.erase(lbnd);
			}
			else if(lbnd->s == i.xs){
				rect_close(*lbnd, i.yc);
				s.erase(lbnd);
				s.insert({i.yc, i.xe, lbnd->e});
			}
			else if(lbnd->e == i.xe){
				rect_close(*lbnd, i.yc);
				s.erase(lbnd);
				s.insert({i.yc, lbnd->s, i.xs});
			}
			else{
				rect_close(*lbnd, i.yc);
				event2 nxt1 = {i.yc, lbnd->s, i.xs};
				event2 nxt2 = {i.yc, i.xe, lbnd->e};
				s.erase(lbnd);
				s.insert(nxt1);
				s.insert(nxt2);
			}
		}
	}
	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 >= 0 && 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;
				if(mok <= rect_list[i].ey){
					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:192:16: 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:207:17: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   for(int i=0; i<v.size(); ){
                ~^~~~~~~~~
demarcation.cpp:209:12: 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:304:16: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for(int i=0; i<rect_list.size(); i++){
               ~^~~~~~~~~~~~~~~~~
demarcation.cpp:311:16: 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:340:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  scanf("%d",&n);
  ~~~~~^~~~~~~~~
demarcation.cpp:343:8: 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 22 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 18 ms 4468 KB Output is correct
5 Correct 6 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 5 ms 3072 KB Output is correct
9 Correct 92 ms 15308 KB Output is correct
10 Correct 5 ms 3072 KB Output is correct
11 Correct 5 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 4 ms 3072 KB Output is correct
2 Correct 5 ms 3072 KB Output is correct
3 Correct 6 ms 3072 KB Output is correct
4 Correct 4 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 5 ms 3072 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 5 ms 3072 KB Output is correct
14 Correct 5 ms 3072 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 3044 KB Output is correct
18 Correct 6 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 6 ms 3072 KB Output is correct
22 Correct 5 ms 3072 KB Output is correct
23 Correct 4 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 6 ms 3072 KB Output is correct
30 Correct 23 ms 3044 KB Output is correct

Subtask #3
23.0 / 23.0

# 결과 실행 시간 메모리 Grader output
1 Correct 3 ms 3120 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 7 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 5 ms 3072 KB Output is correct
13 Correct 6 ms 3072 KB Output is correct
14 Correct 5 ms 3072 KB Output is correct
15 Correct 5 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 4 ms 3072 KB Output is correct
19 Correct 6 ms 3072 KB Output is correct
20 Correct 4 ms 3072 KB Output is correct
21 Correct 5 ms 3072 KB Output is correct
22 Correct 6 ms 3072 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 3072 KB Output is correct
26 Correct 4 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 6 ms 3072 KB Output is correct
30 Correct 5 ms 3072 KB Output is correct
31 Correct 5 ms 3072 KB Output is correct
32 Correct 6 ms 3328 KB Output is correct
33 Correct 8 ms 3440 KB Output is correct
34 Correct 9 ms 3440 KB Output is correct
35 Correct 6 ms 3396 KB Output is correct
36 Correct 6 ms 3452 KB Output is correct
37 Correct 7 ms 3440 KB Output is correct
38 Correct 8 ms 3436 KB Output is correct
39 Correct 6 ms 3200 KB Output is correct

Subtask #4
0 / 50.0

# 결과 실행 시간 메모리 Grader output
1 Correct 20 ms 5552 KB Output is correct
2 Correct 7 ms 3072 KB Output is correct
3 Correct 5 ms 3072 KB Output is correct
4 Correct 13 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 107 ms 15340 KB Output is correct
10 Correct 4 ms 3072 KB Output is correct
11 Correct 7 ms 3200 KB Output is correct
12 Correct 5 ms 3072 KB Output is correct
13 Correct 5 ms 3072 KB Output is correct
14 Correct 5 ms 3072 KB Output is correct
15 Correct 5 ms 3072 KB Output is correct
16 Correct 6 ms 3072 KB Output is correct
17 Correct 6 ms 3072 KB Output is correct
18 Correct 7 ms 3072 KB Output is correct
19 Correct 4 ms 3072 KB Output is correct
20 Correct 4 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 5 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 5 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 5 ms 3072 KB Output is correct
32 Correct 5 ms 3072 KB Output is correct
33 Correct 7 ms 3072 KB Output is correct
34 Correct 6 ms 3072 KB Output is correct
35 Correct 8 ms 3328 KB Output is correct
36 Correct 6 ms 3328 KB Output is correct
37 Correct 9 ms 3440 KB Output is correct
38 Correct 6 ms 3300 KB Output is correct
39 Correct 7 ms 3328 KB Output is correct
40 Correct 7 ms 3328 KB Output is correct
41 Correct 8 ms 3436 KB Output is correct
42 Correct 6 ms 3200 KB Output is correct
43 Correct 9 ms 3640 KB Output is correct
44 Correct 60 ms 9092 KB Output is correct
45 Correct 42 ms 7628 KB Output is correct
46 Correct 42 ms 8292 KB Output is correct
47 Correct 38 ms 7132 KB Output is correct
48 Correct 50 ms 8224 KB Output is correct
49 Correct 68 ms 11240 KB Output is correct
50 Correct 112 ms 14496 KB Output is correct
51 Correct 222 ms 23176 KB Output is correct
52 Correct 126 ms 17564 KB Output is correct
53 Correct 214 ms 23044 KB Output is correct
54 Incorrect 243 ms 21964 KB Output isn't correct
55 Halted 0 ms 0 KB -