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Submission #107484

# Submission time Handle Problem Language Result Execution time Memory
107484 2019-04-24T18:08:37 Z gs14004 Demarcation (BOI14_demarcation) C++17
50 / 100
 201 ms 31340 KB 
#include <bits/stdc++.h>
using namespace std;
using lint = long long;
using pi = pair<int, int>;
const int MAXN = 400005;
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

# Verdict Execution time Memory Grader output
1 Correct 37 ms 13708 KB Output is correct
2 Correct 14 ms 11392 KB Output is correct
3 Correct 14 ms 11264 KB Output is correct
4 Correct 21 ms 12660 KB Output is correct
5 Correct 12 ms 11264 KB Output is correct
6 Correct 15 ms 11264 KB Output is correct
7 Correct 15 ms 11264 KB Output is correct
8 Correct 15 ms 11264 KB Output is correct
9 Correct 99 ms 23572 KB Output is correct
10 Correct 13 ms 11264 KB Output is correct
11 Correct 13 ms 11392 KB Output is correct
12 Correct 11 ms 11264 KB Output is correct
13 Correct 13 ms 11264 KB Output is correct

Subtask #2
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 12 ms 11264 KB Output is correct
2 Correct 13 ms 11264 KB Output is correct
3 Correct 13 ms 11264 KB Output is correct
4 Correct 13 ms 11328 KB Output is correct
5 Correct 12 ms 11264 KB Output is correct
6 Correct 14 ms 11264 KB Output is correct
7 Correct 14 ms 11264 KB Output is correct
8 Correct 13 ms 11264 KB Output is correct
9 Correct 15 ms 11264 KB Output is correct
10 Correct 13 ms 11264 KB Output is correct
11 Correct 13 ms 11264 KB Output is correct
12 Correct 13 ms 11264 KB Output is correct
13 Correct 15 ms 11264 KB Output is correct
14 Correct 14 ms 11264 KB Output is correct
15 Correct 14 ms 11264 KB Output is correct
16 Correct 15 ms 11264 KB Output is correct
17 Correct 13 ms 11264 KB Output is correct
18 Correct 14 ms 11392 KB Output is correct
19 Correct 13 ms 11264 KB Output is correct
20 Correct 14 ms 11392 KB Output is correct
21 Correct 13 ms 11392 KB Output is correct
22 Correct 13 ms 11392 KB Output is correct
23 Correct 13 ms 11264 KB Output is correct
24 Correct 13 ms 11264 KB Output is correct
25 Correct 14 ms 11252 KB Output is correct
26 Correct 15 ms 11264 KB Output is correct
27 Correct 16 ms 11392 KB Output is correct
28 Correct 51 ms 11264 KB Output is correct
29 Correct 13 ms 11264 KB Output is correct
30 Correct 16 ms 11264 KB Output is correct

Subtask #3
23.0 / 23.0

# Verdict Execution time Memory Grader output
1 Correct 12 ms 11264 KB Output is correct
2 Correct 13 ms 11440 KB Output is correct
3 Correct 12 ms 11264 KB Output is correct
4 Correct 13 ms 11264 KB Output is correct
5 Correct 15 ms 11264 KB Output is correct
6 Correct 13 ms 11264 KB Output is correct
7 Correct 12 ms 11264 KB Output is correct
8 Correct 14 ms 11392 KB Output is correct
9 Correct 14 ms 11264 KB Output is correct
10 Correct 12 ms 11264 KB Output is correct
11 Correct 13 ms 11264 KB Output is correct
12 Correct 14 ms 11264 KB Output is correct
13 Correct 12 ms 11264 KB Output is correct
14 Correct 12 ms 11264 KB Output is correct
15 Correct 13 ms 11264 KB Output is correct
16 Correct 12 ms 11264 KB Output is correct
17 Correct 12 ms 11264 KB Output is correct
18 Correct 12 ms 11264 KB Output is correct
19 Correct 12 ms 11392 KB Output is correct
20 Correct 13 ms 11264 KB Output is correct
21 Correct 13 ms 11392 KB Output is correct
22 Correct 13 ms 11392 KB Output is correct
23 Correct 12 ms 11264 KB Output is correct
24 Correct 14 ms 11264 KB Output is correct
25 Correct 13 ms 11264 KB Output is correct
26 Correct 13 ms 11264 KB Output is correct
27 Correct 13 ms 11264 KB Output is correct
28 Correct 14 ms 11392 KB Output is correct
29 Correct 13 ms 11264 KB Output is correct
30 Correct 15 ms 11264 KB Output is correct
31 Correct 13 ms 11392 KB Output is correct
32 Correct 14 ms 11644 KB Output is correct
33 Correct 13 ms 11648 KB Output is correct
34 Correct 14 ms 11632 KB Output is correct
35 Correct 14 ms 11640 KB Output is correct
36 Correct 13 ms 11644 KB Output is correct
37 Correct 14 ms 11604 KB Output is correct
38 Correct 16 ms 11628 KB Output is correct
39 Correct 14 ms 11392 KB Output is correct

Subtask #4
0 / 50.0

# Verdict Execution time Memory Grader output
1 Correct 28 ms 13708 KB Output is correct
2 Correct 14 ms 11324 KB Output is correct
3 Correct 13 ms 11264 KB Output is correct
4 Correct 21 ms 12788 KB Output is correct
5 Correct 12 ms 11264 KB Output is correct
6 Correct 15 ms 11264 KB Output is correct
7 Correct 13 ms 11264 KB Output is correct
8 Correct 12 ms 11264 KB Output is correct
9 Correct 99 ms 23572 KB Output is correct
10 Correct 13 ms 11264 KB Output is correct
11 Correct 12 ms 11392 KB Output is correct
12 Correct 12 ms 11264 KB Output is correct
13 Correct 13 ms 11264 KB Output is correct
14 Correct 13 ms 11264 KB Output is correct
15 Correct 12 ms 11264 KB Output is correct
16 Correct 12 ms 11264 KB Output is correct
17 Correct 12 ms 11264 KB Output is correct
18 Correct 12 ms 11264 KB Output is correct
19 Correct 13 ms 11264 KB Output is correct
20 Correct 12 ms 11392 KB Output is correct
21 Correct 12 ms 11392 KB Output is correct
22 Correct 12 ms 11392 KB Output is correct
23 Correct 14 ms 11264 KB Output is correct
24 Correct 14 ms 11392 KB Output is correct
25 Correct 12 ms 11292 KB Output is correct
26 Correct 13 ms 11392 KB Output is correct
27 Correct 11 ms 11264 KB Output is correct
28 Correct 12 ms 11392 KB Output is correct
29 Correct 14 ms 11264 KB Output is correct
30 Correct 13 ms 11264 KB Output is correct
31 Correct 12 ms 11264 KB Output is correct
32 Correct 12 ms 11264 KB Output is correct
33 Correct 13 ms 11264 KB Output is correct
34 Correct 13 ms 11264 KB Output is correct
35 Correct 13 ms 11644 KB Output is correct
36 Correct 16 ms 11824 KB Output is correct
37 Correct 16 ms 11648 KB Output is correct
38 Correct 17 ms 11520 KB Output is correct
39 Correct 16 ms 11644 KB Output is correct
40 Correct 15 ms 11632 KB Output is correct
41 Correct 16 ms 11752 KB Output is correct
42 Correct 13 ms 11392 KB Output is correct
43 Correct 17 ms 11960 KB Output is correct
44 Correct 60 ms 17412 KB Output is correct
45 Correct 48 ms 15944 KB Output is correct
46 Correct 48 ms 16484 KB Output is correct
47 Correct 45 ms 15444 KB Output is correct
48 Correct 55 ms 16672 KB Output is correct
49 Correct 76 ms 19432 KB Output is correct
50 Correct 111 ms 22512 KB Output is correct
51 Correct 201 ms 31340 KB Output is correct
52 Correct 135 ms 25856 KB Output is correct
53 Correct 190 ms 31196 KB Output is correct
54 Incorrect 190 ms 30132 KB Output isn't correct
55 Halted 0 ms 0 KB -