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Submission #107483

# Submission time Handle Problem Language Result Execution time Memory
107483 2019-04-24T18:05:03 Z gs14004 Demarcation (BOI14_demarcation) C++17
50 / 100
 198 ms 23400 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

# Verdict Execution time Memory Grader output
1 Correct 23 ms 5516 KB Output is correct
2 Correct 5 ms 3072 KB Output is correct
3 Correct 4 ms 3072 KB Output is correct
4 Correct 12 ms 4468 KB Output is correct
5 Correct 4 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 100 ms 15408 KB Output is correct
10 Correct 5 ms 2948 KB Output is correct
11 Correct 5 ms 3200 KB Output is correct
12 Correct 5 ms 3072 KB Output is correct
13 Correct 4 ms 3072 KB Output is correct

Subtask #2
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 4 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 6 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 5 ms 3072 KB Output is correct
12 Correct 5 ms 3072 KB Output is correct
13 Correct 2 ms 3072 KB Output is correct
14 Correct 4 ms 3072 KB Output is correct
15 Correct 4 ms 3072 KB Output is correct
16 Correct 6 ms 3072 KB Output is correct
17 Correct 5 ms 3072 KB Output is correct
18 Correct 5 ms 3200 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 4 ms 3072 KB Output is correct
24 Correct 4 ms 3072 KB Output is correct
25 Correct 5 ms 3072 KB Output is correct
26 Correct 6 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 6 ms 3120 KB Output is correct

Subtask #3
23.0 / 23.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 3072 KB Output is correct
2 Correct 6 ms 3072 KB Output is correct
3 Correct 6 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 6 ms 3328 KB Output is correct
7 Correct 4 ms 3072 KB Output is correct
8 Correct 5 ms 3072 KB Output is correct
9 Correct 5 ms 3116 KB Output is correct
10 Correct 4 ms 3072 KB Output is correct
11 Correct 4 ms 3072 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 2944 KB Output is correct
16 Correct 5 ms 3072 KB Output is correct
17 Correct 5 ms 3072 KB Output is correct
18 Correct 3 ms 3072 KB Output is correct
19 Correct 5 ms 3072 KB Output is correct
20 Correct 6 ms 3072 KB Output is correct
21 Correct 5 ms 3072 KB Output is correct
22 Correct 6 ms 3200 KB Output is correct
23 Correct 5 ms 3072 KB Output is correct
24 Correct 7 ms 3072 KB Output is correct
25 Correct 5 ms 3044 KB Output is correct
26 Correct 6 ms 3072 KB Output is correct
27 Correct 4 ms 3072 KB Output is correct
28 Correct 6 ms 3072 KB Output is correct
29 Correct 5 ms 3092 KB Output is correct
30 Correct 6 ms 3072 KB Output is correct
31 Correct 5 ms 3200 KB Output is correct
32 Correct 8 ms 3328 KB Output is correct
33 Correct 7 ms 3328 KB Output is correct
34 Correct 7 ms 3440 KB Output is correct
35 Correct 8 ms 3448 KB Output is correct
36 Correct 7 ms 3328 KB Output is correct
37 Correct 7 ms 3440 KB Output is correct
38 Correct 10 ms 3436 KB Output is correct
39 Correct 7 ms 3200 KB Output is correct

Subtask #4
0 / 50.0

# Verdict Execution time Memory Grader output
1 Correct 19 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 15 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 6 ms 3072 KB Output is correct
9 Correct 95 ms 15420 KB Output is correct
10 Correct 5 ms 3044 KB Output is correct
11 Correct 6 ms 3200 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 6 ms 3072 KB Output is correct
17 Correct 5 ms 3072 KB Output is correct
18 Correct 4 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 4 ms 3072 KB Output is correct
22 Correct 6 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 6 ms 3200 KB Output is correct
26 Correct 5 ms 3072 KB Output is correct
27 Correct 5 ms 3200 KB Output is correct
28 Correct 4 ms 3072 KB Output is correct
29 Correct 5 ms 3072 KB Output is correct
30 Correct 6 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 4 ms 3072 KB Output is correct
34 Correct 5 ms 3120 KB Output is correct
35 Correct 7 ms 3328 KB Output is correct
36 Correct 7 ms 3328 KB Output is correct
37 Correct 10 ms 3440 KB Output is correct
38 Correct 9 ms 3320 KB Output is correct
39 Correct 7 ms 3452 KB Output is correct
40 Correct 7 ms 3440 KB Output is correct
41 Correct 8 ms 3456 KB Output is correct
42 Correct 5 ms 3200 KB Output is correct
43 Correct 9 ms 3640 KB Output is correct
44 Correct 59 ms 9092 KB Output is correct
45 Correct 42 ms 7628 KB Output is correct
46 Correct 41 ms 8292 KB Output is correct
47 Correct 43 ms 7120 KB Output is correct
48 Correct 52 ms 8224 KB Output is correct
49 Correct 71 ms 11244 KB Output is correct
50 Correct 105 ms 14360 KB Output is correct
51 Correct 195 ms 23400 KB Output is correct
52 Correct 142 ms 17560 KB Output is correct
53 Correct 198 ms 23136 KB Output is correct
54 Incorrect 182 ms 22076 KB Output isn't correct
55 Halted 0 ms 0 KB -