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Submission #107555

# Submission time Handle Problem Language Result Execution time Memory
107555 2019-04-25T06:49:55 Z gs14004 Demarcation (BOI14_demarcation) C++17
100 / 100
 239 ms 25032 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});
			rect_close(*lbnd, i.yc);
			event2 nxt1 = {i.yc, lbnd->s, i.xs};
			event2 nxt2 = {i.yc, i.xe, lbnd->e};
			s.erase(lbnd);
			if(nxt1.s < nxt1.e) s.insert(nxt1);
			if(nxt2.s < nxt2.e) 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;
	lint H = sum[0] / 2;
	for(int i=0; i<rect_list.size(); i++){
		lint mxvi = max(msz[i], sum[0] - sum[i]);
		if(mxvi <= H){
			lint thres = H;
			for(auto &j : gph[i]){
				if(rect_list[j].sy < rect_list[i].sy){
					dfs(j, i);
					thres -= sum[j];
				}
			}
			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);
					}
				}
			}
			for(auto &j : gph[i]){
				dfs(j, i);
				if(sum[j] == H){
					int sx = max(rect_list[i].sx, rect_list[j].sx);
					int ex = min(rect_list[i].ex, rect_list[j].ex);
					int sy = max(rect_list[i].sy, rect_list[j].sy);
					int ey = min(rect_list[i].ey, rect_list[j].ey);
					assert(sy == ey && sx < ex);
					vector<pi> v1, v2;
					cut_polygon(a, v1, v2, sx, ex, sy);
					if(hapdong(v1, v2)){
						save_results(sx, ex, sy);
					}
				}
			}
			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:288:16: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for(int i=0; i<rect_list.size(); i++){
               ~^~~~~~~~~~~~~~~~~
demarcation.cpp:296:16: 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:338:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  scanf("%d",&n);
  ~~~~~^~~~~~~~~
demarcation.cpp:341:8: 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 27 ms 5672 KB Output is correct
2 Correct 4 ms 3072 KB Output is correct
3 Correct 4 ms 3072 KB Output is correct
4 Correct 17 ms 4588 KB Output is correct
5 Correct 4 ms 3072 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 92 ms 16700 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 4 ms 3072 KB Output is correct

Subtask #2
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 3072 KB Output is correct
2 Correct 6 ms 3072 KB Output is correct
3 Correct 5 ms 3072 KB Output is correct
4 Correct 5 ms 3068 KB Output is correct
5 Correct 5 ms 3072 KB Output is correct
6 Correct 6 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 5 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 4 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 3200 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 6 ms 2944 KB Output is correct
25 Correct 7 ms 3072 KB Output is correct
26 Correct 5 ms 3072 KB Output is correct
27 Correct 6 ms 3072 KB Output is correct
28 Correct 6 ms 3072 KB Output is correct
29 Correct 5 ms 2944 KB Output is correct
30 Correct 5 ms 3072 KB Output is correct

Subtask #3
23.0 / 23.0

# Verdict Execution time Memory 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 6 ms 3072 KB Output is correct
7 Correct 4 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 5 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 4 ms 3072 KB Output is correct
15 Correct 5 ms 3244 KB Output is correct
16 Correct 5 ms 3072 KB Output is correct
17 Correct 4 ms 3072 KB Output is correct
18 Correct 5 ms 2944 KB Output is correct
19 Correct 6 ms 3072 KB Output is correct
20 Correct 6 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 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 5 ms 3200 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 3044 KB Output is correct
32 Correct 9 ms 3456 KB Output is correct
33 Correct 7 ms 3440 KB Output is correct
34 Correct 7 ms 3568 KB Output is correct
35 Correct 6 ms 3328 KB Output is correct
36 Correct 8 ms 3452 KB Output is correct
37 Correct 7 ms 3328 KB Output is correct
38 Correct 11 ms 3436 KB Output is correct
39 Correct 6 ms 3200 KB Output is correct

Subtask #4
50.0 / 50.0

# Verdict Execution time Memory Grader output
1 Correct 27 ms 5644 KB Output is correct
2 Correct 6 ms 3072 KB Output is correct
3 Correct 5 ms 3072 KB Output is correct
4 Correct 16 ms 4596 KB Output is correct
5 Correct 6 ms 3072 KB Output is correct
6 Correct 5 ms 3072 KB Output is correct
7 Correct 7 ms 3072 KB Output is correct
8 Correct 5 ms 3116 KB Output is correct
9 Correct 97 ms 16720 KB Output is correct
10 Correct 6 ms 3072 KB Output is correct
11 Correct 5 ms 3200 KB Output is correct
12 Correct 6 ms 3044 KB Output is correct
13 Correct 5 ms 3072 KB Output is correct
14 Correct 5 ms 3100 KB Output is correct
15 Correct 6 ms 3072 KB Output is correct
16 Correct 5 ms 3072 KB Output is correct
17 Correct 4 ms 3072 KB Output is correct
18 Correct 5 ms 3072 KB Output is correct
19 Correct 6 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 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 3200 KB Output is correct
26 Correct 6 ms 3072 KB Output is correct
27 Correct 6 ms 3072 KB Output is correct
28 Correct 6 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 6 ms 3072 KB Output is correct
33 Correct 6 ms 3072 KB Output is correct
34 Correct 5 ms 3072 KB Output is correct
35 Correct 9 ms 3452 KB Output is correct
36 Correct 39 ms 3440 KB Output is correct
37 Correct 9 ms 3436 KB Output is correct
38 Correct 4 ms 3448 KB Output is correct
39 Correct 9 ms 3452 KB Output is correct
40 Correct 8 ms 3456 KB Output is correct
41 Correct 8 ms 3456 KB Output is correct
42 Correct 6 ms 3200 KB Output is correct
43 Correct 12 ms 3640 KB Output is correct
44 Correct 239 ms 9472 KB Output is correct
45 Correct 48 ms 8008 KB Output is correct
46 Correct 41 ms 8556 KB Output is correct
47 Correct 43 ms 7380 KB Output is correct
48 Correct 48 ms 8480 KB Output is correct
49 Correct 82 ms 11980 KB Output is correct
50 Correct 97 ms 14968 KB Output is correct
51 Correct 198 ms 24480 KB Output is correct
52 Correct 144 ms 18952 KB Output is correct
53 Correct 171 ms 24196 KB Output is correct
54 Correct 122 ms 16920 KB Output is correct
55 Correct 45 ms 9436 KB Output is correct
56 Correct 196 ms 24512 KB Output is correct
57 Correct 193 ms 25032 KB Output is correct
58 Correct 134 ms 19216 KB Output is correct
59 Correct 106 ms 19048 KB Output is correct
60 Correct 62 ms 12772 KB Output is correct
61 Correct 32 ms 6184 KB Output is correct
62 Correct 66 ms 8564 KB Output is correct
63 Correct 89 ms 11444 KB Output is correct
64 Correct 78 ms 11364 KB Output is correct
65 Correct 74 ms 11356 KB Output is correct
66 Correct 138 ms 22448 KB Output is correct