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답안 #227028

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
227028 2020-04-25T22:17:24 Z abeker Matching (COCI20_matching) C++17
58 / 110
 404 ms 524292 KB 
#include <bits/stdc++.h>
using namespace std;
 
typedef pair <int, int> pii;
 
const int MAXN = 1e5 + 5;
const int offset = 1 << 17;
const int MAXV = 1e7 + 5;

int n;
bool sol[MAXV];
bool bio[MAXV];
int comp[MAXV];
vector <int> adj[MAXV], rev[MAXV];
stack <int> order;

int add_variables(int vars) {
	n += vars;
	return n - vars;
}

void add_edge(int u, int v) {
	adj[u].push_back(v);
	rev[v].push_back(u);
}

void add_implication(int u1, int neg1, int u2, int neg2) {
	add_edge(2 * u1 + neg1, 2 * u2 + neg2);
	add_edge(2 * u2 + !neg2, 2 * u1 + !neg1);
}

void set_variable(int u, bool val) {
	add_implication(u, val, u, !val);
}

void at_most_one(const vector <pii> &v) {
	int sz = v.size();
	add_variables(sz);
	for (int i = 0; i < sz; i++) {
		add_implication(v[i].first, v[i].second, n - i - 1, 0);
		if (i) {
			add_implication(n - i, 0, n - i - 1, 0);
			add_implication(n - i, 0, v[i].first, !v[i].second);
		}
	}
}

void dfs_forward(int x) {
	bio[x] = true;
	for (auto it : adj[x])
		if (!bio[it])
			dfs_forward(it);
	order.push(x);
}

void dfs_backward(int x, int c) {
	comp[x] = c;
	for (auto it : rev[x])
		if (!comp[it])
			dfs_backward(it, c);
}

bool two_sat() {
	for (int i = 0; i < 2 * n; i++)
		if (!bio[i])
			dfs_forward(i);
	int ptr = 0;
	for (; !order.empty(); order.pop())
		if (!comp[order.top()])
			dfs_backward(order.top(), ++ptr);
	for (int i = 0; i < 2 * n; i++) {
		if (comp[i] == comp[i ^ 1])
			return false;
		sol[i] = comp[i] > comp[i ^ 1];
	}
	return true;
}

int get(int u, int neg) {
	return sol[2 * u + neg];
}

int N;
int x[MAXN], y[MAXN];
vector <pii> tour[2 * offset];
int st[2 * offset], off[2 * offset];
vector <int> hor[MAXN], ver[MAXN];
unordered_map <int, pii> segs;
vector <int> graph[MAXN];
 
void load() {
	scanf("%d", &N);
	for (int i = 0; i < N; i++) {
		scanf("%d%d", x + i, y + i);
		hor[y[i]].push_back(i);
		ver[x[i]].push_back(i);
	}
}
 
void insert(int x, int lo, int hi, int from, int to, int var, int height) {
	if (lo >= to || hi <= from)	
		return;
	if (lo >= from && hi <= to) {
		tour[x].push_back({height, var});
		return;
	}
	int mid = (lo + hi) / 2;
	insert(2 * x, lo, mid, from, to, var, height);
	insert(2 * x + 1, mid, hi, from, to, var, height);
}
 
inline int get_id(int node, int x) {
	return x < off[node] ? st[node] + x : tour[node][x - off[node]].second;
}
 
void add_clause(int x, int u, int v) {
	if (u < off[x] + tour[x].size())
		add_implication(get_id(x, u), 0, get_id(x, v), 0);
}
	
void init(int x) {
	if (tour[x].empty())
		return;
	off[x] = 1;
	sort(tour[x].begin(), tour[x].end());
	while (off[x] < tour[x].size())
		off[x] *= 2;
	st[x] = add_variables(2 * off[x]);
	for (int i = 0; i < off[x]; i++) {
		add_clause(x, 2 * i, i);
		add_clause(x, 2 * i + 1, i);
	}
}
 
int get_bounds(int x, int val) {
	int lo = 0, hi = tour[x].size();
	while (lo < hi) {
		int mid = (lo + hi) / 2;
		if (tour[x][mid].first >= val)
			hi = mid;
		else
			lo = mid + 1;
	}
	return lo;
}
 
void update(int node, int from, int to, int var) {
	from += off[node];
	to += off[node];
	while (from < to) {
		if (from % 2) 
			add_implication(get_id(node, from++), 0, var, 1);
		if (to % 2) 
			add_implication(get_id(node, --to), 0, var, 1);
		from /= 2;
		to /= 2;
	}
}
 
void add_intersections(int x, int down, int up, int var) {
	for (x += offset; x; x /= 2) 
		if (off[x])
			update(x, get_bounds(x, down), get_bounds(x, up + 1), var);
}
 
void bye() {
	puts("NE");
	exit(0);
}
 
void solve() {
	for (int i = 1; i < MAXN; i++) 
		if (hor[i].size() == 2) {
			int tmp = add_variables(1);
			segs[tmp] = {hor[i][0], hor[i][1]};
			int l = MAXN, r = 0;
			for (auto it : hor[i]) {
				graph[it].push_back(tmp);
				l = min(l, x[it]);
				r = max(r, x[it]);
			}
			insert(1, 0, offset, l, r + 1, tmp, i);
		}
	
	for (int i = 0; i < 2 * offset; i++)
		init(i);
	
	for (int i = 1; i < MAXN; i++) 
		if (ver[i].size() == 2) {
			int tmp = add_variables(1);
			segs[tmp] = {ver[i][0], ver[i][1]};
			int l = MAXN, r = 0;
			for (auto it : ver[i]) {
				graph[it].push_back(tmp);
				l = min(l, y[it]);
				r = max(r, y[it]);
			}
			add_intersections(i, l, r, tmp);
		}
	
	for (int i = 0; i < N; i++) 
		if (!graph[i].empty())
			add_implication(graph[i][0], 1, graph[i][1 % graph[i].size()], 0);
		else
			bye();
	
	if (!two_sat())
		bye();
	
	puts("DA");
	for (auto it : segs)
		if (get(it.first, 0))
			printf("%d %d\n", it.second.first + 1, it.second.second + 1);
}
 
int main() {
	double timer = clock();
	load();
	solve();
	fprintf(stderr, "%lf\n", (clock() - timer) / CLOCKS_PER_SEC);
	return 0;
}

Compilation message

matching.cpp: In function 'void add_clause(int, int, int)':
matching.cpp:117:8: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  if (u < off[x] + tour[x].size())
      ~~^~~~~~~~~~~~~~~~~~~~~~~~~
matching.cpp: In function 'void init(int)':
matching.cpp:126:16: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  while (off[x] < tour[x].size())
         ~~~~~~~^~~~~~~~~~~~~~~~
matching.cpp: In function 'void load()':
matching.cpp:92:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  scanf("%d", &N);
  ~~~~~^~~~~~~~~~
matching.cpp:94:8: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
   scanf("%d%d", x + i, y + i);
   ~~~~~^~~~~~~~~~~~~~~~~~~~~~

Subtask #1
5.0 / 5.0

# 결과 실행 시간 메모리 Grader output
1 Correct 284 ms 483576 KB Output is correct
2 Correct 282 ms 483448 KB Output is correct

Subtask #2
6.0 / 6.0

# 결과 실행 시간 메모리 Grader output
1 Correct 284 ms 483576 KB Output is correct
2 Correct 282 ms 483448 KB Output is correct
3 Correct 280 ms 483448 KB Output is correct
4 Correct 248 ms 483636 KB Output is correct
5 Correct 244 ms 483448 KB Output is correct
6 Correct 250 ms 483576 KB Output is correct
7 Correct 246 ms 483448 KB Output is correct

Subtask #3
7.0 / 7.0

# 결과 실행 시간 메모리 Grader output
1 Correct 284 ms 483576 KB Output is correct
2 Correct 282 ms 483448 KB Output is correct
3 Correct 280 ms 483448 KB Output is correct
4 Correct 248 ms 483636 KB Output is correct
5 Correct 244 ms 483448 KB Output is correct
6 Correct 250 ms 483576 KB Output is correct
7 Correct 246 ms 483448 KB Output is correct
8 Correct 253 ms 483704 KB Output is correct
9 Correct 261 ms 483704 KB Output is correct
10 Correct 251 ms 483832 KB Output is correct
11 Correct 284 ms 483704 KB Output is correct
12 Correct 256 ms 483708 KB Output is correct

Subtask #4
40.0 / 40.0

# 결과 실행 시간 메모리 Grader output
1 Correct 284 ms 483576 KB Output is correct
2 Correct 282 ms 483448 KB Output is correct
3 Correct 280 ms 483448 KB Output is correct
4 Correct 248 ms 483636 KB Output is correct
5 Correct 244 ms 483448 KB Output is correct
6 Correct 250 ms 483576 KB Output is correct
7 Correct 246 ms 483448 KB Output is correct
8 Correct 253 ms 483704 KB Output is correct
9 Correct 261 ms 483704 KB Output is correct
10 Correct 251 ms 483832 KB Output is correct
11 Correct 284 ms 483704 KB Output is correct
12 Correct 256 ms 483708 KB Output is correct
13 Correct 298 ms 486776 KB Output is correct
14 Correct 265 ms 487008 KB Output is correct
15 Correct 255 ms 487032 KB Output is correct
16 Correct 255 ms 486776 KB Output is correct
17 Correct 297 ms 486776 KB Output is correct
18 Correct 265 ms 486776 KB Output is correct
19 Correct 261 ms 486776 KB Output is correct
20 Correct 261 ms 486904 KB Output is correct
21 Correct 262 ms 486776 KB Output is correct
22 Correct 295 ms 486776 KB Output is correct
23 Correct 261 ms 486520 KB Output is correct
24 Correct 268 ms 486540 KB Output is correct

Subtask #5
0 / 52.0

# 결과 실행 시간 메모리 Grader output
1 Correct 284 ms 483576 KB Output is correct
2 Correct 282 ms 483448 KB Output is correct
3 Correct 280 ms 483448 KB Output is correct
4 Correct 248 ms 483636 KB Output is correct
5 Correct 244 ms 483448 KB Output is correct
6 Correct 250 ms 483576 KB Output is correct
7 Correct 246 ms 483448 KB Output is correct
8 Correct 253 ms 483704 KB Output is correct
9 Correct 261 ms 483704 KB Output is correct
10 Correct 251 ms 483832 KB Output is correct
11 Correct 284 ms 483704 KB Output is correct
12 Correct 256 ms 483708 KB Output is correct
13 Correct 298 ms 486776 KB Output is correct
14 Correct 265 ms 487008 KB Output is correct
15 Correct 255 ms 487032 KB Output is correct
16 Correct 255 ms 486776 KB Output is correct
17 Correct 297 ms 486776 KB Output is correct
18 Correct 265 ms 486776 KB Output is correct
19 Correct 261 ms 486776 KB Output is correct
20 Correct 261 ms 486904 KB Output is correct
21 Correct 262 ms 486776 KB Output is correct
22 Correct 295 ms 486776 KB Output is correct
23 Correct 261 ms 486520 KB Output is correct
24 Correct 268 ms 486540 KB Output is correct
25 Runtime error 404 ms 524292 KB Execution killed with signal 9 (could be triggered by violating memory limits)
26 Halted 0 ms 0 KB -