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답안 #227036

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
227036 2020-04-25T22:27:28 Z abeker Matching (COCI20_matching) C++17
58 / 110
 432 ms 524288 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;

inline int add_variables(int vars) {
	n += vars;
	assert(n < MAXV);
	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 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 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 (sol[2 * it.first])
			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:98:8: 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:107:16: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  while (off[x] < tour[x].size())
         ~~~~~~~^~~~~~~~~~~~~~~~
matching.cpp: In function 'void load()':
matching.cpp:73:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  scanf("%d", &N);
  ~~~~~^~~~~~~~~~
matching.cpp:75:8: 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 254 ms 483576 KB Output is correct
2 Correct 274 ms 483448 KB Output is correct

Subtask #2
6.0 / 6.0

# 결과 실행 시간 메모리 Grader output
1 Correct 254 ms 483576 KB Output is correct
2 Correct 274 ms 483448 KB Output is correct
3 Correct 259 ms 483448 KB Output is correct
4 Correct 258 ms 483704 KB Output is correct
5 Correct 250 ms 483448 KB Output is correct
6 Correct 273 ms 483576 KB Output is correct
7 Correct 253 ms 483448 KB Output is correct

Subtask #3
7.0 / 7.0

# 결과 실행 시간 메모리 Grader output
1 Correct 254 ms 483576 KB Output is correct
2 Correct 274 ms 483448 KB Output is correct
3 Correct 259 ms 483448 KB Output is correct
4 Correct 258 ms 483704 KB Output is correct
5 Correct 250 ms 483448 KB Output is correct
6 Correct 273 ms 483576 KB Output is correct
7 Correct 253 ms 483448 KB Output is correct
8 Correct 259 ms 483680 KB Output is correct
9 Correct 251 ms 483576 KB Output is correct
10 Correct 257 ms 483704 KB Output is correct
11 Correct 252 ms 483704 KB Output is correct
12 Correct 243 ms 483704 KB Output is correct

Subtask #4
40.0 / 40.0

# 결과 실행 시간 메모리 Grader output
1 Correct 254 ms 483576 KB Output is correct
2 Correct 274 ms 483448 KB Output is correct
3 Correct 259 ms 483448 KB Output is correct
4 Correct 258 ms 483704 KB Output is correct
5 Correct 250 ms 483448 KB Output is correct
6 Correct 273 ms 483576 KB Output is correct
7 Correct 253 ms 483448 KB Output is correct
8 Correct 259 ms 483680 KB Output is correct
9 Correct 251 ms 483576 KB Output is correct
10 Correct 257 ms 483704 KB Output is correct
11 Correct 252 ms 483704 KB Output is correct
12 Correct 243 ms 483704 KB Output is correct
13 Correct 260 ms 486904 KB Output is correct
14 Correct 265 ms 486896 KB Output is correct
15 Correct 279 ms 486776 KB Output is correct
16 Correct 266 ms 486956 KB Output is correct
17 Correct 295 ms 486908 KB Output is correct
18 Correct 268 ms 486912 KB Output is correct
19 Correct 260 ms 486776 KB Output is correct
20 Correct 303 ms 486900 KB Output is correct
21 Correct 259 ms 486816 KB Output is correct
22 Correct 259 ms 486776 KB Output is correct
23 Correct 269 ms 486648 KB Output is correct
24 Correct 299 ms 486520 KB Output is correct

Subtask #5
0 / 52.0

# 결과 실행 시간 메모리 Grader output
1 Correct 254 ms 483576 KB Output is correct
2 Correct 274 ms 483448 KB Output is correct
3 Correct 259 ms 483448 KB Output is correct
4 Correct 258 ms 483704 KB Output is correct
5 Correct 250 ms 483448 KB Output is correct
6 Correct 273 ms 483576 KB Output is correct
7 Correct 253 ms 483448 KB Output is correct
8 Correct 259 ms 483680 KB Output is correct
9 Correct 251 ms 483576 KB Output is correct
10 Correct 257 ms 483704 KB Output is correct
11 Correct 252 ms 483704 KB Output is correct
12 Correct 243 ms 483704 KB Output is correct
13 Correct 260 ms 486904 KB Output is correct
14 Correct 265 ms 486896 KB Output is correct
15 Correct 279 ms 486776 KB Output is correct
16 Correct 266 ms 486956 KB Output is correct
17 Correct 295 ms 486908 KB Output is correct
18 Correct 268 ms 486912 KB Output is correct
19 Correct 260 ms 486776 KB Output is correct
20 Correct 303 ms 486900 KB Output is correct
21 Correct 259 ms 486816 KB Output is correct
22 Correct 259 ms 486776 KB Output is correct
23 Correct 269 ms 486648 KB Output is correct
24 Correct 299 ms 486520 KB Output is correct
25 Runtime error 432 ms 524288 KB Execution killed with signal 9 (could be triggered by violating memory limits)
26 Halted 0 ms 0 KB -