oj.uz

Submission #227021

# Submission time Handle Problem Language Result Execution time Memory
227021 2020-04-25T21:38:45 Z abeker Matching (COCI20_matching) C++17
58 / 110
 2500 ms 435948 KB 
#include <bits/stdc++.h>
using namespace std;

typedef pair <int, int> pii;

const int MAXN = 1e5 + 5;
const int offset = 1 << 17;

class TwoSat {
	int n;
	vector <int> sol;
	vector <bool> bio;
	vector <int> comp;
	vector <vector <int>> adj, rev;
	stack <int> order;
	public:
		int add_variables(int vars) {
			n += vars;
			for (int i = 0; i < 2 * vars; i++) {
				sol.push_back(0);
				bio.push_back(false);
				comp.push_back(0);
				adj.push_back(vector <int> ());
				rev.push_back(vector <int> ());
			}
			return n - vars;
		}
		TwoSat(int _n) {
			n = 0;
			add_variables(_n);
		}
		TwoSat(){}
		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 solve() {
			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> adj[MAXN];
TwoSat Segments;

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())
		Segments.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] = Segments.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) 
			Segments.add_implication(get_id(node, from++), 0, var, 1);
		if (to % 2) 
			Segments.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 = Segments.add_variables(1);
			segs[tmp] = {hor[i][0], hor[i][1]};
			int l = MAXN, r = 0;
			for (auto it : hor[i]) {
				adj[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 = Segments.add_variables(1);
			segs[tmp] = {ver[i][0], ver[i][1]};
			int l = MAXN, r = 0;
			for (auto it : ver[i]) {
				adj[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 (!adj[i].empty())
			Segments.add_implication(adj[i][0], 1, adj[i][1 % adj[i].size()], 0);
		else
			bye();
	
	if (!Segments.solve())
		bye();
	
	puts("DA");
	for (auto it : segs)
		if (Segments.get(it.first, 0))
			printf("%d %d\n", it.second.first + 1, it.second.second + 1);
}

int main() {
	load();
	solve();
	return 0;
}

Compilation message

matching.cpp: In function 'void add_clause(int, int, int)':
matching.cpp:123:8: 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:132:16: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  while (off[x] < tour[x].size())
         ~~~~~~~^~~~~~~~~~~~~~~~
matching.cpp: In function 'void load()':
matching.cpp:98:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  scanf("%d", &N);
  ~~~~~^~~~~~~~~~
matching.cpp:100:8: 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

# Verdict Execution time Memory Grader output
1 Correct 14 ms 13824 KB Output is correct
2 Correct 14 ms 13952 KB Output is correct

Subtask #2
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 14 ms 13824 KB Output is correct
2 Correct 14 ms 13952 KB Output is correct
3 Correct 15 ms 13824 KB Output is correct
4 Correct 15 ms 13824 KB Output is correct
5 Correct 15 ms 13824 KB Output is correct
6 Correct 15 ms 13952 KB Output is correct
7 Correct 13 ms 13824 KB Output is correct

Subtask #3
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 14 ms 13824 KB Output is correct
2 Correct 14 ms 13952 KB Output is correct
3 Correct 15 ms 13824 KB Output is correct
4 Correct 15 ms 13824 KB Output is correct
5 Correct 15 ms 13824 KB Output is correct
6 Correct 15 ms 13952 KB Output is correct
7 Correct 13 ms 13824 KB Output is correct
8 Correct 15 ms 14080 KB Output is correct
9 Correct 14 ms 14080 KB Output is correct
10 Correct 14 ms 14080 KB Output is correct
11 Correct 14 ms 14080 KB Output is correct
12 Correct 15 ms 14080 KB Output is correct

Subtask #4
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 14 ms 13824 KB Output is correct
2 Correct 14 ms 13952 KB Output is correct
3 Correct 15 ms 13824 KB Output is correct
4 Correct 15 ms 13824 KB Output is correct
5 Correct 15 ms 13824 KB Output is correct
6 Correct 15 ms 13952 KB Output is correct
7 Correct 13 ms 13824 KB Output is correct
8 Correct 15 ms 14080 KB Output is correct
9 Correct 14 ms 14080 KB Output is correct
10 Correct 14 ms 14080 KB Output is correct
11 Correct 14 ms 14080 KB Output is correct
12 Correct 15 ms 14080 KB Output is correct
13 Correct 28 ms 19440 KB Output is correct
14 Correct 28 ms 19432 KB Output is correct
15 Correct 28 ms 19440 KB Output is correct
16 Correct 28 ms 19440 KB Output is correct
17 Correct 34 ms 19440 KB Output is correct
18 Correct 34 ms 19440 KB Output is correct
19 Correct 41 ms 19440 KB Output is correct
20 Correct 32 ms 19440 KB Output is correct
21 Correct 27 ms 19440 KB Output is correct
22 Correct 31 ms 19440 KB Output is correct
23 Correct 35 ms 19172 KB Output is correct
24 Correct 34 ms 19176 KB Output is correct

Subtask #5
0 / 52.0

# Verdict Execution time Memory Grader output
1 Correct 14 ms 13824 KB Output is correct
2 Correct 14 ms 13952 KB Output is correct
3 Correct 15 ms 13824 KB Output is correct
4 Correct 15 ms 13824 KB Output is correct
5 Correct 15 ms 13824 KB Output is correct
6 Correct 15 ms 13952 KB Output is correct
7 Correct 13 ms 13824 KB Output is correct
8 Correct 15 ms 14080 KB Output is correct
9 Correct 14 ms 14080 KB Output is correct
10 Correct 14 ms 14080 KB Output is correct
11 Correct 14 ms 14080 KB Output is correct
12 Correct 15 ms 14080 KB Output is correct
13 Correct 28 ms 19440 KB Output is correct
14 Correct 28 ms 19432 KB Output is correct
15 Correct 28 ms 19440 KB Output is correct
16 Correct 28 ms 19440 KB Output is correct
17 Correct 34 ms 19440 KB Output is correct
18 Correct 34 ms 19440 KB Output is correct
19 Correct 41 ms 19440 KB Output is correct
20 Correct 32 ms 19440 KB Output is correct
21 Correct 27 ms 19440 KB Output is correct
22 Correct 31 ms 19440 KB Output is correct
23 Correct 35 ms 19172 KB Output is correct
24 Correct 34 ms 19176 KB Output is correct
25 Correct 905 ms 157676 KB Output is correct
26 Correct 981 ms 157456 KB Output is correct
27 Correct 881 ms 157424 KB Output is correct
28 Correct 1012 ms 158092 KB Output is correct
29 Correct 888 ms 157552 KB Output is correct
30 Correct 982 ms 157172 KB Output is correct
31 Correct 875 ms 157048 KB Output is correct
32 Correct 894 ms 156932 KB Output is correct
33 Correct 794 ms 150204 KB Output is correct
34 Correct 781 ms 150160 KB Output is correct
35 Correct 622 ms 150104 KB Output is correct
36 Execution timed out 2594 ms 435948 KB Time limit exceeded
37 Halted 0 ms 0 KB -