oj.uz

Submission #227016

# Submission time Handle Problem Language Result Execution time Memory
227016 2020-04-25T21:19:50 Z abeker Matching (COCI20_matching) C++17
58 / 110
 2500 ms 435864 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) {
	return lower_bound(tour[x].begin(), tour[x].end(), pii(val, 0)) - tour[x].begin();
}

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 13 ms 13952 KB Output is correct
2 Correct 13 ms 13824 KB Output is correct

Subtask #2
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 13 ms 13952 KB Output is correct
2 Correct 13 ms 13824 KB Output is correct
3 Correct 13 ms 13824 KB Output is correct
4 Correct 12 ms 13824 KB Output is correct
5 Correct 13 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 13 ms 13952 KB Output is correct
2 Correct 13 ms 13824 KB Output is correct
3 Correct 13 ms 13824 KB Output is correct
4 Correct 12 ms 13824 KB Output is correct
5 Correct 13 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 17 ms 14080 KB Output is correct
9 Correct 13 ms 14080 KB Output is correct
10 Correct 14 ms 14080 KB Output is correct
11 Correct 15 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 13 ms 13952 KB Output is correct
2 Correct 13 ms 13824 KB Output is correct
3 Correct 13 ms 13824 KB Output is correct
4 Correct 12 ms 13824 KB Output is correct
5 Correct 13 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 17 ms 14080 KB Output is correct
9 Correct 13 ms 14080 KB Output is correct
10 Correct 14 ms 14080 KB Output is correct
11 Correct 15 ms 14080 KB Output is correct
12 Correct 15 ms 14080 KB Output is correct
13 Correct 27 ms 19440 KB Output is correct
14 Correct 31 ms 19344 KB Output is correct
15 Correct 27 ms 19440 KB Output is correct
16 Correct 27 ms 19440 KB Output is correct
17 Correct 30 ms 19420 KB Output is correct
18 Correct 27 ms 19440 KB Output is correct
19 Correct 26 ms 19440 KB Output is correct
20 Correct 31 ms 19440 KB Output is correct
21 Correct 26 ms 19440 KB Output is correct
22 Correct 26 ms 19440 KB Output is correct
23 Correct 29 ms 19176 KB Output is correct
24 Correct 30 ms 19176 KB Output is correct

Subtask #5
0 / 52.0

# Verdict Execution time Memory Grader output
1 Correct 13 ms 13952 KB Output is correct
2 Correct 13 ms 13824 KB Output is correct
3 Correct 13 ms 13824 KB Output is correct
4 Correct 12 ms 13824 KB Output is correct
5 Correct 13 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 17 ms 14080 KB Output is correct
9 Correct 13 ms 14080 KB Output is correct
10 Correct 14 ms 14080 KB Output is correct
11 Correct 15 ms 14080 KB Output is correct
12 Correct 15 ms 14080 KB Output is correct
13 Correct 27 ms 19440 KB Output is correct
14 Correct 31 ms 19344 KB Output is correct
15 Correct 27 ms 19440 KB Output is correct
16 Correct 27 ms 19440 KB Output is correct
17 Correct 30 ms 19420 KB Output is correct
18 Correct 27 ms 19440 KB Output is correct
19 Correct 26 ms 19440 KB Output is correct
20 Correct 31 ms 19440 KB Output is correct
21 Correct 26 ms 19440 KB Output is correct
22 Correct 26 ms 19440 KB Output is correct
23 Correct 29 ms 19176 KB Output is correct
24 Correct 30 ms 19176 KB Output is correct
25 Correct 876 ms 157760 KB Output is correct
26 Correct 948 ms 157432 KB Output is correct
27 Correct 877 ms 157440 KB Output is correct
28 Correct 885 ms 158108 KB Output is correct
29 Correct 1075 ms 157168 KB Output is correct
30 Correct 885 ms 157304 KB Output is correct
31 Correct 859 ms 156912 KB Output is correct
32 Correct 895 ms 156920 KB Output is correct
33 Correct 785 ms 150056 KB Output is correct
34 Correct 940 ms 150104 KB Output is correct
35 Correct 615 ms 150116 KB Output is correct
36 Execution timed out 2608 ms 435864 KB Time limit exceeded
37 Halted 0 ms 0 KB -