oj.uz

Submission #547223

# Submission time Handle Problem Language Result Execution time Memory
547223 2022-04-09T21:34:53 Z skittles1412 Alternating Current (BOI18_alternating) C++17
0 / 100
 75 ms 14652 KB 
#include "bits/extc++.h"

using namespace std;

template <typename T>
void dbgh(const T& t) {
	cerr << t << endl;
}

template <typename T, typename... U>
void dbgh(const T& t, const U&... u) {
	cerr << t << " | ";
	dbgh(u...);
}

#ifdef DEBUG
#define dbg(...)                                           \
	cerr << "L" << __LINE__ << " [" << #__VA_ARGS__ << "]" \
		 << ": ";                                          \
	dbgh(__VA_ARGS__)
#else
#define cerr   \
	if (false) \
	cerr
#define dbg(...)
#endif

#define endl "\n"
#define long int64_t
#define sz(x) int((x).size())

void solve() {
	int n, m;
	cin >> n >> m;
	array<int, 3> arr[m];
	for (int i = 0; i < m; i++) {
		auto& [l, r, ci] = arr[i];
		cin >> l >> r;
		l--;
		r--;
		ci = i;
		if (l > r) {
			r += n;
		}
	}
	sort(arr, arr + m, [&](const auto& a, const auto& b) -> bool {
		if (a[0] != b[0]) {
			return a[0] < b[0];
		}
		return a[1] > b[1];
	});
	for (auto& [l, r, _] : arr) {
		if (r >= n) {
			r -= n;
		}
	}
	int par[m];
	pair<int, int> mx {-1, -1};
	for (int i = 0; i < 2 * m; i++) {
		int ci = i >= m ? i - m : i;
		auto [l, r, _] = arr[ci];
		if (l > r) {
			r += n;
		}
		if (i >= m) {
			l += n;
			r += n;
		}
		if (r <= mx.first) {
			par[ci] = mx.second;
		} else {
			par[ci] = ci;
			mx = {r, ci};
		}
	}
	for (int i = 0; i < m; i++) {
		int u = i;
		while (par[u] != u) {
			u = par[u];
		}
		par[i] = u;
	}
	vector<int> vals;
	int inds[m];
	for (int i = 0; i < m; i++) {
		if (par[i] == i) {
			inds[i] = sz(vals);
			vals.push_back(i);
		}
		dbg(i, arr[i][0], arr[i][1], par[i]);
	}
	auto covers_all = [&](const vector<pair<int, int>>& arr) -> bool {
		vector<int> e[n];
		for (auto& [l, r] : arr) {
			e[l].push_back(r);
		}
		int mx = -1;
		for (int i = 0; i < n; i++) {
			for (auto& a : e[i]) {
				mx = max(mx, a);
			}
			if (mx < i) {
				return false;
			}
		}
		return true;
	};
	auto check = [&](const vector<bool>& distr) -> void {
		vector<pair<int, int>> segs[2];
		auto add = [&](int i, int l, int r) -> void {
			if (r >= n) {
				r -= n;
			}
			if (l > r) {
				segs[i].emplace_back(l, n - 1);
				segs[i].emplace_back(0, r);
			} else {
				segs[i].emplace_back(l, r);
			}
		};
		bool ans[m];
		for (int i = 0; i < m; i++) {
			auto& [l, r, ci] = arr[i];
			if (par[i] == i) {
				ans[ci] = distr[inds[i]];
			} else {
				ans[ci] = !distr[inds[par[i]]];
			}
			dbg(i, inds[par[i]], ans[ci]);
			add(ans[ci], l, r);
		}
		if (covers_all(segs[0]) && covers_all(segs[1])) {
			for (auto& a : ans) {
				cout << a;
			}
			cout << endl;
			exit(0);
		}
	};
	int k = sz(vals);
	dbg(k);
	if (k % 2 == 0 || k == 1) {
		vector<bool> distr(k);
		for (int i = 0; i < k; i++) {
			distr[i] = i & 1;
		}
		check(distr);
		cout << "impossible" << endl;
		return;
	} else if (k <= 3) {
		for (int i = 0; i < k; i++) {
			vector<bool> distr(k);
			int j = i;
			bool cur = true;
			while (true) {
				distr[j] = cur;
				cur ^= true;
				j = j + 1 == k ? 0 : j + 1;
				if (j == i) {
					break;
				}
			}
			check(distr);
		}
		cout << "impossible" << endl;
		return;
	}
	{
		vector<pair<int, int>> cur;
		for (auto& [l, r, _] : arr) {
			if (l > r) {
				cur.emplace_back(l, n - 1);
				cur.emplace_back(0, r);
			} else {
				cur.emplace_back(l, r);
			}
		}
		if (!covers_all(cur)) {
			cout << "impossible" << endl;
			return;
		}
	}
	auto covers = [&](const vector<pair<int, int>>& segs, int ql, int qr) -> bool {
		if (!sz(segs)) {
			return false;
		}
		vector<pair<int, int>> evts;
		for (auto& [l, r] : segs) {
			evts.emplace_back(l - n, 1);
			evts.emplace_back(r - n + 1, -1);
			evts.emplace_back(l, 1);
			evts.emplace_back(r + 1, -1);
			evts.emplace_back(l + n, 1);
			evts.emplace_back(r + n + 1, -1);
		}
		sort(begin(evts), end(evts));
		int prev = -1, cur = 0;
		for (auto& [ind, x] : evts) {
			if (prev != -1 && ind != prev) {
				if (!cur) {
					if (ql <= ind - 1 && ind - 1 <= qr) {
						return false;
					} else if (ql <= prev && prev <= qr) {
						return false;
					}
				}
			}
			cur += x;
			prev = ind;
		}
		return true;
	};
	bool can[k];
	vector<pair<int, int>> child[k];
	for (int i = 0; i < m; i++) {
		auto& [l, r, _] = arr[i];
		if (l > r) {
			r += n;
		}
		if (par[i] != i) {
			child[inds[par[i]]].emplace_back(l, r);
		}
	}
	array<int, 2> carr[k];
	for (int i = 0; i < k; i++) {
		carr[i] = {arr[vals[i]][0], arr[vals[i]][1]};
	}
	for (int i = 0; i < k; i++) {
		int a = (i + k - 1) % k, b = (i + 1) % k;
		vector<pair<int, int>> cur = child[i];
		cur.emplace_back(carr[a][0], carr[a][1]);
		cur.emplace_back(carr[b][0], carr[b][1]);
		can[i] = covers(cur, carr[i][0], carr[i][1]);
		dbg(i, can[i], carr[a][0], carr[a][1], carr[b][0], carr[b][1], carr[i][0], carr[i][1]);
	}
	int cnt = 0;
	for (auto& a : can) {
		cnt += a;
	}
	for (int i = 0; i < k; i++) {
		int a = i, b = (i + 1) % k, c = (i + 2) % k, d = (i + 3) % k;
		int ccnt = cnt - can[b] - can[c];
		if (ccnt != k - 2) {
			continue;
		}
		vector<pair<int, int>> cur;
		cur.insert(cur.end(), begin(child[b]), end(child[b]));
		cur.insert(cur.end(), begin(child[c]), end(child[c]));
		cur.emplace_back(carr[a][0], carr[a][1]);
		cur.emplace_back(carr[d][0], carr[d][1]);
		if (!covers(cur, carr[b][0], carr[c][1])) {
			continue;
		}
		dbg(i);
		vector<bool> distr(k);
		bool cb = true;
		while (true) {
			distr[c] = cb;
			cb ^= true;
			if (c == b) {
				break;
			}
			c = c + 1 == k ? 0 : c + 1;
		}
		check(distr);
		assert(false);
	}
	cout << "impossible" << endl;
}

int main() {
	cin.tie(nullptr);
	ios_base::sync_with_stdio(false);
	cin.exceptions(ios::failbit);
	solve();
}

Subtask #1
0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 1 ms 212 KB Output is correct
15 Correct 1 ms 212 KB Output is correct
16 Correct 1 ms 212 KB Output is correct
17 Correct 1 ms 212 KB Output is correct
18 Correct 1 ms 316 KB Output is correct
19 Correct 0 ms 212 KB Output is correct
20 Correct 1 ms 212 KB Output is correct
21 Correct 1 ms 212 KB Output is correct
22 Correct 1 ms 212 KB Output is correct
23 Correct 1 ms 212 KB Output is correct
24 Correct 0 ms 212 KB Output is correct
25 Correct 0 ms 212 KB Output is correct
26 Correct 1 ms 212 KB Output is correct
27 Correct 1 ms 212 KB Output is correct
28 Correct 1 ms 212 KB Output is correct
29 Correct 1 ms 212 KB Output is correct
30 Correct 1 ms 212 KB Output is correct
31 Correct 1 ms 212 KB Output is correct
32 Correct 1 ms 212 KB Output is correct
33 Correct 1 ms 212 KB Output is correct
34 Correct 1 ms 212 KB Output is correct
35 Correct 1 ms 212 KB Output is correct
36 Correct 1 ms 316 KB Output is correct
37 Correct 1 ms 216 KB Output is correct
38 Runtime error 1 ms 468 KB Execution killed with signal 6
39 Halted 0 ms 0 KB -

Subtask #2
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 1 ms 212 KB Output is correct
15 Correct 1 ms 212 KB Output is correct
16 Correct 1 ms 212 KB Output is correct
17 Correct 1 ms 212 KB Output is correct
18 Correct 1 ms 316 KB Output is correct
19 Correct 0 ms 212 KB Output is correct
20 Correct 1 ms 212 KB Output is correct
21 Correct 1 ms 212 KB Output is correct
22 Correct 1 ms 212 KB Output is correct
23 Correct 1 ms 212 KB Output is correct
24 Correct 0 ms 212 KB Output is correct
25 Correct 0 ms 212 KB Output is correct
26 Correct 1 ms 212 KB Output is correct
27 Correct 1 ms 212 KB Output is correct
28 Correct 1 ms 212 KB Output is correct
29 Correct 1 ms 212 KB Output is correct
30 Correct 1 ms 212 KB Output is correct
31 Correct 1 ms 212 KB Output is correct
32 Correct 1 ms 212 KB Output is correct
33 Correct 1 ms 212 KB Output is correct
34 Correct 1 ms 212 KB Output is correct
35 Correct 1 ms 212 KB Output is correct
36 Correct 1 ms 316 KB Output is correct
37 Correct 1 ms 216 KB Output is correct
38 Runtime error 1 ms 468 KB Execution killed with signal 6
39 Halted 0 ms 0 KB -

Subtask #3
0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 1 ms 212 KB Output is correct
15 Correct 1 ms 212 KB Output is correct
16 Correct 1 ms 212 KB Output is correct
17 Correct 1 ms 212 KB Output is correct
18 Correct 1 ms 316 KB Output is correct
19 Correct 0 ms 212 KB Output is correct
20 Correct 1 ms 212 KB Output is correct
21 Correct 1 ms 212 KB Output is correct
22 Correct 1 ms 212 KB Output is correct
23 Correct 1 ms 212 KB Output is correct
24 Correct 0 ms 212 KB Output is correct
25 Correct 0 ms 212 KB Output is correct
26 Correct 1 ms 212 KB Output is correct
27 Correct 1 ms 212 KB Output is correct
28 Correct 1 ms 212 KB Output is correct
29 Correct 1 ms 212 KB Output is correct
30 Correct 1 ms 212 KB Output is correct
31 Correct 1 ms 212 KB Output is correct
32 Correct 1 ms 212 KB Output is correct
33 Correct 1 ms 212 KB Output is correct
34 Correct 1 ms 212 KB Output is correct
35 Correct 1 ms 212 KB Output is correct
36 Correct 1 ms 316 KB Output is correct
37 Correct 1 ms 216 KB Output is correct
38 Runtime error 1 ms 468 KB Execution killed with signal 6
39 Halted 0 ms 0 KB -

Subtask #4
0 / 19.0

# Verdict Execution time Memory Grader output
1 Correct 30 ms 6640 KB Output is correct
2 Correct 2 ms 2644 KB Output is correct
3 Correct 16 ms 5888 KB Output is correct
4 Correct 17 ms 5944 KB Output is correct
5 Correct 39 ms 7364 KB Output is correct
6 Correct 66 ms 7868 KB Output is correct
7 Correct 66 ms 9576 KB Output is correct
8 Correct 3 ms 2816 KB Output is correct
9 Correct 3 ms 2508 KB Output is correct
10 Correct 75 ms 11168 KB Output is correct
11 Correct 30 ms 6848 KB Output is correct
12 Correct 35 ms 9052 KB Output is correct
13 Correct 3 ms 2644 KB Output is correct
14 Correct 2 ms 2624 KB Output is correct
15 Correct 39 ms 8512 KB Output is correct
16 Runtime error 39 ms 14652 KB Execution killed with signal 6
17 Halted 0 ms 0 KB -

Subtask #5
0 / 26.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 1 ms 212 KB Output is correct
15 Correct 1 ms 212 KB Output is correct
16 Correct 1 ms 212 KB Output is correct
17 Correct 1 ms 212 KB Output is correct
18 Correct 1 ms 316 KB Output is correct
19 Correct 0 ms 212 KB Output is correct
20 Correct 1 ms 212 KB Output is correct
21 Correct 1 ms 212 KB Output is correct
22 Correct 1 ms 212 KB Output is correct
23 Correct 1 ms 212 KB Output is correct
24 Correct 0 ms 212 KB Output is correct
25 Correct 0 ms 212 KB Output is correct
26 Correct 1 ms 212 KB Output is correct
27 Correct 1 ms 212 KB Output is correct
28 Correct 1 ms 212 KB Output is correct
29 Correct 1 ms 212 KB Output is correct
30 Correct 1 ms 212 KB Output is correct
31 Correct 1 ms 212 KB Output is correct
32 Correct 1 ms 212 KB Output is correct
33 Correct 1 ms 212 KB Output is correct
34 Correct 1 ms 212 KB Output is correct
35 Correct 1 ms 212 KB Output is correct
36 Correct 1 ms 316 KB Output is correct
37 Correct 1 ms 216 KB Output is correct
38 Runtime error 1 ms 468 KB Execution killed with signal 6
39 Halted 0 ms 0 KB -