oj.uz

Submission #518688

# Submission time Handle Problem Language Result Execution time Memory
518688 2022-01-24T12:27:40 Z fleimgruber Keys (IOI21_keys) C++17
100 / 100
 1179 ms 102704 KB 
// --- algolib/union-find.h ---
// union find, optionally with tags for each component. this is useful
// for example when compressing components. enable using template parameter
#include <algorithm>
#include <type_traits>
#include <numeric>
#include <vector>


template<typename T = void, typename enable = void>
class UnionFind {
	std::vector<int> p, size_;

public:
	UnionFind(int n = 0) : p(n), size_(n, 1) {
		std::iota(p.begin(), p.end(), 0);
	}

	int create() {
		int r = p.size();
		p.push_back(r);
		size_.push_back(1);
		return r;
	}

	int find(int i) {
		if (i == p[i])
			return i;
		return p[i] = find(p[i]);
	}
	int operator[](int i) { return find(i); }
	int size(int i) { return size_[find(i)]; }

	bool connected(int a, int b) { return find(a) == find(b); }

	bool connect(int a, int b) {
		a = find(a), b = find(b);
		if (a == b)
			return false;
		if (size_[a] > size_[b])
			std::swap(a, b);
		size_[b] += size_[a];
		p[a] = b;
		return true;
	}
};

// connect(a, b) maintains tag(b)
template<typename T>
class UnionFind<T, typename std::enable_if_t<!std::is_same_v<T, void>>>
	: public UnionFind<void> {
	std::vector<T> tags;

public:
	UnionFind(int n = 0) : UnionFind<void>(n), tags(n) { }

	void create() {
		UnionFind<void>::create();
		tags.emplace_back();
	}

	bool connect(int a, int b) {
		T old = tag(b);
		bool res = UnionFind<void>::connect(a, b);
		set_tag(b, old);
		return res;
	}

	void set_tag(int i, const T& t) { tags[find(i)] = t; }
	const T& tag(int i) { return tags[find(i)]; }
};
// ----------------
#include <bits/stdc++.h>

using namespace std;

const int MAX_N = 300005;

int n;
vector<int> ans;
struct Edge {
	int to, key; // key required
	bool operator<(const Edge& o) const {
		// cannot just use key, otherwise edges get lost (set)
		return tie(key, to) < tie(o.key, o.to);
	}
};
vector<int> out_can[MAX_N]; // only the to
set<Edge> out_blocked[MAX_N];
set<int> keys[MAX_N];
int par[MAX_N]; // parent in tree
UnionFind weakly(MAX_N); // weakly connected components
UnionFind<int> compressed(MAX_N);

// merge i into j, smaller to larger style
void merge(int i, int j) {
	if (compressed.size(i) > compressed.size(j)) {
		out_can[i].swap(out_can[j]);
		out_blocked[i].swap(out_blocked[j]);
		keys[i].swap(keys[j]);
	}
	compressed.connect(i, j); // tag of j is maintained
	out_can[j].insert(out_can[j].end(),
			out_can[i].begin(), out_can[i].end());
	out_can[i].clear();
	for (int key : keys[i])
		if (keys[j].insert(key).second) { // promote
			auto it = out_blocked[j].lower_bound({ -1, key });
			while (it != out_blocked[j].end() && it->key == key) {
				out_can[j].push_back(it->to);
				it = out_blocked[j].erase(it);
			}
		}
	keys[i].clear();
	for (auto& x : out_blocked[i])
		if (keys[j].find(x.key) == keys[j].end())
			out_blocked[j].insert(x);
		else if (!compressed.connected(j, x.to)) // pruning back edges
			out_can[j].push_back(x.to);
	out_blocked[i].clear();
	return;
}

void solve() {
	using pq_key = pair<int, int>; // size, vertex (roots order by size)
	priority_queue<pq_key, vector<pq_key>, greater<pq_key>> roots;
	// tags are the representatives (where keys & edges are stored)
	for (int i = 0; i < n; i++) {
		compressed.set_tag(i, i);
		roots.push({ 1, i });
	}
	// != -1 means we already found an answer of size done_size
	// so stop pushing to pq, but collect remaining components
	int done_size = -1;
	ans.assign(n, 0);
	while (!roots.empty()) {
		auto [_, r] = roots.top();
		roots.pop();
		// find any outgoing edge
		bool has_outgoing = false;
		while (!out_can[r].empty()) {
			int to = out_can[r].back();
			out_can[r].pop_back();
			if (compressed.connected(r, to))
				continue;
			has_outgoing = true;
			if (done_size != -1) // we're larger than the answer
				break;
			if (weakly.connected(r, to)) {
				// merge with self. walk up parents 
				int j = compressed.tag(to);
				do {
					int jp = compressed.tag(par[j]);
					merge(j, jp);
					j = jp;
				} while (j != r);
				// we're still a root, but of larger size
				roots.push({ compressed.size(r), r });				
			} else { // merge with other component
				par[r] = to;
				weakly.connect(r, to);
				// we're no root any longer (no pq push)
			}
			break;
		}
		if (!has_outgoing) {
			int size = compressed.size(r);
			if (done_size != -1 && size != done_size)
				break;
			done_size = size;
			ans[r] = 1;
		}
	}
	for (int i = 0; i < n; i++) // everthing in their components too
		if (ans[compressed.tag(i)])
			ans[i] = 1;
}

vector<int> find_reachable(vector<int> r, vector<int> u,
		vector<int> v, vector<int> c) {
	n = r.size();
	for (int i = 0; i < n; i++)
		keys[i].insert(r[i]);
	for (size_t i = 0; i < u.size(); i++)
		for (int x = 0; x < 2; x++) {
			if (r[u[i]] == c[i])
				out_can[u[i]].push_back(v[i]);
			else
				out_blocked[u[i]].insert({ v[i], c[i] });
			swap(u[i], v[i]);
		}
	solve();
	return ans;
}

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 20 ms 41292 KB Output is correct
2 Correct 20 ms 41328 KB Output is correct
3 Correct 25 ms 41308 KB Output is correct
4 Correct 20 ms 41376 KB Output is correct
5 Correct 19 ms 41292 KB Output is correct
6 Correct 20 ms 41292 KB Output is correct
7 Correct 20 ms 41396 KB Output is correct
8 Correct 20 ms 41352 KB Output is correct
9 Correct 19 ms 41420 KB Output is correct

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 20 ms 41292 KB Output is correct
2 Correct 20 ms 41328 KB Output is correct
3 Correct 25 ms 41308 KB Output is correct
4 Correct 20 ms 41376 KB Output is correct
5 Correct 19 ms 41292 KB Output is correct
6 Correct 20 ms 41292 KB Output is correct
7 Correct 20 ms 41396 KB Output is correct
8 Correct 20 ms 41352 KB Output is correct
9 Correct 19 ms 41420 KB Output is correct
10 Correct 21 ms 41412 KB Output is correct
11 Correct 26 ms 41364 KB Output is correct
12 Correct 21 ms 41340 KB Output is correct
13 Correct 20 ms 41292 KB Output is correct
14 Correct 20 ms 41292 KB Output is correct
15 Correct 21 ms 41404 KB Output is correct
16 Correct 22 ms 41384 KB Output is correct
17 Correct 21 ms 41404 KB Output is correct
18 Correct 19 ms 41400 KB Output is correct
19 Correct 28 ms 41292 KB Output is correct
20 Correct 23 ms 41328 KB Output is correct
21 Correct 26 ms 41336 KB Output is correct
22 Correct 22 ms 41356 KB Output is correct
23 Correct 21 ms 41380 KB Output is correct
24 Correct 21 ms 41420 KB Output is correct
25 Correct 20 ms 41388 KB Output is correct
26 Correct 20 ms 41380 KB Output is correct

Subtask #3
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 20 ms 41292 KB Output is correct
2 Correct 20 ms 41328 KB Output is correct
3 Correct 25 ms 41308 KB Output is correct
4 Correct 20 ms 41376 KB Output is correct
5 Correct 19 ms 41292 KB Output is correct
6 Correct 20 ms 41292 KB Output is correct
7 Correct 20 ms 41396 KB Output is correct
8 Correct 20 ms 41352 KB Output is correct
9 Correct 19 ms 41420 KB Output is correct
10 Correct 21 ms 41412 KB Output is correct
11 Correct 26 ms 41364 KB Output is correct
12 Correct 21 ms 41340 KB Output is correct
13 Correct 20 ms 41292 KB Output is correct
14 Correct 20 ms 41292 KB Output is correct
15 Correct 21 ms 41404 KB Output is correct
16 Correct 22 ms 41384 KB Output is correct
17 Correct 21 ms 41404 KB Output is correct
18 Correct 19 ms 41400 KB Output is correct
19 Correct 28 ms 41292 KB Output is correct
20 Correct 23 ms 41328 KB Output is correct
21 Correct 26 ms 41336 KB Output is correct
22 Correct 22 ms 41356 KB Output is correct
23 Correct 21 ms 41380 KB Output is correct
24 Correct 21 ms 41420 KB Output is correct
25 Correct 20 ms 41388 KB Output is correct
26 Correct 20 ms 41380 KB Output is correct
27 Correct 25 ms 41668 KB Output is correct
28 Correct 23 ms 41804 KB Output is correct
29 Correct 22 ms 41672 KB Output is correct
30 Correct 22 ms 41524 KB Output is correct
31 Correct 21 ms 41504 KB Output is correct
32 Correct 20 ms 41420 KB Output is correct
33 Correct 22 ms 41532 KB Output is correct
34 Correct 22 ms 41452 KB Output is correct
35 Correct 22 ms 41540 KB Output is correct
36 Correct 21 ms 41692 KB Output is correct
37 Correct 22 ms 41676 KB Output is correct
38 Correct 22 ms 41656 KB Output is correct
39 Correct 24 ms 41772 KB Output is correct
40 Correct 22 ms 41520 KB Output is correct
41 Correct 23 ms 41676 KB Output is correct

Subtask #4
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 20 ms 41292 KB Output is correct
2 Correct 20 ms 41328 KB Output is correct
3 Correct 25 ms 41308 KB Output is correct
4 Correct 20 ms 41376 KB Output is correct
5 Correct 19 ms 41292 KB Output is correct
6 Correct 20 ms 41292 KB Output is correct
7 Correct 20 ms 41396 KB Output is correct
8 Correct 20 ms 41352 KB Output is correct
9 Correct 19 ms 41420 KB Output is correct
10 Correct 459 ms 81720 KB Output is correct
11 Correct 727 ms 102704 KB Output is correct
12 Correct 102 ms 51136 KB Output is correct
13 Correct 588 ms 88708 KB Output is correct
14 Correct 231 ms 87084 KB Output is correct

Subtask #5
33.0 / 33.0

# Verdict Execution time Memory Grader output
1 Correct 20 ms 41292 KB Output is correct
2 Correct 20 ms 41328 KB Output is correct
3 Correct 25 ms 41308 KB Output is correct
4 Correct 20 ms 41376 KB Output is correct
5 Correct 19 ms 41292 KB Output is correct
6 Correct 20 ms 41292 KB Output is correct
7 Correct 20 ms 41396 KB Output is correct
8 Correct 20 ms 41352 KB Output is correct
9 Correct 19 ms 41420 KB Output is correct
10 Correct 21 ms 41412 KB Output is correct
11 Correct 26 ms 41364 KB Output is correct
12 Correct 21 ms 41340 KB Output is correct
13 Correct 20 ms 41292 KB Output is correct
14 Correct 20 ms 41292 KB Output is correct
15 Correct 21 ms 41404 KB Output is correct
16 Correct 22 ms 41384 KB Output is correct
17 Correct 21 ms 41404 KB Output is correct
18 Correct 19 ms 41400 KB Output is correct
19 Correct 28 ms 41292 KB Output is correct
20 Correct 23 ms 41328 KB Output is correct
21 Correct 26 ms 41336 KB Output is correct
22 Correct 22 ms 41356 KB Output is correct
23 Correct 21 ms 41380 KB Output is correct
24 Correct 21 ms 41420 KB Output is correct
25 Correct 20 ms 41388 KB Output is correct
26 Correct 20 ms 41380 KB Output is correct
27 Correct 25 ms 41668 KB Output is correct
28 Correct 23 ms 41804 KB Output is correct
29 Correct 22 ms 41672 KB Output is correct
30 Correct 22 ms 41524 KB Output is correct
31 Correct 21 ms 41504 KB Output is correct
32 Correct 20 ms 41420 KB Output is correct
33 Correct 22 ms 41532 KB Output is correct
34 Correct 22 ms 41452 KB Output is correct
35 Correct 22 ms 41540 KB Output is correct
36 Correct 21 ms 41692 KB Output is correct
37 Correct 22 ms 41676 KB Output is correct
38 Correct 22 ms 41656 KB Output is correct
39 Correct 24 ms 41772 KB Output is correct
40 Correct 22 ms 41520 KB Output is correct
41 Correct 23 ms 41676 KB Output is correct
42 Correct 459 ms 81720 KB Output is correct
43 Correct 727 ms 102704 KB Output is correct
44 Correct 102 ms 51136 KB Output is correct
45 Correct 588 ms 88708 KB Output is correct
46 Correct 231 ms 87084 KB Output is correct
47 Correct 22 ms 41336 KB Output is correct
48 Correct 20 ms 41296 KB Output is correct
49 Correct 21 ms 41296 KB Output is correct
50 Correct 226 ms 83936 KB Output is correct
51 Correct 228 ms 87144 KB Output is correct
52 Correct 307 ms 81620 KB Output is correct
53 Correct 300 ms 81556 KB Output is correct
54 Correct 333 ms 81576 KB Output is correct
55 Correct 472 ms 88092 KB Output is correct
56 Correct 366 ms 95544 KB Output is correct
57 Correct 334 ms 92348 KB Output is correct
58 Correct 624 ms 100748 KB Output is correct
59 Correct 1173 ms 95196 KB Output is correct
60 Correct 465 ms 94100 KB Output is correct
61 Correct 480 ms 93748 KB Output is correct
62 Correct 479 ms 90120 KB Output is correct
63 Correct 358 ms 92300 KB Output is correct
64 Correct 25 ms 42056 KB Output is correct
65 Correct 24 ms 42184 KB Output is correct
66 Correct 556 ms 90040 KB Output is correct
67 Correct 44 ms 45892 KB Output is correct
68 Correct 60 ms 48936 KB Output is correct
69 Correct 1179 ms 95288 KB Output is correct
70 Correct 97 ms 56640 KB Output is correct
71 Correct 267 ms 88044 KB Output is correct
72 Correct 1150 ms 95292 KB Output is correct
73 Correct 540 ms 90076 KB Output is correct