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Submission #435251

# Submission time Handle Problem Language Result Execution time Memory
435251 2021-06-23T06:16:34 Z ecnerwala Keys (IOI21_keys) C++17
100 / 100
 1352 ms 49712 KB 
#include "keys.h"

#include <bits/stdc++.h>

namespace ecnerwala {

struct par_compressor {
	mutable std::vector<int> par;
	par_compressor(int N) : par(N, -1) {}
	int get_par(int a) const {
		while (par[a] >= 0) {
			if (par[par[a]] >= 0) par[a] = par[par[a]];
			a = par[a];
		}
		return a;
	}
	void set_par(int a, int b) {
		assert(par[a] < 0 && par[b] < 0);
		assert(a != b);
		par[b] += par[a];
		par[a] = b;
	}
	int cc_sz(int a) const {
		assert(par[a] < 0);
		return -par[a];
	}
};

}

std::vector<int> find_reachable(std::vector<int> R, std::vector<int> U, std::vector<int> V, std::vector<int> C) {
	using namespace ecnerwala;

	int N = int(R.size());
	int M = int(U.size());
	assert(M == int(V.size()));
	assert(M == int(C.size()));

	U.insert(U.end(), V.begin(), V.end());
	V = {};

	std::vector<int> edge_nxt(2*M, -1);

	struct linked_list {
		int st, en;
		linked_list() : st(-1), en(-1) {}
		explicit linked_list(int a) : st(a), en(a) {}
	};
	auto concat = [&](linked_list& a, linked_list& b) {
		if (b.st == -1) return;
		if (a.st == -1) {
			a = b;
			b.st = b.en = -1;
			return;
		}

		edge_nxt[a.en] = b.st;
		a.en = b.en;
		b.st = b.en = -1;
	};

	struct treap_node {
		std::array<int, 2> c = {-1, -1};
		std::mt19937::result_type pri;
		int v;
		linked_list l;
	};
	using edge_set = int;
	std::vector<treap_node> nodes(N+2*M);
	std::mt19937 mt(std::chrono::steady_clock::now().time_since_epoch().count());
	for (auto& n : nodes) n.pri = mt();

	auto edge_set_union = [&](edge_set a_, edge_set b_, linked_list& unlocks) -> edge_set {
		auto dfs = [&](auto self, edge_set a, edge_set b) -> edge_set {
			if (b == -1) return a;
			if (a == -1) return b;
			if (nodes[a].pri > nodes[b].pri) std::swap(a, b);
			// split b by a into x and y
			int x, y;
			{
				int *l = &x, *r = &y;
				while (true) {
					if (b == -1) {
						*l = *r = -1;
						break;
					}
					if (nodes[b].v == nodes[a].v) {
						if (nodes[b].l.st == -2) std::swap(nodes[a].l, nodes[b].l);
						if (nodes[a].l.st == -2) {
							if (nodes[b].l.st != -2) concat(unlocks, nodes[b].l);
						} else {
							concat(nodes[a].l, nodes[b].l);
						}
						*l = nodes[b].c[0];
						*r = nodes[b].c[1];
						break;
					} else if (nodes[b].v < nodes[a].v) {
						*l = b;
						l = &nodes[b].c[1];
						b = nodes[b].c[1];
					} else if (nodes[b].v > nodes[a].v) {
						*r = b;
						r = &nodes[b].c[0];
						b = nodes[b].c[0];
					} else assert(false);
				}
			}
			nodes[a].c[0] = self(self, nodes[a].c[0], x);
			nodes[a].c[1] = self(self, nodes[a].c[1], y);
			return a;
		};
		return dfs(dfs, a_, b_);
	};

	std::vector<linked_list> unlocked_edges(N);
	std::vector<edge_set> locked_edges(N);
	for (int i = 0; i < N; i++) {
		locked_edges[i] = i;
		nodes[i].v = R[i];
		nodes[i].l = linked_list(-2);
	}
	for (int e = 0, o = M; e < 2*M; e++, o++) {
		if (o == 2*M) o = 0;
		int u = U[o];
		int c = C[std::min(e, o)];
		edge_set a = N+e;
		nodes[a].v = c;
		nodes[a].l = linked_list(e);
		locked_edges[u] = edge_set_union(locked_edges[u], a, unlocked_edges[u]);
	}

	par_compressor compressed_node_par(N);
	std::vector<int> forest_par(N, -1);
	par_compressor forest_root(N);

	int best_sz = N+1;

	for (int st = 0; st < N; st++) {
		while (true) {
			int e = unlocked_edges[st].st;
			if (e == -1) {
				best_sz = std::min(best_sz, compressed_node_par.cc_sz(st));
				break;
			}
			unlocked_edges[st].st = edge_nxt[e];
			if (edge_nxt[e] == -1) unlocked_edges[st].en = -1;
			edge_nxt[e] = -1;

			int dest = compressed_node_par.get_par(U[e]);
			int dest_tree = forest_root.get_par(dest);
			if (dest_tree == st) {
				// compress it
				while (dest != st) {
					// merge dest into st
					concat(unlocked_edges[st], unlocked_edges[dest]);
					locked_edges[st] = edge_set_union(locked_edges[st], locked_edges[dest], unlocked_edges[st]);

					compressed_node_par.set_par(dest, st);
					dest = compressed_node_par.get_par(forest_par[dest]);
				}
			} else {
				// Link ourself up to dest and keep going
				forest_par[st] = dest;
				forest_root.set_par(st, dest_tree);
				break;
			}
		}
	}

	std::vector<int> ans(N, false);
	for (int i = 0; i < N; i++) {
		int n = compressed_node_par.get_par(i);
		if (forest_par[n] != -1) continue;
		if (compressed_node_par.cc_sz(n) == best_sz) ans[i] = true;
	}

	return ans;
}

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 1 ms 204 KB Output is correct
5 Correct 1 ms 204 KB Output is correct
6 Correct 1 ms 204 KB Output is correct
7 Correct 1 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 1 ms 204 KB Output is correct

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 1 ms 204 KB Output is correct
5 Correct 1 ms 204 KB Output is correct
6 Correct 1 ms 204 KB Output is correct
7 Correct 1 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 1 ms 204 KB Output is correct
10 Correct 1 ms 204 KB Output is correct
11 Correct 1 ms 204 KB Output is correct
12 Correct 1 ms 204 KB Output is correct
13 Correct 1 ms 204 KB Output is correct
14 Correct 1 ms 204 KB Output is correct
15 Correct 1 ms 204 KB Output is correct
16 Correct 1 ms 204 KB Output is correct
17 Correct 1 ms 204 KB Output is correct
18 Correct 1 ms 204 KB Output is correct
19 Correct 1 ms 204 KB Output is correct
20 Correct 1 ms 204 KB Output is correct
21 Correct 1 ms 204 KB Output is correct
22 Correct 1 ms 204 KB Output is correct
23 Correct 1 ms 204 KB Output is correct
24 Correct 1 ms 204 KB Output is correct
25 Correct 1 ms 204 KB Output is correct
26 Correct 1 ms 204 KB Output is correct

Subtask #3
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 1 ms 204 KB Output is correct
5 Correct 1 ms 204 KB Output is correct
6 Correct 1 ms 204 KB Output is correct
7 Correct 1 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 1 ms 204 KB Output is correct
10 Correct 1 ms 204 KB Output is correct
11 Correct 1 ms 204 KB Output is correct
12 Correct 1 ms 204 KB Output is correct
13 Correct 1 ms 204 KB Output is correct
14 Correct 1 ms 204 KB Output is correct
15 Correct 1 ms 204 KB Output is correct
16 Correct 1 ms 204 KB Output is correct
17 Correct 1 ms 204 KB Output is correct
18 Correct 1 ms 204 KB Output is correct
19 Correct 1 ms 204 KB Output is correct
20 Correct 1 ms 204 KB Output is correct
21 Correct 1 ms 204 KB Output is correct
22 Correct 1 ms 204 KB Output is correct
23 Correct 1 ms 204 KB Output is correct
24 Correct 1 ms 204 KB Output is correct
25 Correct 1 ms 204 KB Output is correct
26 Correct 1 ms 204 KB Output is correct
27 Correct 2 ms 588 KB Output is correct
28 Correct 2 ms 588 KB Output is correct
29 Correct 2 ms 588 KB Output is correct
30 Correct 2 ms 332 KB Output is correct
31 Correct 1 ms 332 KB Output is correct
32 Correct 1 ms 332 KB Output is correct
33 Correct 1 ms 332 KB Output is correct
34 Correct 1 ms 332 KB Output is correct
35 Correct 2 ms 332 KB Output is correct
36 Correct 2 ms 588 KB Output is correct
37 Correct 3 ms 588 KB Output is correct
38 Correct 4 ms 588 KB Output is correct
39 Correct 3 ms 588 KB Output is correct
40 Correct 2 ms 460 KB Output is correct
41 Correct 3 ms 460 KB Output is correct

Subtask #4
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 1 ms 204 KB Output is correct
5 Correct 1 ms 204 KB Output is correct
6 Correct 1 ms 204 KB Output is correct
7 Correct 1 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 1 ms 204 KB Output is correct
10 Correct 453 ms 36268 KB Output is correct
11 Correct 425 ms 49524 KB Output is correct
12 Correct 55 ms 9416 KB Output is correct
13 Correct 498 ms 45660 KB Output is correct
14 Correct 205 ms 49500 KB Output is correct

Subtask #5
33.0 / 33.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 1 ms 204 KB Output is correct
5 Correct 1 ms 204 KB Output is correct
6 Correct 1 ms 204 KB Output is correct
7 Correct 1 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 1 ms 204 KB Output is correct
10 Correct 1 ms 204 KB Output is correct
11 Correct 1 ms 204 KB Output is correct
12 Correct 1 ms 204 KB Output is correct
13 Correct 1 ms 204 KB Output is correct
14 Correct 1 ms 204 KB Output is correct
15 Correct 1 ms 204 KB Output is correct
16 Correct 1 ms 204 KB Output is correct
17 Correct 1 ms 204 KB Output is correct
18 Correct 1 ms 204 KB Output is correct
19 Correct 1 ms 204 KB Output is correct
20 Correct 1 ms 204 KB Output is correct
21 Correct 1 ms 204 KB Output is correct
22 Correct 1 ms 204 KB Output is correct
23 Correct 1 ms 204 KB Output is correct
24 Correct 1 ms 204 KB Output is correct
25 Correct 1 ms 204 KB Output is correct
26 Correct 1 ms 204 KB Output is correct
27 Correct 2 ms 588 KB Output is correct
28 Correct 2 ms 588 KB Output is correct
29 Correct 2 ms 588 KB Output is correct
30 Correct 2 ms 332 KB Output is correct
31 Correct 1 ms 332 KB Output is correct
32 Correct 1 ms 332 KB Output is correct
33 Correct 1 ms 332 KB Output is correct
34 Correct 1 ms 332 KB Output is correct
35 Correct 2 ms 332 KB Output is correct
36 Correct 2 ms 588 KB Output is correct
37 Correct 3 ms 588 KB Output is correct
38 Correct 4 ms 588 KB Output is correct
39 Correct 3 ms 588 KB Output is correct
40 Correct 2 ms 460 KB Output is correct
41 Correct 3 ms 460 KB Output is correct
42 Correct 453 ms 36268 KB Output is correct
43 Correct 425 ms 49524 KB Output is correct
44 Correct 55 ms 9416 KB Output is correct
45 Correct 498 ms 45660 KB Output is correct
46 Correct 205 ms 49500 KB Output is correct
47 Correct 1 ms 204 KB Output is correct
48 Correct 1 ms 204 KB Output is correct
49 Correct 1 ms 204 KB Output is correct
50 Correct 238 ms 49632 KB Output is correct
51 Correct 228 ms 49712 KB Output is correct
52 Correct 237 ms 33132 KB Output is correct
53 Correct 258 ms 33084 KB Output is correct
54 Correct 251 ms 33140 KB Output is correct
55 Correct 686 ms 36292 KB Output is correct
56 Correct 427 ms 49584 KB Output is correct
57 Correct 262 ms 49628 KB Output is correct
58 Correct 861 ms 49524 KB Output is correct
59 Correct 1255 ms 42948 KB Output is correct
60 Correct 1116 ms 43072 KB Output is correct
61 Correct 1058 ms 42940 KB Output is correct
62 Correct 768 ms 38372 KB Output is correct
63 Correct 221 ms 40632 KB Output is correct
64 Correct 4 ms 1100 KB Output is correct
65 Correct 4 ms 1100 KB Output is correct
66 Correct 770 ms 38368 KB Output is correct
67 Correct 28 ms 5224 KB Output is correct
68 Correct 34 ms 8432 KB Output is correct
69 Correct 1210 ms 42944 KB Output is correct
70 Correct 81 ms 16692 KB Output is correct
71 Correct 241 ms 49516 KB Output is correct
72 Correct 1352 ms 42948 KB Output is correct
73 Correct 852 ms 38372 KB Output is correct