oj.uz

Submission #843369

# Submission time Handle Problem Language Result Execution time Memory
843369 2023-09-04T00:48:47 Z radoslav11 Longest Trip (IOI23_longesttrip) C++17
100 / 100
 13 ms 1632 KB 
#include <algorithm>
#include <cassert>
#include <functional>
#include <iostream>
#include <map>
#include <numeric>
#include <random>
#include <set>
#include <utility>
#include <vector>
#include "longesttrip.h"

using namespace std;

map<pair<vector<int>, vector<int>>, bool> memo;

bool safe_are_connected(vector<int> S_left, vector<int> S_right) {
	if(S_left.size() == 0 || S_right.size() == 0) return false;
	if(memo.count(make_pair(S_left, S_right))) {
		return memo[make_pair(S_left, S_right)];
	}

	bool ret = are_connected(S_left, S_right);
	memo[make_pair(S_left, S_right)] = ret;
	memo[make_pair(S_right, S_left)] = ret;
	return ret;
}

vector<vector<int>> create_adj(
	int N, vector<int> nodes, vector<pair<int, int>> edges
) {
	vector<vector<int>> adj(N);
	vector<bool> in_nodes(N, false);
	for(auto n: nodes) in_nodes[n] = true;

	for(auto e: edges) {
		if(!in_nodes[e.first] || !in_nodes[e.second]) continue;
		adj[e.first].push_back(e.second);
		adj[e.second].push_back(e.first);
	}
	return adj;
}

void add_edge(int u, int v, vector<set<int>> &adj_set) {
	adj_set[u].insert(v);
	adj_set[v].insert(u);
}

void remove_edge(int u, int v, vector<set<int>> &adj_set) {
	adj_set[u].erase(v);
	adj_set[v].erase(u);
}

int only_par(int u, vector<set<int>> &adj_set, int from = -1) {
	assert(adj_set[u].size() <= 2);
	for(auto nei: adj_set[u]) {
		if(nei != from) return nei;
	}
	return -1;
}

void prune_tree(
	int l1, int l2, int l3, vector<int> &leaves, vector<set<int>> &adj_set
) {
	leaves.push_back(l3);

	int u = l1, v = l2;

	while(adj_set[u].size() == 1) {
		int pu = only_par(u, adj_set);
		remove_edge(u, pu, adj_set);
		add_edge(v, u, adj_set);

		v = u;
		u = pu;
	}

	leaves.push_back(v);
}

vector<int> solve_tree(int N, vector<int> nodes, vector<vector<int>> adj) {
	vector<set<int>> adj_set(N);
	for(int i = 0; i < N; i++) {
		adj_set[i] = set<int>(adj[i].begin(), adj[i].end());
	}

	// We assume that the tree is connected here
	vector<int> leaves;
	for(auto node: nodes) {
		if(adj_set[node].size() == 1) {
			leaves.push_back(node);
		}
	}

	mt19937 mt(42);
	while(leaves.size() >= 3) {
		shuffle(leaves.begin(), leaves.end(), mt);
		int l1 = leaves.back();
		leaves.pop_back();
		int l2 = leaves.back();
		leaves.pop_back();
		int l3 = leaves.back();
		leaves.pop_back();

		if(safe_are_connected({l1}, {l2})) {
			prune_tree(l1, l2, l3, leaves, adj_set);
		} else if(safe_are_connected({l1}, {l3})) {
			prune_tree(l1, l3, l2, leaves, adj_set);
		} else {
			// Delta >= 1, means that l2 and l3 are connected
			prune_tree(l2, l3, l1, leaves, adj_set);
		}
	}

	// for(auto node: nodes) {
	// 	cerr << node << "| ";
	// 	for(auto nei: adj_set[node]) {
	// 		cerr << nei << " ";
	// 	}
	// 	cerr << endl;
	// }

	// It's a path
	vector<int> path;
	vector<bool> used(N, false);

	int u = leaves[0];
	int last = -1;
	while(u != -1) {
		path.push_back(u);
		used[u] = true;
		int nlast = u;
		u = only_par(u, adj_set, last);
		last = nlast;
	}

	if(leaves.size() == 2) {
		u = leaves[1];
		vector<int> rev_path;
		while(!used[u]) {
			rev_path.push_back(u);
			int nlast = u;
			u = only_par(u, adj_set, last);
			last = nlast;
		}

		reverse(rev_path.begin(), rev_path.end());
		path.insert(path.end(), rev_path.begin(), rev_path.end());
	}

	return path;
}

pair<int, int> find_one_edge_old(
	vector<int> S_left, vector<int> S_right, mt19937 &mt
) {
	assert(S_left.size() >= 1 && S_right.size() >= 1);

	if(S_left.size() == 1 && S_right.size() == 1) {
		return {S_left[0], S_right[0]};
	}

	shuffle(S_left.begin(), S_left.end(), mt);
	shuffle(S_right.begin(), S_right.end(), mt);

	int mid_left = S_left.size() / 2;
	int mid_right = S_right.size() / 2;

	vector<int> left_left(S_left.begin(), S_left.begin() + mid_left);
	vector<int> left_right(S_left.begin() + mid_left, S_left.end());
	vector<int> right_left(S_right.begin(), S_right.begin() + mid_right);
	vector<int> right_right(S_right.begin() + mid_right, S_right.end());

	if(safe_are_connected(left_left, right_left)) {
		return find_one_edge_old(left_left, right_left, mt);
	} else if(safe_are_connected(left_left, right_right)) {
		return find_one_edge_old(left_left, right_right, mt);
	} else if(safe_are_connected(left_right, right_left)) {
		return find_one_edge_old(left_right, right_left, mt);
	} else {
		return find_one_edge_old(left_right, right_right, mt);
	}
}

pair<int, int> find_one_edge(
	vector<int> S_left, vector<int> S_right, mt19937 &mt
) {
	assert(S_left.size() >= 1 && S_right.size() >= 1);

	if(S_left.size() == 1 && S_right.size() == 1) {
		return {S_left[0], S_right[0]};
	}

	if(S_left.size() < S_right.size()) {
		swap(S_left, S_right);
	}

	shuffle(S_left.begin(), S_left.end(), mt);

	int mid_left = S_left.size() / 2;
	vector<int> left_left(S_left.begin(), S_left.begin() + mid_left);
	vector<int> left_right(S_left.begin() + mid_left, S_left.end());

	if(safe_are_connected(left_left, S_right)) {
		return find_one_edge(left_left, S_right, mt);
	} else {
		return find_one_edge(left_right, S_right, mt);
	}
}

vector<int> longest_trip(int N, int D) {
	assert(D >= 1);
	memo.clear();

	vector<int> comps[2];
	vector<pair<int, int>> edges;

	vector<int> order(N);
	iota(order.begin(), order.end(), 0);

	mt19937 mt(43);
	shuffle(order.begin(), order.end(), mt);

	comps[0].push_back(order[0]);
	int other = 1;
	int tail_0 = order[0];

	while(true) {
		while(other < N && safe_are_connected({tail_0}, {order[other]})) {
			comps[0].push_back(order[other]);
			edges.push_back({tail_0, order[other]});
			tail_0 = order[other];
			other++;
		}

		if(other == N) {
			vector<int> all_nodes(N);
			iota(all_nodes.begin(), all_nodes.end(), 0);
			auto adj = create_adj(N, all_nodes, edges);
			return solve_tree(N, all_nodes, adj);
		} else {
			// Maybe we have two components
			comps[1].push_back(order[other]);
			int tail_1 = order[other];
			other++;

			bool no_link = true;
			while(other < N) {
				vector<pair<int, int>> opts = {{tail_0, 0}, {tail_1, 1}};

				if(mt() % 2 == 0) {
					swap(opts[0], opts[1]);
				}

				int group = opts[0].second, tail = opts[0].first;
				if(safe_are_connected({tail}, {order[other]})) {
					comps[group].push_back(order[other]);
					edges.push_back({tail, order[other]});
					if(group == 0) {
						tail_0 = order[other];
					} else {
						tail_1 = order[other];
					}

					no_link = false;
				} else if(no_link) {
					group = opts[1].second, tail = opts[1].first;
					comps[group].push_back(order[other]);
					edges.push_back({tail, order[other]});
					if(group == 0) {
						tail_0 = order[other];
					} else {
						tail_1 = order[other];
					}
					no_link = true;
				} else {
					if(safe_are_connected({tail_0}, {tail_1})) {
						edges.push_back({tail_0, tail_1});

						// Merge groups
						reverse(comps[1].begin(), comps[1].end());
						comps[0].insert(
							comps[0].end(), comps[1].begin(), comps[1].end()
						);
						comps[1].clear();
						tail_0 = comps[0].back();
						break;
					} else {
						group = opts[1].second, tail = opts[1].first;
						comps[group].push_back(order[other]);
						edges.push_back({tail, order[other]});
						if(group == 0) {
							tail_0 = order[other];
						} else {
							tail_1 = order[other];
						}
						no_link = true;
					}
				}


				other++;
			}

			if(other == N) {
				if(safe_are_connected(comps[0], comps[1])) {
					edges.push_back(find_one_edge(comps[0], comps[1], mt));
					vector<int> all_nodes(N);
					iota(all_nodes.begin(), all_nodes.end(), 0);
					auto adj = create_adj(N, all_nodes, edges);
					return solve_tree(N, all_nodes, adj);
				}

				// Two disjoint paths, so just get the longer one
				if(comps[0].size() < comps[1].size()) swap(comps[0], comps[1]);

				auto adj = create_adj(N, comps[0], edges);
				return solve_tree(N, comps[0], adj);
			}
		}
	}
}

Subtask #0
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 3 ms 720 KB Output is correct

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 344 KB Output is correct
2 Correct 6 ms 344 KB Output is correct
3 Correct 5 ms 344 KB Output is correct
4 Correct 6 ms 344 KB Output is correct
5 Correct 6 ms 344 KB Output is correct

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 344 KB Output is correct
2 Correct 6 ms 344 KB Output is correct
3 Correct 5 ms 344 KB Output is correct
4 Correct 5 ms 344 KB Output is correct
5 Correct 5 ms 344 KB Output is correct
6 Correct 9 ms 344 KB Output is correct
7 Correct 8 ms 344 KB Output is correct
8 Correct 6 ms 600 KB Output is correct
9 Correct 7 ms 604 KB Output is correct
10 Correct 6 ms 616 KB Output is correct
11 Correct 6 ms 592 KB Output is correct
12 Correct 6 ms 596 KB Output is correct
13 Correct 7 ms 1032 KB Output is correct

Subtask #3
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 344 KB Output is correct
2 Correct 7 ms 344 KB Output is correct
3 Correct 5 ms 344 KB Output is correct
4 Correct 6 ms 344 KB Output is correct
5 Correct 5 ms 344 KB Output is correct
6 Correct 11 ms 600 KB Output is correct
7 Correct 9 ms 596 KB Output is correct
8 Correct 6 ms 600 KB Output is correct
9 Correct 6 ms 612 KB Output is correct
10 Correct 6 ms 940 KB Output is correct
11 Correct 7 ms 684 KB Output is correct
12 Correct 6 ms 592 KB Output is correct
13 Correct 7 ms 976 KB Output is correct
14 Correct 11 ms 344 KB Output is correct
15 Correct 10 ms 344 KB Output is correct
16 Correct 9 ms 452 KB Output is correct
17 Correct 9 ms 344 KB Output is correct
18 Correct 7 ms 344 KB Output is correct
19 Correct 8 ms 856 KB Output is correct
20 Correct 8 ms 856 KB Output is correct
21 Correct 7 ms 788 KB Output is correct
22 Correct 7 ms 788 KB Output is correct
23 Correct 7 ms 872 KB Output is correct
24 Correct 7 ms 700 KB Output is correct
25 Correct 8 ms 344 KB Output is correct
26 Correct 9 ms 344 KB Output is correct
27 Correct 9 ms 344 KB Output is correct
28 Correct 7 ms 344 KB Output is correct
29 Correct 7 ms 344 KB Output is correct
30 Correct 7 ms 692 KB Output is correct
31 Correct 7 ms 700 KB Output is correct
32 Correct 7 ms 948 KB Output is correct
33 Correct 7 ms 344 KB Output is correct
34 Correct 9 ms 1108 KB Output is correct
35 Correct 7 ms 344 KB Output is correct
36 Correct 6 ms 800 KB Output is correct
37 Correct 9 ms 704 KB Output is correct
38 Correct 7 ms 544 KB Output is correct
39 Correct 7 ms 608 KB Output is correct
40 Correct 7 ms 604 KB Output is correct
41 Correct 8 ms 684 KB Output is correct
42 Correct 7 ms 588 KB Output is correct
43 Correct 7 ms 860 KB Output is correct
44 Correct 7 ms 604 KB Output is correct
45 Correct 10 ms 344 KB Output is correct
46 Correct 11 ms 344 KB Output is correct
47 Correct 12 ms 344 KB Output is correct
48 Correct 10 ms 344 KB Output is correct
49 Correct 10 ms 344 KB Output is correct
50 Correct 7 ms 696 KB Output is correct
51 Correct 8 ms 440 KB Output is correct
52 Correct 9 ms 696 KB Output is correct
53 Correct 7 ms 344 KB Output is correct
54 Correct 8 ms 856 KB Output is correct
55 Correct 9 ms 600 KB Output is correct
56 Correct 7 ms 872 KB Output is correct
57 Correct 8 ms 688 KB Output is correct
58 Correct 8 ms 608 KB Output is correct
59 Correct 8 ms 1376 KB Output is correct
60 Correct 8 ms 864 KB Output is correct
61 Correct 8 ms 604 KB Output is correct
62 Correct 8 ms 600 KB Output is correct
63 Correct 8 ms 864 KB Output is correct
64 Correct 8 ms 1116 KB Output is correct

Subtask #4
60.0 / 60.0

# Verdict Execution time Memory Grader output
1 Correct 10 ms 516 KB Output is correct
2 Correct 6 ms 344 KB Output is correct
3 Correct 5 ms 344 KB Output is correct
4 Correct 5 ms 344 KB Output is correct
5 Correct 6 ms 344 KB Output is correct
6 Correct 9 ms 344 KB Output is correct
7 Correct 10 ms 344 KB Output is correct
8 Correct 7 ms 600 KB Output is correct
9 Correct 7 ms 600 KB Output is correct
10 Correct 6 ms 972 KB Output is correct
11 Correct 6 ms 600 KB Output is correct
12 Correct 6 ms 820 KB Output is correct
13 Correct 8 ms 880 KB Output is correct
14 Correct 11 ms 344 KB Output is correct
15 Correct 8 ms 344 KB Output is correct
16 Correct 9 ms 344 KB Output is correct
17 Correct 8 ms 344 KB Output is correct
18 Correct 8 ms 600 KB Output is correct
19 Correct 7 ms 600 KB Output is correct
20 Correct 7 ms 856 KB Output is correct
21 Correct 9 ms 344 KB Output is correct
22 Correct 9 ms 344 KB Output is correct
23 Correct 6 ms 344 KB Output is correct
24 Correct 7 ms 496 KB Output is correct
25 Correct 6 ms 344 KB Output is correct
26 Correct 6 ms 948 KB Output is correct
27 Correct 7 ms 696 KB Output is correct
28 Correct 9 ms 696 KB Output is correct
29 Correct 7 ms 856 KB Output is correct
30 Correct 9 ms 596 KB Output is correct
31 Correct 8 ms 692 KB Output is correct
32 Correct 9 ms 344 KB Output is correct
33 Correct 11 ms 596 KB Output is correct
34 Correct 9 ms 344 KB Output is correct
35 Correct 13 ms 344 KB Output is correct
36 Correct 9 ms 344 KB Output is correct
37 Correct 8 ms 980 KB Output is correct
38 Correct 10 ms 696 KB Output is correct
39 Correct 8 ms 496 KB Output is correct
40 Correct 7 ms 344 KB Output is correct
41 Correct 8 ms 856 KB Output is correct
42 Correct 9 ms 600 KB Output is correct
43 Correct 7 ms 792 KB Output is correct
44 Correct 7 ms 1020 KB Output is correct
45 Correct 7 ms 876 KB Output is correct
46 Correct 7 ms 876 KB Output is correct
47 Correct 7 ms 1024 KB Output is correct
48 Correct 7 ms 544 KB Output is correct
49 Correct 9 ms 700 KB Output is correct
50 Correct 7 ms 1032 KB Output is correct
51 Correct 7 ms 552 KB Output is correct
52 Correct 7 ms 744 KB Output is correct
53 Correct 7 ms 652 KB Output is correct
54 Correct 8 ms 1632 KB Output is correct
55 Correct 8 ms 548 KB Output is correct
56 Correct 7 ms 656 KB Output is correct
57 Correct 8 ms 608 KB Output is correct
58 Correct 7 ms 668 KB Output is correct
59 Correct 7 ms 544 KB Output is correct
60 Correct 7 ms 600 KB Output is correct
61 Correct 8 ms 852 KB Output is correct
62 Correct 7 ms 1304 KB Output is correct
63 Correct 7 ms 800 KB Output is correct
64 Correct 8 ms 904 KB Output is correct
65 Correct 8 ms 688 KB Output is correct
66 Correct 8 ms 804 KB Output is correct
67 Correct 8 ms 604 KB Output is correct
68 Correct 7 ms 684 KB Output is correct
69 Correct 8 ms 616 KB Output is correct
70 Correct 8 ms 552 KB Output is correct
71 Correct 9 ms 688 KB Output is correct
72 Correct 8 ms 1044 KB Output is correct
73 Correct 8 ms 604 KB Output is correct
74 Correct 10 ms 1216 KB Output is correct
75 Correct 8 ms 548 KB Output is correct
76 Correct 9 ms 1028 KB Output is correct
77 Correct 7 ms 796 KB Output is correct
78 Correct 8 ms 608 KB Output is correct
79 Correct 8 ms 968 KB Output is correct
80 Correct 8 ms 696 KB Output is correct
81 Correct 8 ms 688 KB Output is correct
82 Correct 8 ms 1376 KB Output is correct