oj.uz

Submission #843317

# Submission time Handle Problem Language Result Execution time Memory
843317 2023-09-03T22:30:53 Z radoslav11 Longest Trip (IOI23_longesttrip) C++17
85 / 100
 12 ms 1112 KB 
#include <algorithm>
#include <cassert>
#include <functional>
#include <iostream>
#include <numeric>
#include <random>
#include <set>
#include <utility>
#include <vector>
#include "longesttrip.h"

using namespace std;

bool safe_are_connected(vector<int> S_left, vector<int> S_right) {
	if(S_left.size() == 0 || S_right.size() == 0) return false;
	return are_connected(S_left, S_right);
}

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(are_connected({l1}, {l2})) {
			prune_tree(l1, l2, l3, leaves, adj_set);
		} else if(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);

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

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

	mt19937 mt(42);
	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 && 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++;

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

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

				bool try_other = false;

				int group = opts[0].second, tail = opts[0].first;
				if(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];
					}
					try_other = true;
				} 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];
					}
				}

				group = opts[1].second, tail = opts[1].first;
				if(try_other && are_connected({tail}, {order[other]})) {
					edges.push_back({tail, order[other]});

					// 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();
					other++;
					break;
				}

				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 1 ms 344 KB Output is correct
2 Correct 1 ms 344 KB Output is correct

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 10 ms 344 KB Output is correct
2 Correct 5 ms 344 KB Output is correct
3 Correct 5 ms 344 KB Output is correct
4 Correct 5 ms 600 KB Output is correct
5 Correct 5 ms 600 KB Output is correct

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 10 ms 344 KB Output is correct
2 Correct 7 ms 596 KB Output is correct
3 Correct 5 ms 344 KB Output is correct
4 Correct 4 ms 340 KB Output is correct
5 Correct 5 ms 344 KB Output is correct
6 Correct 9 ms 344 KB Output is correct
7 Correct 6 ms 344 KB Output is correct
8 Correct 5 ms 344 KB Output is correct
9 Correct 5 ms 856 KB Output is correct
10 Correct 5 ms 344 KB Output is correct
11 Correct 6 ms 344 KB Output is correct
12 Correct 5 ms 600 KB Output is correct
13 Correct 6 ms 604 KB Output is correct

Subtask #3
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 344 KB Output is correct
2 Correct 8 ms 592 KB Output is correct
3 Correct 5 ms 344 KB Output is correct
4 Correct 4 ms 440 KB Output is correct
5 Correct 6 ms 696 KB Output is correct
6 Correct 9 ms 344 KB Output is correct
7 Correct 7 ms 344 KB Output is correct
8 Correct 5 ms 600 KB Output is correct
9 Correct 4 ms 344 KB Output is correct
10 Correct 5 ms 344 KB Output is correct
11 Correct 5 ms 344 KB Output is correct
12 Correct 5 ms 600 KB Output is correct
13 Correct 5 ms 444 KB Output is correct
14 Correct 9 ms 344 KB Output is correct
15 Correct 10 ms 344 KB Output is correct
16 Correct 7 ms 344 KB Output is correct
17 Correct 8 ms 344 KB Output is correct
18 Correct 7 ms 600 KB Output is correct
19 Correct 6 ms 600 KB Output is correct
20 Correct 6 ms 600 KB Output is correct
21 Correct 6 ms 344 KB Output is correct
22 Correct 6 ms 600 KB Output is correct
23 Correct 5 ms 772 KB Output is correct
24 Correct 5 ms 600 KB Output is correct
25 Correct 8 ms 344 KB Output is correct
26 Correct 11 ms 344 KB Output is correct
27 Correct 8 ms 344 KB Output is correct
28 Correct 7 ms 344 KB Output is correct
29 Correct 8 ms 344 KB Output is correct
30 Correct 6 ms 440 KB Output is correct
31 Correct 7 ms 444 KB Output is correct
32 Correct 7 ms 436 KB Output is correct
33 Correct 6 ms 344 KB Output is correct
34 Correct 8 ms 856 KB Output is correct
35 Correct 7 ms 444 KB Output is correct
36 Correct 6 ms 600 KB Output is correct
37 Correct 6 ms 604 KB Output is correct
38 Correct 8 ms 444 KB Output is correct
39 Correct 8 ms 604 KB Output is correct
40 Correct 7 ms 600 KB Output is correct
41 Correct 8 ms 344 KB Output is correct
42 Correct 9 ms 856 KB Output is correct
43 Correct 7 ms 600 KB Output is correct
44 Correct 8 ms 444 KB Output is correct
45 Correct 9 ms 344 KB Output is correct
46 Correct 10 ms 344 KB Output is correct
47 Correct 8 ms 344 KB Output is correct
48 Correct 11 ms 344 KB Output is correct
49 Correct 9 ms 344 KB Output is correct
50 Correct 7 ms 696 KB Output is correct
51 Correct 8 ms 696 KB Output is correct
52 Correct 8 ms 440 KB Output is correct
53 Correct 10 ms 692 KB Output is correct
54 Correct 7 ms 600 KB Output is correct
55 Correct 7 ms 600 KB Output is correct
56 Correct 6 ms 1032 KB Output is correct
57 Correct 7 ms 600 KB Output is correct
58 Correct 8 ms 604 KB Output is correct
59 Correct 7 ms 600 KB Output is correct
60 Correct 7 ms 804 KB Output is correct
61 Correct 8 ms 604 KB Output is correct
62 Correct 8 ms 600 KB Output is correct
63 Correct 7 ms 600 KB Output is correct
64 Correct 7 ms 600 KB Output is correct

Subtask #4
45.0 / 60.0

# Verdict Execution time Memory Grader output
1 Correct 7 ms 344 KB Output is correct
2 Correct 5 ms 344 KB Output is correct
3 Correct 5 ms 344 KB Output is correct
4 Correct 4 ms 344 KB Output is correct
5 Correct 5 ms 600 KB Output is correct
6 Correct 9 ms 344 KB Output is correct
7 Correct 6 ms 344 KB Output is correct
8 Correct 5 ms 600 KB Output is correct
9 Correct 5 ms 344 KB Output is correct
10 Correct 7 ms 600 KB Output is correct
11 Correct 4 ms 344 KB Output is correct
12 Correct 5 ms 600 KB Output is correct
13 Correct 5 ms 596 KB Output is correct
14 Correct 10 ms 344 KB Output is correct
15 Correct 12 ms 600 KB Output is correct
16 Correct 8 ms 344 KB Output is correct
17 Correct 6 ms 600 KB Output is correct
18 Correct 8 ms 344 KB Output is correct
19 Correct 6 ms 600 KB Output is correct
20 Correct 6 ms 600 KB Output is correct
21 Correct 11 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 6 ms 344 KB Output is correct
25 Correct 6 ms 344 KB Output is correct
26 Correct 6 ms 436 KB Output is correct
27 Correct 8 ms 436 KB Output is correct
28 Correct 7 ms 440 KB Output is correct
29 Correct 7 ms 600 KB Output is correct
30 Correct 7 ms 344 KB Output is correct
31 Correct 7 ms 344 KB Output is correct
32 Correct 10 ms 344 KB Output is correct
33 Correct 11 ms 344 KB Output is correct
34 Correct 11 ms 344 KB Output is correct
35 Correct 8 ms 344 KB Output is correct
36 Correct 10 ms 344 KB Output is correct
37 Correct 8 ms 464 KB Output is correct
38 Correct 8 ms 692 KB Output is correct
39 Correct 9 ms 436 KB Output is correct
40 Correct 7 ms 636 KB Output is correct
41 Correct 7 ms 600 KB Output is correct
42 Correct 7 ms 600 KB Output is correct
43 Correct 6 ms 856 KB Output is correct
44 Correct 5 ms 516 KB Output is correct
45 Correct 6 ms 924 KB Output is correct
46 Correct 6 ms 344 KB Output is correct
47 Correct 6 ms 600 KB Output is correct
48 Correct 7 ms 448 KB Output is correct
49 Correct 6 ms 444 KB Output is correct
50 Correct 7 ms 608 KB Output is correct
51 Correct 7 ms 444 KB Output is correct
52 Correct 9 ms 688 KB Output is correct
53 Correct 9 ms 344 KB Output is correct
54 Correct 8 ms 1112 KB Output is correct
55 Correct 8 ms 860 KB Output is correct
56 Correct 7 ms 444 KB Output is correct
57 Correct 7 ms 696 KB Output is correct
58 Correct 6 ms 604 KB Output is correct
59 Correct 8 ms 600 KB Output is correct
60 Correct 7 ms 1112 KB Output is correct
61 Correct 7 ms 692 KB Output is correct
62 Correct 6 ms 528 KB Output is correct
63 Correct 7 ms 444 KB Output is correct
64 Correct 8 ms 704 KB Output is correct
65 Correct 8 ms 604 KB Output is correct
66 Correct 7 ms 600 KB Output is correct
67 Partially correct 7 ms 620 KB Output is partially correct
68 Partially correct 8 ms 600 KB Output is partially correct
69 Partially correct 9 ms 860 KB Output is partially correct
70 Partially correct 8 ms 600 KB Output is partially correct
71 Correct 7 ms 608 KB Output is correct
72 Partially correct 9 ms 856 KB Output is partially correct
73 Partially correct 8 ms 856 KB Output is partially correct
74 Partially correct 8 ms 604 KB Output is partially correct
75 Partially correct 8 ms 600 KB Output is partially correct
76 Partially correct 7 ms 868 KB Output is partially correct
77 Correct 7 ms 600 KB Output is correct
78 Correct 7 ms 604 KB Output is correct
79 Partially correct 8 ms 700 KB Output is partially correct
80 Partially correct 7 ms 700 KB Output is partially correct
81 Partially correct 7 ms 600 KB Output is partially correct
82 Partially correct 7 ms 448 KB Output is partially correct