oj.uz

Submission #843339

# Submission time Handle Problem Language Result Execution time Memory
843339 2023-09-03T23:14:05 Z radoslav11 Longest Trip (IOI23_longesttrip) C++17
85 / 100
 16 ms 1376 KB 
#include <algorithm>
#include <cassert>
#include <functional>
#include <iostream>
#include <numeric>
#include <random>
#include <set>
#include <utility>
#include <vector>
#include <map>
#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(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 && 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 first_is_free = true;	
			while(other < N) {
				while(other < N && safe_are_connected({tail_1}, {order[other]})) {
					comps[1].push_back(order[other]);
					edges.push_back({tail_1, order[other]});
					tail_1 = order[other];
					other++;
					first_is_free = false;
				}


				if(other < N && (first_is_free || 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++;
					first_is_free = false;
				} else if(other < N) {
					edges.push_back({tail_1, tail_0});
					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;
				}
			}

			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 2 ms 536 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 9 ms 344 KB Output is correct
3 Correct 6 ms 344 KB Output is correct
4 Correct 6 ms 452 KB Output is correct
5 Correct 7 ms 600 KB Output is correct

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 9 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 7 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 9 ms 344 KB Output is correct
8 Correct 9 ms 696 KB Output is correct
9 Correct 6 ms 864 KB Output is correct
10 Correct 6 ms 608 KB Output is correct
11 Correct 8 ms 1044 KB Output is correct
12 Correct 6 ms 1036 KB Output is correct
13 Correct 7 ms 1028 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 8 ms 344 KB Output is correct
3 Correct 6 ms 596 KB Output is correct
4 Correct 5 ms 344 KB Output is correct
5 Correct 6 ms 600 KB Output is correct
6 Correct 10 ms 344 KB Output is correct
7 Correct 8 ms 344 KB Output is correct
8 Correct 7 ms 736 KB Output is correct
9 Correct 6 ms 856 KB Output is correct
10 Correct 6 ms 732 KB Output is correct
11 Correct 8 ms 1188 KB Output is correct
12 Correct 7 ms 1040 KB Output is correct
13 Correct 6 ms 1036 KB Output is correct
14 Correct 11 ms 344 KB Output is correct
15 Correct 13 ms 600 KB Output is correct
16 Correct 10 ms 600 KB Output is correct
17 Correct 9 ms 600 KB Output is correct
18 Correct 8 ms 604 KB Output is correct
19 Correct 8 ms 856 KB Output is correct
20 Correct 7 ms 612 KB Output is correct
21 Correct 7 ms 1216 KB Output is correct
22 Correct 8 ms 1112 KB Output is correct
23 Correct 8 ms 1112 KB Output is correct
24 Correct 8 ms 788 KB Output is correct
25 Correct 11 ms 344 KB Output is correct
26 Correct 9 ms 344 KB Output is correct
27 Correct 8 ms 344 KB Output is correct
28 Correct 8 ms 344 KB Output is correct
29 Correct 9 ms 600 KB Output is correct
30 Correct 8 ms 440 KB Output is correct
31 Correct 10 ms 444 KB Output is correct
32 Correct 8 ms 436 KB Output is correct
33 Correct 8 ms 344 KB Output is correct
34 Correct 10 ms 1112 KB Output is correct
35 Correct 10 ms 344 KB Output is correct
36 Correct 9 ms 656 KB Output is correct
37 Correct 11 ms 924 KB Output is correct
38 Correct 10 ms 776 KB Output is correct
39 Correct 8 ms 644 KB Output is correct
40 Correct 9 ms 760 KB Output is correct
41 Correct 9 ms 744 KB Output is correct
42 Correct 10 ms 600 KB Output is correct
43 Correct 9 ms 1132 KB Output is correct
44 Correct 8 ms 648 KB Output is correct
45 Correct 10 ms 344 KB Output is correct
46 Correct 10 ms 344 KB Output is correct
47 Correct 10 ms 344 KB Output is correct
48 Correct 10 ms 344 KB Output is correct
49 Correct 11 ms 344 KB Output is correct
50 Correct 9 ms 688 KB Output is correct
51 Correct 13 ms 504 KB Output is correct
52 Correct 10 ms 436 KB Output is correct
53 Correct 8 ms 600 KB Output is correct
54 Correct 12 ms 856 KB Output is correct
55 Correct 10 ms 1112 KB Output is correct
56 Correct 7 ms 868 KB Output is correct
57 Correct 13 ms 868 KB Output is correct
58 Correct 11 ms 1080 KB Output is correct
59 Correct 16 ms 856 KB Output is correct
60 Correct 11 ms 904 KB Output is correct
61 Correct 10 ms 840 KB Output is correct
62 Correct 9 ms 700 KB Output is correct
63 Correct 9 ms 1032 KB Output is correct
64 Correct 10 ms 856 KB Output is correct

Subtask #4
45.0 / 60.0

# Verdict Execution time Memory Grader output
1 Correct 9 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 600 KB Output is correct
5 Correct 6 ms 344 KB Output is correct
6 Correct 11 ms 344 KB Output is correct
7 Correct 8 ms 544 KB Output is correct
8 Correct 6 ms 600 KB Output is correct
9 Correct 6 ms 600 KB Output is correct
10 Correct 7 ms 612 KB Output is correct
11 Correct 6 ms 1376 KB Output is correct
12 Correct 6 ms 976 KB Output is correct
13 Correct 7 ms 872 KB Output is correct
14 Correct 12 ms 344 KB Output is correct
15 Correct 9 ms 344 KB Output is correct
16 Correct 9 ms 344 KB Output is correct
17 Correct 10 ms 600 KB Output is correct
18 Correct 8 ms 856 KB Output is correct
19 Correct 7 ms 644 KB Output is correct
20 Correct 9 ms 608 KB Output is correct
21 Correct 9 ms 344 KB Output is correct
22 Correct 8 ms 344 KB Output is correct
23 Correct 10 ms 344 KB Output is correct
24 Correct 11 ms 600 KB Output is correct
25 Correct 10 ms 344 KB Output is correct
26 Correct 9 ms 692 KB Output is correct
27 Correct 8 ms 440 KB Output is correct
28 Correct 8 ms 440 KB Output is correct
29 Correct 8 ms 600 KB Output is correct
30 Correct 13 ms 856 KB Output is correct
31 Correct 10 ms 704 KB Output is correct
32 Correct 10 ms 344 KB Output is correct
33 Correct 11 ms 344 KB Output is correct
34 Correct 10 ms 344 KB Output is correct
35 Correct 13 ms 344 KB Output is correct
36 Correct 10 ms 344 KB Output is correct
37 Correct 9 ms 696 KB Output is correct
38 Correct 13 ms 504 KB Output is correct
39 Correct 10 ms 440 KB Output is correct
40 Correct 8 ms 1112 KB Output is correct
41 Correct 11 ms 600 KB Output is correct
42 Correct 11 ms 780 KB Output is correct
43 Correct 7 ms 1196 KB Output is correct
44 Correct 7 ms 804 KB Output is correct
45 Correct 7 ms 984 KB Output is correct
46 Correct 7 ms 616 KB Output is correct
47 Partially correct 9 ms 724 KB Output is partially correct
48 Partially correct 12 ms 1096 KB Output is partially correct
49 Partially correct 8 ms 900 KB Output is partially correct
50 Partially correct 10 ms 880 KB Output is partially correct
51 Partially correct 9 ms 652 KB Output is partially correct
52 Correct 10 ms 600 KB Output is correct
53 Correct 9 ms 600 KB Output is correct
54 Correct 9 ms 988 KB Output is correct
55 Correct 8 ms 724 KB Output is correct
56 Partially correct 11 ms 664 KB Output is partially correct
57 Partially correct 9 ms 600 KB Output is partially correct
58 Partially correct 11 ms 1112 KB Output is partially correct
59 Partially correct 11 ms 600 KB Output is partially correct
60 Correct 9 ms 600 KB Output is correct
61 Correct 10 ms 856 KB Output is correct
62 Correct 7 ms 980 KB Output is correct
63 Partially correct 11 ms 848 KB Output is partially correct
64 Partially correct 11 ms 856 KB Output is partially correct
65 Partially correct 11 ms 696 KB Output is partially correct
66 Partially correct 10 ms 896 KB Output is partially correct
67 Correct 9 ms 736 KB Output is correct
68 Correct 9 ms 884 KB Output is correct
69 Partially correct 12 ms 920 KB Output is partially correct
70 Partially correct 10 ms 632 KB Output is partially correct
71 Partially correct 11 ms 908 KB Output is partially correct
72 Partially correct 14 ms 1200 KB Output is partially correct
73 Partially correct 10 ms 636 KB Output is partially correct
74 Partially correct 10 ms 628 KB Output is partially correct
75 Correct 10 ms 1216 KB Output is correct
76 Partially correct 9 ms 632 KB Output is partially correct
77 Partially correct 13 ms 1156 KB Output is partially correct
78 Partially correct 12 ms 920 KB Output is partially correct
79 Partially correct 10 ms 956 KB Output is partially correct
80 Partially correct 10 ms 836 KB Output is partially correct
81 Correct 9 ms 716 KB Output is correct
82 Partially correct 10 ms 636 KB Output is partially correct