oj.uz

Submission #843322

# Submission time Handle Problem Language Result Execution time Memory
843322 2023-09-03T22:57:38 Z radoslav11 Longest Trip (IOI23_longesttrip) C++17
85 / 100
 12 ms 1300 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++;

			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++;
			}

			if(other < N) {
				reverse(comps[1].begin(), comps[1].end());
				tail_1 = comps[1].back();
			}

			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(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];
					}
					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 && safe_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 0 ms 344 KB Output is correct
2 Correct 2 ms 768 KB Output is correct

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 344 KB Output is correct
2 Correct 7 ms 344 KB Output is correct
3 Correct 6 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 10 ms 600 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 11 ms 344 KB Output is correct
7 Correct 10 ms 344 KB Output is correct
8 Correct 6 ms 856 KB Output is correct
9 Correct 6 ms 856 KB Output is correct
10 Correct 6 ms 1240 KB Output is correct
11 Correct 7 ms 856 KB Output is correct
12 Correct 6 ms 596 KB Output is correct
13 Correct 6 ms 600 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 6 ms 344 KB Output is correct
4 Correct 5 ms 344 KB Output is correct
5 Correct 6 ms 600 KB Output is correct
6 Correct 11 ms 344 KB Output is correct
7 Correct 8 ms 344 KB Output is correct
8 Correct 7 ms 600 KB Output is correct
9 Correct 6 ms 600 KB Output is correct
10 Correct 8 ms 1064 KB Output is correct
11 Correct 6 ms 596 KB Output is correct
12 Correct 6 ms 720 KB Output is correct
13 Correct 6 ms 600 KB Output is correct
14 Correct 10 ms 344 KB Output is correct
15 Correct 10 ms 344 KB Output is correct
16 Correct 11 ms 344 KB Output is correct
17 Correct 8 ms 344 KB Output is correct
18 Correct 8 ms 712 KB Output is correct
19 Correct 7 ms 776 KB Output is correct
20 Correct 7 ms 776 KB Output is correct
21 Correct 7 ms 796 KB Output is correct
22 Correct 7 ms 672 KB Output is correct
23 Correct 6 ms 692 KB Output is correct
24 Correct 6 ms 872 KB Output is correct
25 Correct 8 ms 344 KB Output is correct
26 Correct 10 ms 344 KB Output is correct
27 Correct 8 ms 344 KB Output is correct
28 Correct 11 ms 600 KB Output is correct
29 Correct 8 ms 344 KB Output is correct
30 Correct 8 ms 436 KB Output is correct
31 Correct 8 ms 948 KB Output is correct
32 Correct 8 ms 704 KB Output is correct
33 Correct 7 ms 344 KB Output is correct
34 Correct 9 ms 1112 KB Output is correct
35 Correct 9 ms 856 KB Output is correct
36 Correct 7 ms 556 KB Output is correct
37 Correct 8 ms 1140 KB Output is correct
38 Correct 9 ms 896 KB Output is correct
39 Correct 8 ms 640 KB Output is correct
40 Correct 9 ms 976 KB Output is correct
41 Correct 10 ms 856 KB Output is correct
42 Correct 8 ms 600 KB Output is correct
43 Correct 8 ms 648 KB Output is correct
44 Correct 8 ms 904 KB Output is correct
45 Correct 10 ms 344 KB Output is correct
46 Correct 10 ms 344 KB Output is correct
47 Correct 11 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 8 ms 948 KB Output is correct
51 Correct 10 ms 440 KB Output is correct
52 Correct 10 ms 500 KB Output is correct
53 Correct 7 ms 600 KB Output is correct
54 Correct 9 ms 600 KB Output is correct
55 Correct 9 ms 600 KB Output is correct
56 Correct 7 ms 944 KB Output is correct
57 Correct 9 ms 880 KB Output is correct
58 Correct 11 ms 944 KB Output is correct
59 Correct 10 ms 956 KB Output is correct
60 Correct 10 ms 568 KB Output is correct
61 Correct 9 ms 628 KB Output is correct
62 Correct 9 ms 716 KB Output is correct
63 Correct 9 ms 1168 KB Output is correct
64 Correct 9 ms 712 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 7 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 10 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 6 ms 640 KB Output is correct
10 Correct 6 ms 772 KB Output is correct
11 Correct 8 ms 816 KB Output is correct
12 Correct 7 ms 856 KB Output is correct
13 Correct 6 ms 600 KB Output is correct
14 Correct 10 ms 344 KB Output is correct
15 Correct 10 ms 344 KB Output is correct
16 Correct 9 ms 344 KB Output is correct
17 Correct 8 ms 600 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 11 ms 344 KB Output is correct
23 Correct 8 ms 344 KB Output is correct
24 Correct 8 ms 344 KB Output is correct
25 Correct 9 ms 344 KB Output is correct
26 Correct 7 ms 440 KB Output is correct
27 Correct 8 ms 440 KB Output is correct
28 Correct 9 ms 696 KB Output is correct
29 Correct 7 ms 600 KB Output is correct
30 Correct 8 ms 704 KB Output is correct
31 Correct 8 ms 856 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 10 ms 344 KB Output is correct
36 Correct 12 ms 344 KB Output is correct
37 Correct 8 ms 432 KB Output is correct
38 Correct 11 ms 952 KB Output is correct
39 Correct 10 ms 724 KB Output is correct
40 Correct 8 ms 600 KB Output is correct
41 Correct 10 ms 1112 KB Output is correct
42 Correct 10 ms 1228 KB Output is correct
43 Correct 8 ms 876 KB Output is correct
44 Correct 7 ms 860 KB Output is correct
45 Correct 7 ms 700 KB Output is correct
46 Correct 7 ms 876 KB Output is correct
47 Correct 9 ms 996 KB Output is correct
48 Correct 8 ms 876 KB Output is correct
49 Correct 9 ms 724 KB Output is correct
50 Correct 8 ms 788 KB Output is correct
51 Correct 8 ms 644 KB Output is correct
52 Correct 11 ms 596 KB Output is correct
53 Correct 9 ms 856 KB Output is correct
54 Correct 9 ms 1172 KB Output is correct
55 Correct 9 ms 864 KB Output is correct
56 Correct 9 ms 660 KB Output is correct
57 Correct 8 ms 636 KB Output is correct
58 Correct 8 ms 892 KB Output is correct
59 Correct 9 ms 1136 KB Output is correct
60 Correct 9 ms 1112 KB Output is correct
61 Correct 10 ms 692 KB Output is correct
62 Correct 7 ms 1300 KB Output is correct
63 Correct 11 ms 916 KB Output is correct
64 Correct 12 ms 568 KB Output is correct
65 Correct 10 ms 628 KB Output is correct
66 Correct 10 ms 920 KB Output is correct
67 Correct 9 ms 560 KB Output is correct
68 Partially correct 9 ms 820 KB Output is partially correct
69 Partially correct 9 ms 888 KB Output is partially correct
70 Partially correct 10 ms 656 KB Output is partially correct
71 Correct 10 ms 880 KB Output is correct
72 Partially correct 12 ms 896 KB Output is partially correct
73 Partially correct 9 ms 628 KB Output is partially correct
74 Partially correct 11 ms 980 KB Output is partially correct
75 Partially correct 12 ms 888 KB Output is partially correct
76 Partially correct 11 ms 820 KB Output is partially correct
77 Correct 10 ms 944 KB Output is correct
78 Correct 9 ms 624 KB Output is correct
79 Partially correct 9 ms 632 KB Output is partially correct
80 Partially correct 10 ms 1200 KB Output is partially correct
81 Partially correct 10 ms 1084 KB Output is partially correct
82 Partially correct 11 ms 1048 KB Output is partially correct