oj.uz

Submission #843811

# Submission time Handle Problem Language Result Execution time Memory
843811 2023-09-04T15:18:48 Z m1nk Longest Trip (IOI23_longesttrip) C++17
100 / 100
 13 ms 1712 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 2 ms 792 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 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 8 ms 344 KB Output is correct
2 Correct 6 ms 344 KB Output is correct
3 Correct 8 ms 344 KB Output is correct
4 Correct 5 ms 344 KB Output is correct
5 Correct 6 ms 724 KB Output is correct
6 Correct 10 ms 344 KB Output is correct
7 Correct 7 ms 344 KB Output is correct
8 Correct 7 ms 612 KB Output is correct
9 Correct 6 ms 600 KB Output is correct
10 Correct 7 ms 1164 KB Output is correct
11 Correct 6 ms 596 KB Output is correct
12 Correct 6 ms 596 KB Output is correct
13 Correct 7 ms 1712 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 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 504 KB Output is correct
7 Correct 9 ms 344 KB Output is correct
8 Correct 7 ms 600 KB Output is correct
9 Correct 6 ms 604 KB Output is correct
10 Correct 7 ms 1024 KB Output is correct
11 Correct 6 ms 752 KB Output is correct
12 Correct 6 ms 596 KB Output is correct
13 Correct 6 ms 784 KB Output is correct
14 Correct 9 ms 344 KB Output is correct
15 Correct 8 ms 344 KB Output is correct
16 Correct 11 ms 344 KB Output is correct
17 Correct 10 ms 344 KB Output is correct
18 Correct 8 ms 600 KB Output is correct
19 Correct 7 ms 856 KB Output is correct
20 Correct 7 ms 856 KB Output is correct
21 Correct 8 ms 1044 KB Output is correct
22 Correct 7 ms 796 KB Output is correct
23 Correct 7 ms 960 KB Output is correct
24 Correct 7 ms 884 KB Output is correct
25 Correct 8 ms 544 KB Output is correct
26 Correct 9 ms 344 KB Output is correct
27 Correct 7 ms 344 KB Output is correct
28 Correct 9 ms 344 KB Output is correct
29 Correct 7 ms 344 KB Output is correct
30 Correct 7 ms 436 KB Output is correct
31 Correct 7 ms 436 KB Output is correct
32 Correct 7 ms 692 KB Output is correct
33 Correct 6 ms 344 KB Output is correct
34 Correct 8 ms 344 KB Output is correct
35 Correct 7 ms 344 KB Output is correct
36 Correct 7 ms 600 KB Output is correct
37 Correct 8 ms 880 KB Output is correct
38 Correct 9 ms 704 KB Output is correct
39 Correct 8 ms 788 KB Output is correct
40 Correct 7 ms 604 KB Output is correct
41 Correct 7 ms 1004 KB Output is correct
42 Correct 9 ms 928 KB Output is correct
43 Correct 7 ms 864 KB Output is correct
44 Correct 8 ms 904 KB Output is correct
45 Correct 12 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 8 ms 344 KB Output is correct
49 Correct 12 ms 344 KB Output is correct
50 Correct 7 ms 700 KB Output is correct
51 Correct 9 ms 692 KB Output is correct
52 Correct 9 ms 692 KB Output is correct
53 Correct 7 ms 600 KB Output is correct
54 Correct 7 ms 856 KB Output is correct
55 Correct 8 ms 600 KB Output is correct
56 Correct 7 ms 1180 KB Output is correct
57 Correct 10 ms 1060 KB Output is correct
58 Correct 9 ms 868 KB Output is correct
59 Correct 8 ms 692 KB Output is correct
60 Correct 8 ms 800 KB Output is correct
61 Correct 8 ms 868 KB Output is correct
62 Correct 8 ms 1012 KB Output is correct
63 Correct 8 ms 692 KB Output is correct
64 Correct 8 ms 884 KB Output is correct

Subtask #4
60.0 / 60.0

# 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 7 ms 344 KB Output is correct
5 Correct 6 ms 344 KB Output is correct
6 Correct 12 ms 344 KB Output is correct
7 Correct 10 ms 600 KB Output is correct
8 Correct 8 ms 600 KB Output is correct
9 Correct 9 ms 516 KB Output is correct
10 Correct 7 ms 628 KB Output is correct
11 Correct 7 ms 764 KB Output is correct
12 Correct 6 ms 740 KB Output is correct
13 Correct 8 ms 1136 KB Output is correct
14 Correct 11 ms 344 KB Output is correct
15 Correct 10 ms 344 KB Output is correct
16 Correct 12 ms 456 KB Output is correct
17 Correct 10 ms 600 KB Output is correct
18 Correct 9 ms 600 KB Output is correct
19 Correct 9 ms 772 KB Output is correct
20 Correct 9 ms 692 KB Output is correct
21 Correct 10 ms 344 KB Output is correct
22 Correct 11 ms 344 KB Output is correct
23 Correct 9 ms 344 KB Output is correct
24 Correct 9 ms 600 KB Output is correct
25 Correct 8 ms 600 KB Output is correct
26 Correct 8 ms 692 KB Output is correct
27 Correct 8 ms 436 KB Output is correct
28 Correct 9 ms 956 KB Output is correct
29 Correct 8 ms 856 KB Output is correct
30 Correct 8 ms 716 KB Output is correct
31 Correct 8 ms 344 KB Output is correct
32 Correct 13 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 10 ms 344 KB Output is correct
36 Correct 12 ms 600 KB Output is correct
37 Correct 9 ms 692 KB Output is correct
38 Correct 10 ms 692 KB Output is correct
39 Correct 10 ms 604 KB Output is correct
40 Correct 8 ms 344 KB Output is correct
41 Correct 9 ms 776 KB Output is correct
42 Correct 9 ms 600 KB Output is correct
43 Correct 8 ms 632 KB Output is correct
44 Correct 8 ms 1020 KB Output is correct
45 Correct 9 ms 616 KB Output is correct
46 Correct 8 ms 632 KB Output is correct
47 Correct 8 ms 1292 KB Output is correct
48 Correct 9 ms 812 KB Output is correct
49 Correct 9 ms 648 KB Output is correct
50 Correct 7 ms 700 KB Output is correct
51 Correct 8 ms 912 KB Output is correct
52 Correct 9 ms 600 KB Output is correct
53 Correct 9 ms 568 KB Output is correct
54 Correct 9 ms 1112 KB Output is correct
55 Correct 8 ms 600 KB Output is correct
56 Correct 8 ms 732 KB Output is correct
57 Correct 9 ms 768 KB Output is correct
58 Correct 8 ms 704 KB Output is correct
59 Correct 9 ms 976 KB Output is correct
60 Correct 7 ms 604 KB Output is correct
61 Correct 8 ms 344 KB Output is correct
62 Correct 8 ms 1120 KB Output is correct
63 Correct 9 ms 620 KB Output is correct
64 Correct 9 ms 788 KB Output is correct
65 Correct 8 ms 856 KB Output is correct
66 Correct 8 ms 868 KB Output is correct
67 Correct 9 ms 1128 KB Output is correct
68 Correct 10 ms 928 KB Output is correct
69 Correct 10 ms 1112 KB Output is correct
70 Correct 9 ms 800 KB Output is correct
71 Correct 8 ms 960 KB Output is correct
72 Correct 9 ms 892 KB Output is correct
73 Correct 10 ms 1376 KB Output is correct
74 Correct 10 ms 548 KB Output is correct
75 Correct 10 ms 928 KB Output is correct
76 Correct 9 ms 608 KB Output is correct
77 Correct 9 ms 952 KB Output is correct
78 Correct 9 ms 788 KB Output is correct
79 Correct 10 ms 936 KB Output is correct
80 Correct 8 ms 632 KB Output is correct
81 Correct 9 ms 628 KB Output is correct
82 Correct 10 ms 1156 KB Output is correct