oj.uz

Submission #843336

# Submission time Handle Problem Language Result Execution time Memory
843336 2023-09-03T23:10:40 Z radoslav11 Longest Trip (IOI23_longesttrip) C++17
85 / 100
 14 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++;
			
			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++;
				}

				if(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++;
				} 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 668 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 6 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 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 8 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 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 600 KB Output is correct
10 Correct 6 ms 848 KB Output is correct
11 Correct 6 ms 864 KB Output is correct
12 Correct 8 ms 864 KB Output is correct
13 Correct 7 ms 1140 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 600 KB Output is correct
3 Correct 6 ms 344 KB Output is correct
4 Correct 7 ms 344 KB Output is correct
5 Correct 6 ms 600 KB Output is correct
6 Correct 12 ms 344 KB Output is correct
7 Correct 9 ms 344 KB Output is correct
8 Correct 6 ms 600 KB Output is correct
9 Correct 7 ms 952 KB Output is correct
10 Correct 7 ms 852 KB Output is correct
11 Correct 7 ms 864 KB Output is correct
12 Correct 7 ms 664 KB Output is correct
13 Correct 8 ms 608 KB Output is correct
14 Correct 11 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 9 ms 468 KB Output is correct
18 Correct 9 ms 600 KB Output is correct
19 Correct 8 ms 952 KB Output is correct
20 Correct 8 ms 1132 KB Output is correct
21 Correct 8 ms 928 KB Output is correct
22 Correct 7 ms 1292 KB Output is correct
23 Correct 9 ms 1328 KB Output is correct
24 Correct 7 ms 1056 KB Output is correct
25 Correct 11 ms 344 KB Output is correct
26 Correct 9 ms 344 KB Output is correct
27 Correct 10 ms 344 KB Output is correct
28 Correct 8 ms 344 KB Output is correct
29 Correct 11 ms 496 KB Output is correct
30 Correct 9 ms 440 KB Output is correct
31 Correct 11 ms 436 KB Output is correct
32 Correct 10 ms 440 KB Output is correct
33 Correct 10 ms 600 KB Output is correct
34 Correct 14 ms 600 KB Output is correct
35 Correct 12 ms 860 KB Output is correct
36 Correct 9 ms 848 KB Output is correct
37 Correct 14 ms 884 KB Output is correct
38 Correct 10 ms 1148 KB Output is correct
39 Correct 10 ms 668 KB Output is correct
40 Correct 10 ms 940 KB Output is correct
41 Correct 9 ms 856 KB Output is correct
42 Correct 10 ms 852 KB Output is correct
43 Correct 9 ms 648 KB Output is correct
44 Correct 11 ms 596 KB Output is correct
45 Correct 13 ms 496 KB Output is correct
46 Correct 13 ms 340 KB Output is correct
47 Correct 12 ms 340 KB Output is correct
48 Correct 10 ms 344 KB Output is correct
49 Correct 12 ms 344 KB Output is correct
50 Correct 9 ms 692 KB Output is correct
51 Correct 10 ms 696 KB Output is correct
52 Correct 11 ms 500 KB Output is correct
53 Correct 8 ms 856 KB Output is correct
54 Correct 10 ms 788 KB Output is correct
55 Correct 10 ms 856 KB Output is correct
56 Correct 7 ms 920 KB Output is correct
57 Correct 11 ms 816 KB Output is correct
58 Correct 13 ms 1144 KB Output is correct
59 Correct 11 ms 636 KB Output is correct
60 Correct 9 ms 884 KB Output is correct
61 Correct 10 ms 1060 KB Output is correct
62 Correct 11 ms 608 KB Output is correct
63 Correct 9 ms 932 KB Output is correct
64 Correct 9 ms 876 KB Output is correct

Subtask #4
45.0 / 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 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
6 Correct 11 ms 344 KB Output is correct
7 Correct 9 ms 344 KB Output is correct
8 Correct 6 ms 600 KB Output is correct
9 Correct 6 ms 856 KB Output is correct
10 Correct 6 ms 692 KB Output is correct
11 Correct 6 ms 868 KB Output is correct
12 Correct 6 ms 1040 KB Output is correct
13 Correct 7 ms 1376 KB Output is correct
14 Correct 10 ms 500 KB Output is correct
15 Correct 10 ms 344 KB Output is correct
16 Correct 9 ms 344 KB Output is correct
17 Correct 9 ms 600 KB Output is correct
18 Correct 9 ms 600 KB Output is correct
19 Correct 8 ms 604 KB Output is correct
20 Correct 8 ms 1116 KB Output is correct
21 Correct 11 ms 344 KB Output is correct
22 Correct 9 ms 344 KB Output is correct
23 Correct 9 ms 344 KB Output is correct
24 Correct 8 ms 344 KB Output is correct
25 Correct 8 ms 344 KB Output is correct
26 Correct 9 ms 440 KB Output is correct
27 Correct 9 ms 948 KB Output is correct
28 Correct 8 ms 436 KB Output is correct
29 Correct 8 ms 344 KB Output is correct
30 Correct 10 ms 600 KB Output is correct
31 Correct 12 ms 740 KB Output is correct
32 Correct 11 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 11 ms 344 KB Output is correct
36 Correct 14 ms 344 KB Output is correct
37 Correct 9 ms 1208 KB Output is correct
38 Correct 10 ms 696 KB Output is correct
39 Correct 11 ms 692 KB Output is correct
40 Correct 8 ms 856 KB Output is correct
41 Correct 11 ms 608 KB Output is correct
42 Correct 10 ms 600 KB Output is correct
43 Correct 8 ms 712 KB Output is correct
44 Correct 7 ms 1136 KB Output is correct
45 Correct 7 ms 1052 KB Output is correct
46 Correct 9 ms 1128 KB Output is correct
47 Partially correct 10 ms 904 KB Output is partially correct
48 Partially correct 11 ms 852 KB Output is partially correct
49 Partially correct 12 ms 656 KB Output is partially correct
50 Partially correct 10 ms 636 KB Output is partially correct
51 Partially correct 9 ms 676 KB Output is partially correct
52 Correct 8 ms 600 KB Output is correct
53 Correct 8 ms 600 KB Output is correct
54 Correct 10 ms 1164 KB Output is correct
55 Correct 10 ms 628 KB Output is correct
56 Partially correct 11 ms 628 KB Output is partially correct
57 Partially correct 9 ms 796 KB Output is partially correct
58 Partially correct 9 ms 872 KB Output is partially correct
59 Partially correct 10 ms 676 KB Output is partially correct
60 Correct 10 ms 600 KB Output is correct
61 Correct 9 ms 1000 KB Output is correct
62 Correct 7 ms 540 KB Output is correct
63 Partially correct 12 ms 652 KB Output is partially correct
64 Partially correct 11 ms 908 KB Output is partially correct
65 Partially correct 10 ms 1056 KB Output is partially correct
66 Partially correct 12 ms 1136 KB Output is partially correct
67 Correct 12 ms 1072 KB Output is correct
68 Correct 9 ms 568 KB Output is correct
69 Partially correct 10 ms 712 KB Output is partially correct
70 Partially correct 9 ms 936 KB Output is partially correct
71 Partially correct 10 ms 908 KB Output is partially correct
72 Partially correct 11 ms 900 KB Output is partially correct
73 Partially correct 9 ms 896 KB Output is partially correct
74 Partially correct 10 ms 620 KB Output is partially correct
75 Partially correct 9 ms 632 KB Output is partially correct
76 Partially correct 10 ms 576 KB Output is partially correct
77 Partially correct 11 ms 660 KB Output is partially correct
78 Partially correct 10 ms 696 KB Output is partially correct
79 Partially correct 10 ms 904 KB Output is partially correct
80 Partially correct 9 ms 636 KB Output is partially correct
81 Correct 10 ms 628 KB Output is correct
82 Partially correct 10 ms 872 KB Output is partially correct