oj.uz

Submission #843297

# Submission time Handle Problem Language Result Execution time Memory
843297 2023-09-03T21:52:13 Z radoslav11 Longest Trip (IOI23_longesttrip) C++17
70 / 100
 16 ms 1028 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(
	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(left_left, right_left, mt);
	} else if(safe_are_connected(left_left, right_right)) {
		return find_one_edge(left_left, right_right, mt);
	} else if(safe_are_connected(left_right, right_left)) {
		return find_one_edge(left_right, right_left, mt);
	} else {
		return find_one_edge(left_right, right_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;
	while(other < N && are_connected({order[0]}, {order[other]})) {
		comps[0].push_back(order[other]);
		edges.push_back({order[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);
		// cerr << "Solving tree" << endl;
		return solve_tree(N, all_nodes, adj);
	} else {
		// Maybe we have two components
		comps[1].push_back(order[other]);

		// cerr << "Other: ";
		// cerr << order[other] << endl;

		for(int i = other + 1; i < N; i++) {
			if(are_connected({order[0]}, {order[i]})) {
				comps[0].push_back(order[i]);
				edges.push_back({order[0], order[i]});
			} else {
				comps[1].push_back(order[i]);
				edges.push_back({order[other], order[i]});
			}
		}

		// cerr << "Comps:" << endl;
		// for(int i = 0; i < 2; i++) {
		// 	 for(int j = 0; j < comps[i].size(); j++) {
		// 		cerr << comps[i][j] << " ";
		// 	}
		// 	cerr << endl;
		// }

		// Check if this is one component
		if(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 596 KB Output is correct
2 Correct 4 ms 700 KB Output is correct

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 7 ms 344 KB Output is correct
2 Correct 10 ms 344 KB Output is correct
3 Correct 9 ms 344 KB Output is correct
4 Correct 10 ms 344 KB Output is correct
5 Correct 12 ms 344 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 8 ms 344 KB Output is correct
3 Correct 10 ms 596 KB Output is correct
4 Correct 10 ms 344 KB Output is correct
5 Correct 12 ms 600 KB Output is correct
6 Correct 10 ms 344 KB Output is correct
7 Correct 14 ms 344 KB Output is correct
8 Correct 11 ms 344 KB Output is correct
9 Correct 10 ms 344 KB Output is correct
10 Correct 11 ms 444 KB Output is correct
11 Correct 11 ms 864 KB Output is correct
12 Correct 12 ms 932 KB Output is correct
13 Correct 11 ms 448 KB Output is correct

Subtask #3
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 7 ms 344 KB Output is correct
2 Correct 10 ms 344 KB Output is correct
3 Correct 9 ms 600 KB Output is correct
4 Correct 9 ms 344 KB Output is correct
5 Correct 11 ms 344 KB Output is correct
6 Correct 9 ms 344 KB Output is correct
7 Correct 13 ms 344 KB Output is correct
8 Correct 10 ms 344 KB Output is correct
9 Correct 10 ms 344 KB Output is correct
10 Correct 11 ms 448 KB Output is correct
11 Correct 10 ms 448 KB Output is correct
12 Correct 11 ms 704 KB Output is correct
13 Correct 12 ms 1028 KB Output is correct
14 Correct 10 ms 344 KB Output is correct
15 Correct 8 ms 344 KB Output is correct
16 Correct 13 ms 344 KB Output is correct
17 Correct 10 ms 596 KB Output is correct
18 Correct 11 ms 344 KB Output is correct
19 Correct 12 ms 344 KB Output is correct
20 Correct 11 ms 344 KB Output is correct
21 Correct 12 ms 532 KB Output is correct
22 Correct 13 ms 604 KB Output is correct
23 Correct 12 ms 700 KB Output is correct
24 Correct 11 ms 440 KB Output is correct
25 Correct 9 ms 344 KB Output is correct
26 Correct 8 ms 344 KB Output is correct
27 Correct 10 ms 344 KB Output is correct
28 Correct 10 ms 344 KB Output is correct
29 Correct 9 ms 344 KB Output is correct
30 Correct 9 ms 440 KB Output is correct
31 Correct 9 ms 500 KB Output is correct
32 Correct 7 ms 696 KB Output is correct
33 Correct 10 ms 344 KB Output is correct
34 Correct 10 ms 344 KB Output is correct
35 Correct 9 ms 344 KB Output is correct
36 Correct 11 ms 448 KB Output is correct
37 Correct 11 ms 448 KB Output is correct
38 Correct 10 ms 444 KB Output is correct
39 Correct 8 ms 448 KB Output is correct
40 Correct 8 ms 444 KB Output is correct
41 Correct 9 ms 600 KB Output is correct
42 Correct 8 ms 344 KB Output is correct
43 Correct 7 ms 448 KB Output is correct
44 Correct 7 ms 600 KB Output is correct
45 Correct 10 ms 344 KB Output is correct
46 Correct 11 ms 344 KB Output is correct
47 Correct 12 ms 344 KB Output is correct
48 Correct 15 ms 344 KB Output is correct
49 Correct 13 ms 344 KB Output is correct
50 Correct 12 ms 636 KB Output is correct
51 Correct 15 ms 596 KB Output is correct
52 Correct 12 ms 692 KB Output is correct
53 Correct 11 ms 344 KB Output is correct
54 Correct 13 ms 600 KB Output is correct
55 Correct 11 ms 344 KB Output is correct
56 Correct 12 ms 704 KB Output is correct
57 Correct 11 ms 444 KB Output is correct
58 Correct 14 ms 444 KB Output is correct
59 Correct 15 ms 696 KB Output is correct
60 Correct 16 ms 444 KB Output is correct
61 Correct 13 ms 864 KB Output is correct
62 Correct 13 ms 516 KB Output is correct
63 Correct 14 ms 600 KB Output is correct
64 Correct 15 ms 600 KB Output is correct

Subtask #4
30.0 / 60.0

# Verdict Execution time Memory Grader output
1 Correct 7 ms 344 KB Output is correct
2 Correct 11 ms 344 KB Output is correct
3 Correct 9 ms 344 KB Output is correct
4 Correct 10 ms 600 KB Output is correct
5 Partially correct 11 ms 344 KB Output is partially correct
6 Correct 10 ms 344 KB Output is correct
7 Correct 16 ms 600 KB Output is correct
8 Correct 11 ms 344 KB Output is correct
9 Correct 10 ms 344 KB Output is correct
10 Partially correct 13 ms 700 KB Output is partially correct
11 Partially correct 11 ms 700 KB Output is partially correct
12 Partially correct 12 ms 852 KB Output is partially correct
13 Partially correct 12 ms 852 KB Output is partially correct
14 Correct 10 ms 344 KB Output is correct
15 Correct 10 ms 596 KB Output is correct
16 Correct 12 ms 344 KB Output is correct
17 Correct 13 ms 344 KB Output is correct
18 Correct 10 ms 344 KB Output is correct
19 Correct 11 ms 344 KB Output is correct
20 Correct 13 ms 756 KB Output is correct
21 Correct 9 ms 344 KB Output is correct
22 Correct 10 ms 344 KB Output is correct
23 Correct 8 ms 344 KB Output is correct
24 Correct 9 ms 344 KB Output is correct
25 Correct 9 ms 344 KB Output is correct
26 Correct 10 ms 696 KB Output is correct
27 Correct 9 ms 436 KB Output is correct
28 Correct 7 ms 692 KB Output is correct
29 Correct 9 ms 344 KB Output is correct
30 Correct 10 ms 600 KB Output is correct
31 Correct 9 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 12 ms 344 KB Output is correct
36 Correct 13 ms 344 KB Output is correct
37 Correct 12 ms 444 KB Output is correct
38 Correct 12 ms 440 KB Output is correct
39 Correct 12 ms 464 KB Output is correct
40 Correct 10 ms 344 KB Output is correct
41 Correct 11 ms 344 KB Output is correct
42 Correct 14 ms 344 KB Output is correct
43 Partially correct 12 ms 608 KB Output is partially correct
44 Partially correct 11 ms 448 KB Output is partially correct
45 Partially correct 11 ms 448 KB Output is partially correct
46 Partially correct 12 ms 604 KB Output is partially correct
47 Partially correct 12 ms 856 KB Output is partially correct
48 Partially correct 12 ms 856 KB Output is partially correct
49 Partially correct 11 ms 448 KB Output is partially correct
50 Partially correct 9 ms 860 KB Output is partially correct
51 Partially correct 8 ms 600 KB Output is partially correct
52 Correct 7 ms 600 KB Output is correct
53 Correct 7 ms 340 KB Output is correct
54 Correct 7 ms 444 KB Output is correct
55 Correct 7 ms 620 KB Output is correct
56 Partially correct 11 ms 704 KB Output is partially correct
57 Partially correct 10 ms 604 KB Output is partially correct
58 Partially correct 10 ms 704 KB Output is partially correct
59 Partially correct 8 ms 704 KB Output is partially correct
60 Correct 7 ms 340 KB Output is correct
61 Correct 8 ms 344 KB Output is correct
62 Partially correct 11 ms 704 KB Output is partially correct
63 Partially correct 11 ms 444 KB Output is partially correct
64 Partially correct 12 ms 448 KB Output is partially correct
65 Partially correct 15 ms 440 KB Output is partially correct
66 Partially correct 15 ms 600 KB Output is partially correct
67 Partially correct 14 ms 860 KB Output is partially correct
68 Partially correct 13 ms 448 KB Output is partially correct
69 Partially correct 13 ms 444 KB Output is partially correct
70 Partially correct 15 ms 856 KB Output is partially correct
71 Partially correct 14 ms 604 KB Output is partially correct
72 Partially correct 13 ms 604 KB Output is partially correct
73 Partially correct 16 ms 856 KB Output is partially correct
74 Partially correct 13 ms 448 KB Output is partially correct
75 Partially correct 14 ms 672 KB Output is partially correct
76 Partially correct 14 ms 448 KB Output is partially correct
77 Partially correct 14 ms 604 KB Output is partially correct
78 Partially correct 14 ms 604 KB Output is partially correct
79 Partially correct 13 ms 700 KB Output is partially correct
80 Partially correct 14 ms 444 KB Output is partially correct
81 Partially correct 12 ms 704 KB Output is partially correct
82 Partially correct 14 ms 524 KB Output is partially correct