oj.uz

Submission #843238

# Submission time Handle Problem Language Result Execution time Memory
843238 2023-09-03T20:01:00 Z radoslav11 Longest Trip (IOI23_longesttrip) C++17
15 / 100
 1000 ms 2097152 KB 
#include <cassert>
#include <algorithm>
#include <functional>
#include <iostream>
#include <numeric>
#include <random>
#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 prune_tree(
	int l1, int l2, int l3, vector<int> &leaves, vector<int> &par,
	vector<int> &deg
) {
	leaves.push_back(l3);

	int u = l1, v = l2;
	while(deg[u] == 1) {
		int pu = par[u];
		par[u] = v;
		deg[v]++;
		deg[pu]--;

		v = u;
		u = pu;
	}

	leaves.push_back(v);
}

vector<int> solve_tree(int N, vector<int> nodes, vector<vector<int>> adj) {
	// We assume that the tree is connected here
	int root = nodes[0];
	vector<int> deg(N, 0);
	for(auto node: nodes) deg[node] = adj[node].size();

	for(auto node: nodes) {
		if(deg[node] >= 3) {
			root = node;
			break;
		}
	}

	vector<int> par(nodes.size(), 0);
	vector<int> leaves;
	function<void(int, int)> dfs = [&](int node, int parent) {
		par[node] = parent;
		bool is_leaf = true;
		for(auto child: adj[node]) {
			if(child == parent) continue;
			dfs(child, node);
			is_leaf = false;
		}

		if(is_leaf) leaves.push_back(node);
	};

	dfs(root, -1);

	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, par, deg);
		} else if(are_connected({l1}, {l3})) {
			prune_tree(l1, l3, l2, leaves, par, deg);
		} else {
			// Delta >= 1, means that l2 and l3 are connected
			prune_tree(l2, l3, l1, leaves, par, deg);
		}
	}

	// It's a path
	vector<int> path;
	vector<bool> used(N, false);

	int u = leaves[0];
	while(u != -1) {
		path.push_back(u);
		used[u] = true;
		u = par[u];
	}

	if(leaves.size() == 2) {
		u = leaves[1];
		vector<int> rev_path;
		while(!used[u]) {
			rev_path.push_back(u);
			u = par[u];
		}

		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 1 ms 344 KB Output is correct
2 Execution timed out 1789 ms 2097152 KB Time limit exceeded
3 Halted 0 ms 0 KB -

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 344 KB Output is correct
2 Correct 12 ms 344 KB Output is correct
3 Correct 8 ms 344 KB Output is correct
4 Correct 10 ms 600 KB Output is correct
5 Correct 11 ms 856 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 10 ms 352 KB Output is correct
3 Correct 8 ms 344 KB Output is correct
4 Correct 10 ms 440 KB Output is correct
5 Correct 10 ms 600 KB Output is correct
6 Correct 9 ms 344 KB Output is correct
7 Correct 13 ms 600 KB Output is correct
8 Correct 10 ms 344 KB Output is correct
9 Correct 10 ms 540 KB Output is correct
10 Correct 10 ms 460 KB Output is correct
11 Correct 12 ms 484 KB Output is correct
12 Correct 11 ms 700 KB Output is correct
13 Correct 12 ms 704 KB Output is correct

Subtask #3
0.0 / 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 9 ms 344 KB Output is correct
4 Correct 10 ms 600 KB Output is correct
5 Correct 11 ms 600 KB Output is correct
6 Correct 12 ms 344 KB Output is correct
7 Correct 12 ms 600 KB Output is correct
8 Correct 10 ms 344 KB Output is correct
9 Correct 10 ms 600 KB Output is correct
10 Correct 12 ms 484 KB Output is correct
11 Correct 11 ms 856 KB Output is correct
12 Correct 12 ms 700 KB Output is correct
13 Correct 10 ms 704 KB Output is correct
14 Correct 10 ms 344 KB Output is correct
15 Correct 11 ms 344 KB Output is correct
16 Execution timed out 1678 ms 2097152 KB Time limit exceeded
17 Halted 0 ms 0 KB -

Subtask #4
0.0 / 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 8 ms 344 KB Output is correct
4 Correct 9 ms 344 KB Output is correct
5 Partially correct 11 ms 700 KB Output is partially correct
6 Correct 9 ms 344 KB Output is correct
7 Correct 11 ms 600 KB Output is correct
8 Correct 10 ms 600 KB Output is correct
9 Correct 9 ms 344 KB Output is correct
10 Partially correct 10 ms 704 KB Output is partially correct
11 Partially correct 10 ms 704 KB Output is partially correct
12 Partially correct 10 ms 1112 KB Output is partially correct
13 Partially correct 12 ms 856 KB Output is partially correct
14 Correct 9 ms 344 KB Output is correct
15 Correct 10 ms 344 KB Output is correct
16 Execution timed out 1774 ms 2097152 KB Time limit exceeded
17 Halted 0 ms 0 KB -