oj.uz

답안 #843362

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
843362 2023-09-04T00:32:55 Z radoslav11 가장 긴 여행 (IOI23_longesttrip) C++17
85 / 100
 12 ms 1476 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++;

			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

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 2 ms 600 KB Output is correct

Subtask #1
5.0 / 5.0

# 결과 실행 시간 메모리 Grader output
1 Correct 10 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 7 ms 344 KB Output is correct
5 Correct 7 ms 344 KB Output is correct

Subtask #2
10.0 / 10.0

# 결과 실행 시간 메모리 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 7 ms 344 KB Output is correct
5 Correct 7 ms 600 KB Output is correct
6 Correct 9 ms 344 KB Output is correct
7 Correct 9 ms 344 KB Output is correct
8 Correct 6 ms 472 KB Output is correct
9 Correct 6 ms 856 KB Output is correct
10 Correct 7 ms 612 KB Output is correct
11 Correct 6 ms 872 KB Output is correct
12 Correct 7 ms 696 KB Output is correct
13 Correct 7 ms 356 KB Output is correct

Subtask #3
25.0 / 25.0

# 결과 실행 시간 메모리 Grader output
1 Correct 8 ms 356 KB Output is correct
2 Correct 7 ms 356 KB Output is correct
3 Correct 6 ms 356 KB Output is correct
4 Correct 6 ms 356 KB Output is correct
5 Correct 6 ms 356 KB Output is correct
6 Correct 9 ms 356 KB Output is correct
7 Correct 7 ms 448 KB Output is correct
8 Correct 7 ms 484 KB Output is correct
9 Correct 7 ms 600 KB Output is correct
10 Correct 7 ms 600 KB Output is correct
11 Correct 8 ms 796 KB Output is correct
12 Correct 5 ms 592 KB Output is correct
13 Correct 7 ms 600 KB Output is correct
14 Correct 11 ms 344 KB Output is correct
15 Correct 11 ms 344 KB Output is correct
16 Correct 10 ms 344 KB Output is correct
17 Correct 8 ms 344 KB Output is correct
18 Correct 8 ms 344 KB Output is correct
19 Correct 9 ms 1012 KB Output is correct
20 Correct 8 ms 692 KB Output is correct
21 Correct 7 ms 600 KB Output is correct
22 Correct 7 ms 788 KB Output is correct
23 Correct 7 ms 600 KB Output is correct
24 Correct 6 ms 600 KB Output is correct
25 Correct 11 ms 344 KB Output is correct
26 Correct 11 ms 344 KB Output is correct
27 Correct 8 ms 344 KB Output is correct
28 Correct 9 ms 344 KB Output is correct
29 Correct 10 ms 344 KB Output is correct
30 Correct 8 ms 696 KB Output is correct
31 Correct 9 ms 696 KB Output is correct
32 Correct 10 ms 696 KB Output is correct
33 Correct 8 ms 344 KB Output is correct
34 Correct 8 ms 344 KB Output is correct
35 Correct 9 ms 604 KB Output is correct
36 Correct 8 ms 872 KB Output is correct
37 Correct 9 ms 688 KB Output is correct
38 Correct 10 ms 564 KB Output is correct
39 Correct 10 ms 856 KB Output is correct
40 Correct 9 ms 628 KB Output is correct
41 Correct 8 ms 696 KB Output is correct
42 Correct 9 ms 600 KB Output is correct
43 Correct 9 ms 888 KB Output is correct
44 Correct 9 ms 608 KB Output is correct
45 Correct 9 ms 344 KB Output is correct
46 Correct 12 ms 344 KB Output is correct
47 Correct 9 ms 344 KB Output is correct
48 Correct 9 ms 344 KB Output is correct
49 Correct 9 ms 344 KB Output is correct
50 Correct 8 ms 700 KB Output is correct
51 Correct 9 ms 952 KB Output is correct
52 Correct 10 ms 692 KB Output is correct
53 Correct 8 ms 1476 KB Output is correct
54 Correct 9 ms 1112 KB Output is correct
55 Correct 9 ms 600 KB Output is correct
56 Correct 8 ms 864 KB Output is correct
57 Correct 8 ms 1064 KB Output is correct
58 Correct 9 ms 572 KB Output is correct
59 Correct 9 ms 720 KB Output is correct
60 Correct 10 ms 1376 KB Output is correct
61 Correct 11 ms 620 KB Output is correct
62 Correct 10 ms 1336 KB Output is correct
63 Correct 10 ms 928 KB Output is correct
64 Correct 10 ms 564 KB Output is correct

Subtask #4
45.0 / 60.0

# 결과 실행 시간 메모리 Grader output
1 Correct 9 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 6 ms 344 KB Output is correct
5 Correct 5 ms 600 KB Output is correct
6 Correct 9 ms 344 KB Output is correct
7 Correct 8 ms 344 KB Output is correct
8 Correct 6 ms 624 KB Output is correct
9 Correct 6 ms 344 KB Output is correct
10 Correct 5 ms 344 KB Output is correct
11 Correct 6 ms 500 KB Output is correct
12 Correct 6 ms 592 KB Output is correct
13 Correct 5 ms 344 KB Output is correct
14 Correct 10 ms 344 KB Output is correct
15 Correct 9 ms 344 KB Output is correct
16 Correct 9 ms 344 KB Output is correct
17 Correct 8 ms 344 KB Output is correct
18 Correct 7 ms 600 KB Output is correct
19 Correct 7 ms 1112 KB Output is correct
20 Correct 7 ms 600 KB Output is correct
21 Correct 9 ms 596 KB Output is correct
22 Correct 12 ms 344 KB Output is correct
23 Correct 9 ms 600 KB Output is correct
24 Correct 8 ms 344 KB Output is correct
25 Correct 9 ms 344 KB Output is correct
26 Correct 8 ms 692 KB Output is correct
27 Correct 8 ms 856 KB Output is correct
28 Correct 8 ms 692 KB Output is correct
29 Correct 7 ms 600 KB Output is correct
30 Correct 8 ms 344 KB Output is correct
31 Correct 8 ms 980 KB Output is correct
32 Correct 9 ms 344 KB Output is correct
33 Correct 10 ms 344 KB Output is correct
34 Correct 10 ms 344 KB Output is correct
35 Correct 10 ms 340 KB Output is correct
36 Correct 9 ms 344 KB Output is correct
37 Correct 8 ms 700 KB Output is correct
38 Correct 9 ms 692 KB Output is correct
39 Correct 10 ms 696 KB Output is correct
40 Correct 9 ms 956 KB Output is correct
41 Correct 9 ms 608 KB Output is correct
42 Correct 9 ms 532 KB Output is correct
43 Correct 6 ms 856 KB Output is correct
44 Correct 7 ms 1052 KB Output is correct
45 Correct 6 ms 600 KB Output is correct
46 Correct 7 ms 968 KB Output is correct
47 Correct 8 ms 1044 KB Output is correct
48 Correct 8 ms 816 KB Output is correct
49 Correct 9 ms 724 KB Output is correct
50 Correct 10 ms 856 KB Output is correct
51 Correct 9 ms 564 KB Output is correct
52 Correct 8 ms 600 KB Output is correct
53 Correct 8 ms 600 KB Output is correct
54 Partially correct 9 ms 624 KB Output is partially correct
55 Correct 8 ms 872 KB Output is correct
56 Correct 8 ms 556 KB Output is correct
57 Correct 9 ms 628 KB Output is correct
58 Correct 9 ms 828 KB Output is correct
59 Correct 9 ms 832 KB Output is correct
60 Correct 9 ms 1368 KB Output is correct
61 Correct 9 ms 856 KB Output is correct
62 Correct 8 ms 1052 KB Output is correct
63 Correct 9 ms 812 KB Output is correct
64 Partially correct 10 ms 628 KB Output is partially correct
65 Partially correct 9 ms 712 KB Output is partially correct
66 Partially correct 10 ms 1148 KB Output is partially correct
67 Partially correct 9 ms 648 KB Output is partially correct
68 Partially correct 10 ms 1456 KB Output is partially correct
69 Partially correct 9 ms 876 KB Output is partially correct
70 Partially correct 9 ms 708 KB Output is partially correct
71 Correct 9 ms 700 KB Output is correct
72 Partially correct 9 ms 1384 KB Output is partially correct
73 Correct 10 ms 1156 KB Output is correct
74 Partially correct 9 ms 572 KB Output is partially correct
75 Partially correct 9 ms 568 KB Output is partially correct
76 Partially correct 9 ms 940 KB Output is partially correct
77 Correct 9 ms 872 KB Output is correct
78 Correct 9 ms 824 KB Output is correct
79 Partially correct 10 ms 876 KB Output is partially correct
80 Partially correct 9 ms 1072 KB Output is partially correct
81 Partially correct 10 ms 568 KB Output is partially correct
82 Partially correct 10 ms 736 KB Output is partially correct