# | Time | Username | Problem | Language | Result | Execution time | Memory |
---|---|---|---|---|---|---|---|
1252992 | madamadam3 | World Map (IOI25_worldmap) | C++20 | 0 ms | 0 KiB |
#include "worldmap.h"
#include <bits/stdc++.h>
using namespace std;
// #define int long long int
using vi = vector<int>;
using vvi = vector<vi>;
void dfs(int u, vector<bool> &vis, vvi &adj, vi &tour) {
vis[u] = true;
tour.push_back(u);
// sort(adj[u].begin(), adj[u].end(), [&](int a, int b) {return adj[a].size() < adj[b].size();});
for (int v : adj[u]) {
if (vis[v]) continue;
dfs(v, vis, adj, tour);
tour.push_back(u);
}
}
vvi map_from_root(int root, int n, int m, vvi &adj, vector<set<pair<int, int>>> &diags) {
vector<bool> vis(n+1, false); vi tour; set<int> seen;
dfs(root, vis, adj,tour);
int K = 3 * n - 1;
vector<set<pair<int, int>>> diags(2*K-1);
set<pair<int, int>> used;
vvi ans(K, vi(K, root)), dgs(n+1);
int cidx = 0;
for (int i = 0; i < tour.size(); i++) {
dgs[tour[i]].push_back(cidx+1);
for (; cidx < 3 * i + 3; cidx++) {
for (auto &el : diags[cidx]) {
ans[el.first][el.second] = tour[i];
}
}
}
for (int i = 1; i <= n; i++) {
int aidx = 0;
for (auto &gd : dgs[i]) {
for (auto &el : diags[gd]) {
if (aidx >= adj[i].size()) break;
ans[el.first][el.second] = adj[i][aidx++];
}
}
}
return ans;
}
bool is_valid(int n, int m, vvi &mp, vi a, vi b) {
set<pair<int, int>> reqs; for (int i = 0; i < m; i++) reqs.insert({a[i], b[i]}), reqs.insert({b[i], a[i]});
int K = mp.size();
set<pair<int, int>> us;
bool valid = true;
for (int i = 0; i < K; i++) {
for (int j = 0; j < K; j++) {
if (!valid) break;
if (i > 0) {
valid = valid && reqs.count({mp[i-1][j], mp[i][j]});
us.insert({mp[i-1][j], mp[i][j]});
}
if (j > 0) {
valid = valid && reqs.count({mp[i][j-1], mp[i][j]});
us.insert({mp[i][j-1], mp[i][j]});
}
if (i < K - 1) {
valid = valid && reqs.count({mp[i+1][j], mp[i][j]});
us.insert({mp[i+1][j], mp[i][j]});
}
if (j < K - 1) {
valid = valid && reqs.count({mp[i][j+1], mp[i][j]});
us.insert({mp[i][j+1], mp[i][j]});
}
}
}
return valid && us.size() == reqs.size();
}
vvi create_map(int n, int m, vi a, vi b) {
vvi adj(n+1, vi()); for (int i = 0; i < m; i++) adj[a[i]].push_back(b[i]), adj[b[i]].push_back(a[i]);
int K = 3 * n - 1;
vector<set<pair<int, int>>> diags(2*K-1);
for (int i = 0; i < K; i++) {
for (int j = 0; j < K; j++) {
int md = i + j;
diags[md].insert({i, j});
}
}
vector<int> indices(n); iota(indices.begin(), indices.end(), 1);
sort(indices.begin(), indices.end(), [&](int a, int b) {return adj[a].size() < adj[b].size();});
for (auto &root : indices) {
vvi mp = map_from_root(root, n, m, adj, diags);
if (is_valid(n, m, mp, a, b)) {
return mp;
}
}
return map_from_root(1, n, m, adj, diags);
}