Submission #1255881

#	Time	Username	Problem	Language	Result	Execution time	Memory
1255881		madamadam3	세계 지도 (IOI25_worldmap)	C++20	34 / 100	1098 ms	3656 KiB

worldmap

#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);
  }
}

inline int diagonal_length(int K, int s) {
  return (s < K) ? (s + 1) : (2*K - 1 - s);
}

bool check_works(int n, int K) {
  int tl_fine = 0;
  int cdx = 0;
  for (int i = 0; i < n; i++) {
    int cnt = 0;
    while (cnt < (n-1) && cdx < (2*K-1)) {
      cnt += diagonal_length(K, cdx);
      cdx+=2;
    }
    
    cdx+=2;
    if (cdx >= (2*K-1)) return false;
    if (cnt >= (n-1)) tl_fine++;
  }

  return tl_fine >= n;
}

bool validate(int n, int m, vi a, vi b, vvi ret) {
  set<pair<int, int>> adjacencies;
  set<pair<int, int>> expected;

  for (int i = 0; i < m; i++) {
    expected.insert({min(a[i], b[i]), max(a[i], b[i])});
  }

  int k = ret.size();
  for (int i = 0; i < k; i++) {
    for (int j = 0; j < k; j++) {
      if (i > 0 && ret[i-1][j] != ret[i][j]) adjacencies.insert({min(ret[i][j], ret[i-1][j]), max(ret[i][j], ret[i-1][j])});
      if (j > 0 && ret[i][j-1] != ret[i][j]) adjacencies.insert({min(ret[i][j], ret[i][j-1]), max(ret[i][j], ret[i][j-1])});
      if (i < k-1 && ret[i+1][j] != ret[i][j]) adjacencies.insert({min(ret[i][j], ret[i+1][j]), max(ret[i][j], ret[i+1][j])});
      if (j < k-1 && ret[i][j+1] != ret[i][j]) adjacencies.insert({min(ret[i][j], ret[i][j+1]), max(ret[i][j], ret[i][j+1])});
    }
  }

  for (auto &el : adjacencies) {
    if (!expected.count(el)) return false;
  }

  for (auto &el :expected) {
    if (!adjacencies.count(el)) return false;
  }

  return true;
}

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 ladj = 1; for (int i = 2; i <= n; i++) if (adj[i].size() > adj[ladj].size()) ladj = i;
  
  int lo = 2*n, hi = 3*n;
  while (lo < hi) {
    int mid = lo + (hi - lo) / 2;
    
    if (check_works(n, mid)) {
      hi = mid;
    } else {
      lo = mid + 1;
    }
  }

  int K = lo - 1;
  cerr << "Using K = " << K << "\n";

  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<bool> vis(n+1, false); vi tour; set<int> seen;
  dfs(1, vis, adj,tour);

  vvi ans(K, vi(K, 1)), dgs(n+1);

  int cdx = 0;
  set<int> used;
  for (int i = 0; i < tour.size(); i++) {
    for (auto &el : diags[cdx]) {
      ans[el.first][el.second] = tour[i];
    }

    cdx++;
    if (used.count(tour[i]) || tour[i] == ladj) continue;
    used.insert(tour[i]);

    int cnt = 0;
    while (cnt < (n - 1)) {
      cnt += diags[cdx].size();
      dgs[tour[i]].push_back(cdx);
      cdx++;
      for (auto &el : diags[cdx]) {
        ans[el.first][el.second] = tour[i];
      }
      cdx++;
    }
  }

  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()) {
          ans[el.first][el.second] = i;
          continue;
        }
        ans[el.first][el.second] = adj[i][aidx++];
      }
    }
  }

  // cerr << "Is the answer valid? " << validate(n, m, a, b, ans) << "\n";
  return ans;
}

• Subtask 0: 0 / 0
• Subtask 1: 5 / 5
• Subtask 2: 0 / 10
• Subtask 3: 7 / 7
• Subtask 4: 8 / 8
• Subtask 5: 14 / 14
• Subtask 6: 0 / 56