Submission #319140

#	Time	Username	Problem	Language	Result	Execution time	Memory
319140		VROOM_VARUN	Towns (IOI15_towns)	C++14	100 / 100	23 ms	1012 KiB

towns

/*
ID: varunra2
LANG: C++
TASK: towns
*/

#include <bits/stdc++.h>
#include "towns.h"
using namespace std;

#ifdef DEBUG
#include "lib/debug.h"
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define debug_arr(...) \
  cerr << "[" << #__VA_ARGS__ << "]:", debug_arr(__VA_ARGS__)
#pragma GCC diagnostic ignored "-Wsign-compare"
//#pragma GCC diagnostic ignored "-Wunused-parameter"
//#pragma GCC diagnostic ignored "-Wunused-variable"
#else
#define debug(...) 42
#endif

#define EPS 1e-9
#define IN(A, B, C) assert(B <= A && A <= C)
#define INF (int)1e9
#define MEM(a, b) memset(a, (b), sizeof(a))
#define MOD 1000000007
#define MP make_pair
#define PB push_back
#define all(cont) cont.begin(), cont.end()
#define rall(cont) cont.end(), cont.begin()
#define x first
#define y second

const double PI = acos(-1.0);
typedef long long ll;
typedef long double ld;
typedef pair<int, int> PII;
typedef map<int, int> MPII;
typedef multiset<int> MSETI;
typedef set<int> SETI;
typedef set<string> SETS;
typedef vector<int> VI;
typedef vector<PII> VII;
typedef vector<VI> VVI;
typedef vector<string> VS;

#define rep(i, a, b) for (int i = a; i < (b); ++i)
#define trav(a, x) for (auto& a : x)
#define sz(x) (int)(x).size()
typedef pair<int, int> pii;
typedef vector<int> vi;
#pragma GCC diagnostic ignored "-Wsign-compare"
// util functions

int n;
const int mx = 150;
int vals[mx][mx];
map<PII, int> mp;

int qrys = 0;

// int getDistance(int i, int j) { return vals[i][j]; }

int gt(int i, int j) {
  if (i > j) swap(i, j);
  if (i == j) return 0;
  if (mp[MP(i, j)]) return mp[MP(i, j)];
  mp[MP(i, j)] = getDistance(i, j);
  qrys++;
  return mp[MP(i, j)];
}

int rootdist(int d1, int d2, int dtot) {
  // d1 + d2 - 2 * dlca = dtot
  // (d1 + d2 - dtot)/2 = dlca
  return (d1 + d2 - dtot) / 2;
}

int leafdist(int d1, int d2, int dtot) {
  // what is the dist(d1, dlca)
  // dist(d1, dlca) = d1 - rootdist(dlca)
  return d1 - rootdist(d1, d2, dtot);
}

void calc(int from, VI& d) {
  for (int i = 0; i < n; i++) {
    if (i == from) continue;
    d[i] = gt(from, i);
  }
}

int ind1;
int ind2;

VI d0;
VI d1;
VI d2;  // we won't be using this
VI lcadists;

void init() {
  mp.clear();
  d0.clear();
  d1.clear();
  d2.clear();
  lcadists.clear();
  d0.assign(n, 0);
  d1.assign(n, 0);
  d2.assign(n, 0);
  lcadists.assign(n, 0);
  qrys = 0;
}

int find(int lcdist) {
  int val1 = d0[ind1] - lcdist;
  int val2 = d1[ind2] - val1;
  int cur = max(val1, val2);
  return cur;
}

VI cop;

int radius;

VI findHubs() {
  // we will use 2n - 3 queries to find the hubs/radius/center
  calc(0, d0);
  ind1 = max_element(all(d0)) - d0.begin();
  calc(ind1, d1);
  ind2 = max_element(all(d1)) - d1.begin();
  // good till
  // diameter is from ind1 -> ind2
  // hub lies on the path from 0 -> ind1 && ind1 -> ind2
  // so since we rooted the tree at 0
  // the hub lies on the path from ind1 -> lca(ind1, ind2)
  int ret = 2 * INF;
  VI hubs;
  // sort(all(lcadists));
  for (int i = 0; i < n; i++) {
    // lcadists actually holds distance from ind1 -> lca(ind1, i)
    lcadists[i] = leafdist(d0[ind1], d0[i], d1[i]);
    int cur = max(lcadists[i], d1[ind2] - lcadists[i]);
    if (cur < ret) {
      ret = cur;
      hubs.clear();
      hubs = {i};
    } else if (cur == ret and lcadists[i] != lcadists[hubs[0]]) {
      hubs.PB(i);
    }
  }
  radius = ret;
  hubs.resize(2);
  return hubs;
}

int ccnt(int dep) {
  int ret = 0;
  for (auto& x : cop) {
    if (x >= dep) ret++;
  }
  return ret;
}

int chk;

bool same(int i, int j) {
  if (lcadists[i] < chk and lcadists[j] < chk)
    return true;  // same children subtree
  if (lcadists[i] > chk and lcadists[j] > chk)
    return true;                                    // outside hub subtree
  if (lcadists[i] == chk and lcadists[j] == chk) {  // same subtree
    if (d1[i] + d1[j] - gt(i, j) > 2 * chk) return true;
  }
  return false;
}

bool balanced(int depth) {
  // debug(depth);
  chk = depth;
  // we need to check if an array contains a majority using (3n/2 - 2) checks
  // http://www.cs.yale.edu/publications/techreports/tr252.pdf
  // ^ paper describes how to do it

  VI bucket;
  VI list;

  // phase 1

  for (int i = 0; i < n; i++) {
    if (list.empty())
      list.PB(i);
    else if (same(list.back(), i))
      bucket.PB(i);
    else {
      list.PB(i);
      if (!bucket.empty()) {
        list.PB(bucket.back());
        bucket.pop_back();
      }
    }
  }

  // debug(bucket);
  // debug(list);

  // phase 2

  int T = list.back();

  while (!list.empty()) {
    int last = list.back();
    list.pop_back();
    if (same(last, T)) {
      if (list.empty()) {
        bucket.PB(last);
      } else
        list.pop_back();
    } else {
      if (bucket.empty()) return true;
      bucket.pop_back();
    }
  }

  // impa fan :yay:

  // debug(bucket);
  return bucket.empty();
}

int hubDistance(int n, int sub) {
  ::n = n;
  init();
  auto hubs = findHubs();

  int hubcheck;

  // for(auto& x: hubs) {
  // if(balanced(lcadists[x])) return radius;
  // }
  // return -radius;

  if (sz(hubs) == 1) {
    hubcheck = hubs[0];
  }

  // debug(lcadists);

  int ind = 0;

  int cnt = 0;
  if (sz(hubs) == 2) {
    if (lcadists[hubs[0]] > lcadists[hubs[1]]) swap(hubs[1], hubs[0]);
    // we need to count how many leafs are in the subtree of hubs[0]
    for (int i = 0; i < n; i++) {
      if (lcadists[i] <= lcadists[hubs[0]]) cnt++;
    }
    // if ((n - cnt) > n / 2)
    // hubcheck = hubs[1], ind = 1;
    // else
    // hubcheck = hubs[0];
    if (cnt == n / 2) {
      return radius;
    }
    if (cnt > n / 2) {
      hubcheck = hubs[0];
    } else
      hubcheck = hubs[1], ind = 1;
  }
  // debug(hubs);
  // debug(lcadists);
  // debug(ind1);
  // debug(lcadists[ind1]);
  // debug(lcadists[0]);

  if (balanced(lcadists[hubcheck])) return radius;
  // if (sz(hubs) == 1) return -radius;
  // if (balanced(lcadists[hubs[ind ^ 1]])) {
  // debug(cnt);
  // debug(n);
  // debug(n - cnt);
  // debug(n / 2);
  // debug(ind);
  // }
  return -radius;
}

// int main() {
// #ifndef ONLINE_JUDGE
//   freopen("towns.in", "r", stdin);
//   freopen("towns.out", "w", stdout);
// #endif
//   cin.sync_with_stdio(0);
//   cin.tie(0);
//   int subbb;
//   cin >> subbb;
//   int t;
//   cin >> t;
//   while (t--) {
//     int n;
//     cin >> n;
//     for (int i = 0; i < n; i++) {
//       for (int j = 0; j < n; j++) {
//         cin >> vals[i][j];
//       }
//     }

//     cout << hubDistance(n, 2) << '\n';
//   }
//   return 0;
// }

Compilation message (stderr)

towns.cpp: In function 'VI findHubs()':
towns.cpp:128:31: warning: conversion from '__gnu_cxx::__normal_iterator<int*, std::vector<int> >::difference_type' {aka 'long int'} to 'int' may change value [-Wconversion]
  128 |   ind1 = max_element(all(d0)) - d0.begin();
      |          ~~~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~
towns.cpp:130:31: warning: conversion from '__gnu_cxx::__normal_iterator<int*, std::vector<int> >::difference_type' {aka 'long int'} to 'int' may change value [-Wconversion]
  130 |   ind2 = max_element(all(d1)) - d1.begin();
      |          ~~~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~
towns.cpp: In function 'int hubDistance(int, int)':
towns.cpp:230:31: warning: declaration of 'n' shadows a global declaration [-Wshadow]
  230 | int hubDistance(int n, int sub) {
      |                               ^
towns.cpp:56:5: note: shadowed declaration is here
   56 | int n;
      |     ^
towns.cpp:248:7: warning: variable 'ind' set but not used [-Wunused-but-set-variable]
  248 |   int ind = 0;
      |       ^~~
towns.cpp:230:28: warning: unused parameter 'sub' [-Wunused-parameter]
  230 | int hubDistance(int n, int sub) {
      |                        ~~~~^~~
towns.cpp:275:33: warning: 'hubcheck' may be used uninitialized in this function [-Wmaybe-uninitialized]
  275 |   if (balanced(lcadists[hubcheck])) return radius;
      |                                 ^

• Subtask 1: 13 / 13
• Subtask 2: 12 / 12
• Subtask 3: 13 / 13
• Subtask 4: 10 / 10
• Subtask 5: 13 / 13
• Subtask 6: 39 / 39