Submission #647601

#	Time	Username	Problem	Language	Result	Execution time	Memory
647601		Pety	Boarding Passes (BOI22_passes)	C++14	100 / 100	272 ms	18248 KiB

passes

#include <bits/stdc++.h>
#define ll long long

using namespace std;

const double INF = 1e12;
const int MOD = 1e9 + 7;

int n, g, sum[15][100002];
vector<int>poz[15];
vector<double>calc[15][15];
double dp[(1 << 15)];

string s;

double expected(double n) {
  if (n < 2)
    return 0.0;
  return (double)n * (n - 1) / 4;
}

double func (int i, int mask, int k) {
  if (poz[i].size() - 1 - k < 0)
    return INF;
  double aux = expected(k) + expected(poz[i].size() - 1 - k);
  for (int j = 0; j < g; j++)
    if (mask & (1 << j))
      aux += calc[i][j][k];
  return aux;
}

int main () 
{
  ios_base::sync_with_stdio(false);
  cin.tie(0); cout.tie(0);
  cin >> s;
  int n = s.size();
  s = '#' + s;
  for (int i = 0; i < 15; i++)
    poz[i].push_back(0);
  g = 0;
  for (int i = 1; i <= n; i++) {
    g = max(g, s[i] - 'A' + 1);
    poz[s[i] - 'A'].push_back(i);
    for (int j = 0; j < 15; j++)
      sum[j][i] = sum[j][i - 1] + (s[i] - 'A' == j);
  }
  for (int i = 0; i < g; i++) {
    for (int j = 0; j < g; j++) {
      if (i == j)
        continue;
      calc[i][j].resize(poz[i].size() + 1);
      ll pas = 0;
      for (int k = 0; k < poz[i].size(); k++) {
        calc[i][j][k] += pas;
        if (k + 1 < poz[i].size())
          pas += sum[j][poz[i][k + 1]];
      }
      pas = 0;
      for (int k = poz[i].size() - 1; k >= 0; k--) {
        calc[i][j][k] += pas;
        pas += sum[j][n] - sum[j][poz[i][k] - 1];
      }
    }
  }
  for (int mask = 0; mask < (1 << g); mask++)
    dp[mask] = INF;
  dp[0] = 0;
  for (int mask = 0; mask < (1 << g); mask++) {
    for (int i = 0; i < g; i++)
      if (!(mask & (1 << i))) {
        int st = 0, dr = poz[i].size() - 1;
        while (dr - st > 2) {
          int m1 = st + (dr - st) / 3, m2 = dr - (dr - st) / 3;
          double v1 = func(i, mask, m1), v2 = func(i, mask, m2);
          if (v1 > v2) 
            st = m1;
          else
            dr = m2;
        }
        double cur = min({func(i, mask, st), func(i, mask, st + 1), func(i, mask, st + 2)});
        dp[mask ^ (1 << i)] = min(dp[mask] + cur, dp[mask ^ (1 << i)]);
      }
  }
  cout << fixed << setprecision(7) << dp[(1 << g) - 1];
  return 0;
}

Compilation message (stderr)

passes.cpp: In function 'int main()':
passes.cpp:54:25: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   54 |       for (int k = 0; k < poz[i].size(); k++) {
      |                       ~~^~~~~~~~~~~~~~~
passes.cpp:56:19: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   56 |         if (k + 1 < poz[i].size())
      |             ~~~~~~^~~~~~~~~~~~~~~

• Subtask 1: 5 / 5
• Subtask 2: 25 / 25
• Subtask 3: 30 / 30
• Subtask 4: 40 / 40