제출 #603854

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
603854		slime	Boarding Passes (BOI22_passes)	C++14	100 / 100	642 ms	361168 KiB

passes

#include "bits/stdc++.h"
using namespace std;
#define int long long
const int MAXN = 3e5 + 10;
const int MOD = 1e9 + 7;
#define ll __int128
mt19937_64 rng((int)std::chrono::steady_clock::now().time_since_epoch().count());
int rnd(int x, int y) {
  int u = uniform_int_distribution<int>(x, y)(rng); return u;
}
ll read() { int x; cin >> x; return (ll)x; }
long long bm(long long b, long long p) {
  if(p==0) return 1 % MOD;
  long long r = bm(b, p >> 1);
  if(p&1) return (((r*r) % MOD) * b) % MOD;
  return (r*r) % MOD;
}
long long inv(long long b) { 
  return bm(b, MOD-2);
}
long long f[MAXN];
long long nCr(int n, int r) { 
  long long ans = f[n]; ans *= inv(f[r]); ans %= MOD;
  ans *= inv(f[n-r]); ans %= MOD; return ans;
}
long long fib[MAXN], lucas[MAXN];
void precomp() { 
  for(int i=0; i<MAXN; i++) f[i] = (i == 0 ? 1 % MOD : (f[i-1] * i) % MOD); 
  lucas[0] = 2;
  lucas[1] = 1;
  for(int i=2; i<MAXN; i++) lucas[i] = (lucas[i-2] + lucas[i-1]) % MOD;
  fib[0] = 0;
  fib[1] = 1;
  for(int i=2; i<MAXN; i++) fib[i] = (fib[i-2] + fib[i-1]) % MOD;
}
int fastlog(int x) {
  return (x == 0 ? -1 : 64 - __builtin_clzll(x) - 1);
}
void gay(int i) { cout << "Case #" << i << ": "; }
int csb(int l, int r, int k) { // count number of [l, r] such that i & 2^k > 0
  if(l > r) return 0;
  if(l == 0) {
    int s = r / (1ll << (k+1)); // number of complete cycles
    int t = r % (1ll << (k+1));
    int ans = s * (1ll << k);
    ans += (t >= (1ll << k) ? t - (1ll << k) + 1 : 0);
    return ans;
  }
  else return csb(0, r, k) - csb(0, l - 1, k);
}
int lis(vector<int> a) {
  int n = a.size();
  int bucket[n+1];
  for(int i=1; i<=n; i++) bucket[i] = 1e18;
  int ans = 1;
  for(int x: a) {
    auto it = lower_bound(bucket + 1, bucket +n +1, x);
    int d = distance(bucket, it);
    ans = max(ans, d);
    bucket[d] = min(bucket[d], x);
  }
  return ans;
}
void solve(int tc) {
  string s;
  cin >> s;
  int n = s.size();
  s = " " + s;
  int glob = 0;
  for(int i=0; i<15; i++) {
    bool ok = 0;
    for(int j=1; j<=n; j++) ok |= (s[j] == i + 'A');
    if(ok) glob += (1 << i);
  }
  double dp[glob + 1]; // only consider submasks of glob
  for(int i=0; i<=glob; i++) dp[i] = 1e18;
  dp[0] = 0;

  int ps[n+2][15][15];
  int ss[n+2][15][15];
  for(int i=0; i<=n+1; i++) for(int j=0; j<15; j++) for(int k=0; k<15; k++) ps[i][j][k] = ss[i][j][k] = 0;
  int cnt[15];
  for(int i=0; i<15; i++) cnt[i] = 0;
  for(int i=1; i<=n; i++) {
    for(int j=0; j<15; j++) {
      for(int k=0; k<15; k++) {
        ps[i][j][k] = ps[i-1][j][k] + (s[i] - 'A' == k ? cnt[j] : 0);
      }
    }
    cnt[s[i] - 'A']++;
  }
  for(int i=0; i<15; i++) cnt[i] = 0;
  for(int i=n; i>=1; i--) {
    for(int j=0; j<15; j++) {
      for(int k=0; k<15; k++) {
        ss[i][j][k] = ss[i+1][j][k] + (s[i] - 'A' == k ? cnt[j] : 0);
      }
    }
    cnt[s[i] - 'A']++;
  }
  vector<int> woah[15];
  for(int i=0; i<15; i++) woah[i].push_back(0);
  for(int i=1; i<=n; i++) woah[s[i] - 'A'].push_back(i);
  for(int i=0; i<15; i++) woah[i].push_back(n + 1);
  for(int i=1; i<=glob; i++) {
    if((glob | i) != glob) continue;
    for(int j=0; j<15; j++) {
      if(!(i & (1<<j))) continue;
      /*
      int cntt = 0;
      for(int k=1; k<=n; k++) {
        cntt += (s[k] - 'A' == j);
      }
      
      int ppass[cntt + 1], spass[cntt + 2];
      ppass[0] = spass[cntt + 1] = 0;
      int ptr = 0, sum = 0;
      for(int k=1; k<=n; k++) {
        int o = (i & (1 << (s[k] - 'A')));
        if(o ) {
          if(s[k] - 'A' == j) {
            ptr++;
            ppass[ptr] = ppass[ptr - 1] + sum;
          }
          else {
            sum++;
          }
        }
      }
      ptr = cntt + 1, sum = 0;
      for(int k=n; k>=1; k--) {
        int o = (i & (1 << (s[k] - 'A')));
        if(o ) {
          if(s[k] - 'A' == j) {
            ptr--;
            spass[ptr] = spass[ptr + 1] + sum;
          }
          else {
            sum++;
          }
        }
      }
      double mi = 1e18;
      for(int k=0; k<=cntt; k++) {
        mi = min(mi, k * (k-1) * 0.25 + (cntt-k) * (cntt-k-1) * 0.25 + ppass[k] + spass[k+1]);
      }
      dp[i] = min(dp[i], dp[i-(1<<j)] + mi);

      continue;
      */
      int lb = 0, rb = cnt[j];
      while(lb < rb) {
        int mid = (lb + rb) >> 1;
        double sm1 = 0, sm2 = 0;
        for(int k=0; k<15; k++) {
          if((i & (1<<k)) && k != j) {
            sm1 += ps[woah[j][mid]][k][j] + ss[woah[j][mid+1]][k][j];
            sm2 += ps[woah[j][mid+1]][k][j] + ss[woah[j][mid+2]][k][j];
          }
        }
        sm1 += mid * (mid-1) * 0.25 + (cnt[j]-mid) * (cnt[j]-mid-1) * 0.25;
        sm2 += (mid+1) * mid * 0.25 + (cnt[j]-(mid+1)) * (cnt[j]-(mid+1)-1) * 0.25;
        if(sm1 > sm2) lb = mid + 1;
        else rb = mid;
      }
      double fin = 0;
      for(int k=0; k<15; k++) if((i & (1<<k)) && k != j) fin += ps[woah[j][lb]][k][j] + ss[woah[j][lb+1]][k][j];
      fin += lb * (lb-1) * 0.25 + (cnt[j]-lb) * (cnt[j]-lb-1) * 0.25;
      dp[i] = min(dp[i], dp[i-(1<<j)] + fin);
    }
  }
  cout << fixed << setprecision(5) << dp[glob] << "\n";
} 
int32_t main() {
  precomp();
  ios::sync_with_stdio(0); cin.tie(0);
  int t = 1; //cin >> t;
  for(int i=1; i<=t; i++) solve(i);
}
// I don't know geometry.
// Teaming is unfair.

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