| # | Submission time | Handle | Problem | Language | Result | Execution time | Memory |
|---|---|---|---|---|---|---|---|
| 1028160 | 2024-07-19T14:41:59 Z | anango | Boarding Passes (BOI22_passes) | C++17 | 0 ms | 0 KB |
#include <bits/stdc++.h>
#define int long long
using namespace std;
int INF = 1LL<<62;
void solve() {
string S; cin >> S;
int n = S.size();
vector<int> ar(n); for (int i=0; i<n; i++) ar[i] = (S[i]-'A');
int G = *max_element(ar.begin(), ar.end()); G++;
int pref[n+1][G]; //count of character c, before index i
int suff[n+1][G]; //count of character c, after or equal to index i
for (int i=0; i<=n; i++) {
for (int j=0; j<G; j++) {
pref[i][j] = suff[i][j] = 0;
}
}
for (int i=0; i<n; i++) {
for (int j=0; j<=G; j++) {
if (j==ar[i]) {
pref[i+1][j] = pref[i][j]+1;
}
else {
pref[i+1][j] = pref[i][j];
}
}
}
for (int i=n-1; i>=0; i--) {
for (int j=0; j<G; j++) {
if (j==ar[i]) {
suff[i][j] = suff[i+1][j]+1;
}
else {
suff[i][j] = suff[i+1][j];
}
}
}
//everyone before L boards from the front, everyone after or equal to it boards from the back.
vector<vector<int>> counts(G,vector<int>(G,0)); //counts[i][j] = sum of subsequences of (i,j) before l, and subsequences of (j,i) after L
//counts[i][j] = sum of pref[k][j] for k<=L and ar[k]=i, and analogous expression for the suffix
//first, get initial count values (for everyone boarding from the back)
for (int j=0; j<G; j++) {
for (int k=0; k<n; k++) {
int i = ar[k];
//cout << "adding " << i <<" " << j <<" " << k <<" " << j << " " << suff[k][j] << endl;
counts[i][j] += suff[k+1][j];
}
}
/*for (int i=0; i<G; i++) {
for (int j=0; j<G; j++) {
cout << i <<" " << j <<" " << counts[i][j] << endl;
}
}*/
int ans = 1LL<<62;
for (int L=0; L<n; L++) {
//counts[i][j] = number of swaps required if i goes after j
vector<int> dp(1<<G,INF); //dp[mask] = min cost if this mask is at the beginning of the ordering
dp[0] = 0;
for (int mask=0; mask<1<<G; mask++) {
for (int addon=0; addon<G; addon++) {
if (mask&(1<<addon)) continue;
int al = 0;
for (int j=0; j<G; j++) {
if (mask&(1<<j)) {
al+=counts[addon][j];
}
}
//cout << mask <<" " << addon <<" " << al <<endl;
dp[mask | (1<<addon)] = min(dp[mask | (1<<addon)],dp[mask]+al);
}
}
int self=0;
for (int i=0; i<G; i++) {
self+=counts[i][i];
}
ans=min(ans,2*dp[(1<<G)-1]+self);
//transfer L to the right
int cur = ar[L];
for (int j=0; j<G; j++) {
int delta = suff[L+1][j];
int delta2 = pref[L][j];
counts[cur][j] -= delta-delta2;
}
/*cout << "TRANSFERRED TO " << L+1 << endl;
for (int i=0; i<G; i++) {
for (int j=0; j<G; j++) {
cout << i <<" " << j <<" " << counts[i][j] << endl;
}
}
cout << endl;*/
}
ans=min(ans,2*dp[(1<<G)-1]+self);
long double a2 = ans;
a2/=(long double)2;
cout << setprecision(100) << a2 << endl;
}
signed main() {
int local=0;
if (local) {
// for getting input from input.txt
freopen("input.txt", "r", stdin);
// for writing output to output.txt
freopen("output.txt", "w", stdout);
}
/*#ifdef ONLINE_JUDGE
ios_base::sync_with_stdio(false);
cin.tie(NULL);
#endif*/ //fast IO
solve();
}