#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)
//and assuming that these are already boarded since the back breaker may not be the same for each group - that was false assumption
//so precomp counts then ternary search on the breakpoint
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];
}
}
vector<vector<vector<int>>> acounts;
acounts.push_back(counts);
for (int L=0; L<n; L++) {
//counts[i][j] = number of swaps required if i goes after j
//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;
}
acounts.push_back(counts);
/*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;*/
}
vector<int> dp;
dp=vector<int>(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 l = 0; int r = n;
vector<pair<int,int>> costs;
while (l<r) {
int m1,m2;
m1=l+(r-l)/3;
m2=r-(r-l)/3;
int am1 = 0;
for (int j=0; j<G; j++) {
if (mask&(1<<j)) {
am1+=2*acounts[m1][addon][j];
}
if (j==addon) {
am1+=acounts[m1][addon][j];
}
}
int am2 = 0;
for (int j=0; j<G; j++) {
if (mask&(1<<j)) {
am2+=2*acounts[m2][addon][j];
}
if (j==addon) {
am2+=acounts[m2][addon][j];
}
}
costs.push_back({m1,am1});
costs.push_back({m2,am2});
//cout << "adding " << mask <<" " << addon <<" " << l <<" " << r <<" " << m1 <<" " << m2 <<" " << am1 <<" " << am2 << endl;
if (am1>am2) {
l=m1+1; r=r;
}
else if (am1<am2) {
l=l; r=m2-1;
}
else {
l=m1+1; r=m2;
}
//cout << mask <<" " << addon <<" " << al <<endl;
}
sort(costs.begin(), costs.end());
costs.erase(unique(costs.begin(), costs.end()),costs.end());
/*for (auto i:costs) {
cout << i.first <<" " << i.second << endl;
}*/
int dec=0;
int minimum=INF;
for (int i=0; i<((int)costs.size())-1; i++) {
if (costs[i].second<costs[i+1].second) dec=1;
if (costs[i].second>costs[i+1].second && dec) assert(0==1);
minimum=min(minimum,costs[i].second);
}
int al = 0;
for (int j=0; j<G; j++) {
if (mask&(1<<j)) {
al+=2*acounts[l][addon][j];
}
if (j==addon) {
al+=acounts[l][addon][j];
}
}
if (al>minimum) {
//cout << al << " "<<minimum << endl;
}
/assert(al<=minimum);
dp[mask | (1<<addon)] = min(dp[mask | (1<<addon)],dp[mask]+min(al,minimum));
}
}
int ans=dp[(1<<G)-1];
int a2 = ans/2;
cout << a2;
if (ans%2==1) cout << ".50";
cout << 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();
}
Compilation message
passes.cpp: In function 'void solve()':
passes.cpp:148:13: error: expected primary-expression before '/' token
148 | /assert(al<=minimum);
| ^
passes.cpp: In function 'int main()':
passes.cpp:164:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
164 | freopen("input.txt", "r", stdin);
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
passes.cpp:166:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
166 | freopen("output.txt", "w", stdout);
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~
