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#include <bits/stdc++.h>
#define int long long
#define double long double
#define rep(i,n) for(int i =0; i<n; i++)
#define all(a) a.begin(),a.end()
using namespace std;
string s;
int n;
double f(int n)
{
return ((double) n)*((double) (n-1))/4.0;
}
string ord;
vector<double>mem;
vector<vector<int>>pos;
int g;
// cost to add the group gr with all members of that group with and index <= to maxi boarding on the left
double cost(int bor, int gr, int maxi)
{
double sum = 0;
int firstr = maxi+1;
sum+=f(pos[gr].size()-firstr) + f(firstr);
vector<int>otherpos;
rep(i,n) if(((1<<(s[i]-'A'))&bor)==0) otherpos.push_back(i);
rep(i,firstr)
{
sum+=upper_bound(all(otherpos),pos[gr][i])-otherpos.begin();
}
for(int i = firstr; i < pos[gr].size(); i++) sum+=otherpos.end()-upper_bound(all(otherpos),pos[gr][i]);
return sum;
}
vector<int>lookup;
double dfs(int bor)
{
if(mem[bor]>-0.9) return mem[bor];
double sol = 1e18;
rep(i,g)
{
if(!((1<<i)&bor)) continue;
int nbor = bor^(1<<i);
if(!pos[i].size()) return mem[bor]=dfs(nbor);
int start = -1, end = pos[i].size()-1;
while(end-start>1)
{
int c = (start+end)/2;
double l =cost(bor,i,c), r=cost(bor,i,c+1);
if(r>=l) end=c;
else start=c;
};
sol=min(sol, cost(bor,i,end)+dfs(nbor));
// vector<int>otherpos;
// rep(j,n) if(((1<<(s[j]-'A'))&bor)==0) otherpos.push_back(j);
// double sum = dfs(nbor);
// rep(j,pos[i].size())
// {
// sum+=min(0.5*((double) j)+(lower_bound(all(otherpos),pos[i][j])-otherpos.begin()),
// (otherpos.end()-upper_bound(all(otherpos),pos[i][j])) + 0.5*((double)pos[i].size()-j-1));
// }
// double sol1=1e18;
// rep(firstr,pos[i].size()+1)
// {
// double sum2 = f(pos[i].size()-firstr) + f(firstr);
// rep(j,firstr) sum2+=upper_bound(all(otherpos),pos[i][j])-otherpos.begin();
// for(int j = firstr; j < pos[i].size(); j++) sum2+=otherpos.end()-upper_bound(all(otherpos),pos[i][j]);
// sol1=min(sol1,sum2+dfs(nbor));
// }
// assert(sum==sol1);
// sol=min(sum,sol);
}
return mem[bor] = sol;
}
signed main()
{
cin>>s;
s.size();
n=s.size();
cout.precision(300);
char maxx=0;
rep(i,n) maxx=max(maxx, s[i]);
g=maxx-'A'+1;
pos.resize(g);
rep(i,n) pos[(s[i]-'A')].push_back(i);
lookup.assign(g,0);
rep(i,g) lookup[i]=i;
mem.assign(1<<g,-1.0);
mem[0]=0;
cout<<dfs((1<<g)-1)<<'\n';
}
컴파일 시 표준 에러 (stderr) 메시지
passes.cpp: In function 'long double cost(long long int, long long int, long long int)':
passes.cpp:39:27: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
39 | for(int i = firstr; i < pos[gr].size(); i++) sum+=otherpos.end()-upper_bound(all(otherpos),pos[gr][i]);
| ~~^~~~~~~~~~~~~~~~
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