This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
//#pragma GCC optimize("O3")
//#pragma GCC target("avx,avx2,fma")
#define sz(x) int((x).size())
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
using namespace std;
using ll = long long;
using ld = long double; // or double, if TL is tight
using str = string;
using ii = pair<int, int>;
using pl = pair<ll, ll>;
using vi = vector<int>;
using vll = vector<ll>;
int main() {
cin.tie(0);
ios_base::sync_with_stdio(0);
int n, k;
cin >> n >> k;
string s0, s;
cin >> s0;
ll re0 = 0;
int nrB = 0, sum = 0;
for(auto it : s0) {
if(it == 'A') {
++sum;
s += 'A';
re0 += nrB;
if(nrB && sum) {
s += 'B';
--nrB;
--sum;
}
} else {
if(sum) {
s += 'B';
--sum;
} else {
++nrB;
}
}
}
vi A, P(n + 1);
vll SA;
P[0] = -1;
for(auto it : s) {
if(it == 'A'){
A.push_back(nrB);
if(SA.empty())
SA.push_back(A.back());
else
SA.push_back(A.back() + SA.back());
}
else {
++nrB;
P[nrB] = (int)A.size() - 1;
}
}
auto cost = [&](ll st, ll dr) {
ll sa = 0;
if(P[st] != -1) sa = SA[P[st]];
return st * P[st] - sa - st * dr + SA[dr];
};
const ll INF = 1e18;
vector<vll> DP(n, vll(k + 1, INF));
for(int i = 0; i < n; ++i) {
DP[i][1] = cost(0, i);
for(int j = 2; j <= k; ++j)
for(int p = 1; p <= i; ++p)
DP[i][j] = min(DP[i][j], DP[p - 1][j - 1] + cost(p, i));
}
ll re = INF;
for(auto it : DP[n - 1]) re = min(re, it);
cout << re + re0 << "\n";
return 0;
}
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