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>
using namespace std;
#define sz(v) int(v.size())
#define ar array
typedef long long ll;
const int N = 1e6+10, MOD = 1e9+7;
const ll INF = 1e18+10;
int n, K, small[N];
ll ps[N], l_use[N];
vector<int> one, two;
struct Line {
ll m, b;
int id;
ll calc(ll x) {
return m * x + b;
}
};
struct CHT {
deque<Line> lines;
void add(ll m, ll b, int id) {
while (sz(lines) >= 2) {
auto A = lines.end()[-2];
auto B = lines.end()[-1];
if ((b - A.b) * (A.m - B.m) <= (B.b - A.b) * (A.m - m)) lines.pop_back();
else break;
}
lines.push_back({m, b, id});
}
Line qry(ll x) {
while (sz(lines) >= 2 && lines[0].calc(x) >= lines[1].calc(x)) {
lines.pop_front();
}
return lines[0];
}
};
pair<ll, int> calc(ll d) {
vector<pair<ll, int>> dp(n);
CHT lines;
for (int i = 0; i < n; i++) {
lines.add(-i, (long long) i * i - i + l_use[i] + (i == 0 ? 0 : dp[i-1].first), i);
auto line = lines.qry(i);
dp[i].first = line.calc(i) + ps[i] + d;
dp[i].second = line.id ? dp[line.id-1].second + 1 : 1;
int l = small[i];
if (l <= i) {
if (l == 0) dp[i] = min(dp[i], make_pair(d + 0LL, 1));
else dp[i] = min(dp[i], make_pair(d + dp[l-1].first, dp[l-1].second + 1));
}
}
return dp[n-1];
}
void solve() {
cin >> n >> K;
for (int i = 0; i < 2 * n; i++) {
char c; cin >> c;
if (c == 'A') one.push_back(i);
else two.push_back(i);
}
for (int i = 0; i < n; i++) {
small[i] = lower_bound(two.begin(), two.end(), one[i]) - two.begin();
}
for (int i = 0; i < n; i++) {
ps[i] = small[i] + (i ? ps[i-1] : 0);
}
for (int i = 0; i < n; i++) {
l_use[i] = -(i ? ps[i-1] : 0);
int use = lower_bound(small, small + n, i) - small - 1; // [i..use]
if (use >= i) {
l_use[i] -= ps[use] - (i ? ps[i-1] : 0) - (long long) i * (use - i + 1);
}
}
// cerr << calc(0).first << ' ' << calc(0).second << endl;
ll lo = -1, hi = (long long) 2e12, mid = (lo + hi) / 2;
while (lo < mid && mid < hi) {
auto [cost, cnt] = calc(mid);
if (cnt <= K) hi = mid;
else lo = mid;
mid = (lo + hi) / 2;
}
auto [cost, cnt] = calc(hi);
// cerr << lo << ' ' << cost << ' ' << cnt << endl;
cout << cost - hi * cnt << '\n';
}
int main() {
ios::sync_with_stdio(false); cin.tie(0);
int T = 1;
// cin >> T;
while (T--) solve();
}
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