#include <bits/stdc++.h>
#define int long long
using namespace std;
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#define rep(i, a, b) for(int i = (a); i < (b); i++)
#define sz(v) ((int)((v).size()))
template<typename T>
void chmax(T &x, const T &v) { if (x < v) x = v; }
template<typename T>
void chmin(T &x, const T &v) { if (x > v) x = v; }
using pii = pair<int, int>;
using vi = vector<int>;
string to_string(string s) { return s; }
template <typename T> string to_string(T v) {
bool first = true;
string res = "[";
for (const auto &x : v) {
if (!first)
res += ", ";
first = false;
res += to_string(x);
}
res += "]";
return res;
}
void dbg_out() { cout << endl; }
template <typename Head, typename... Tail> void dbg_out(Head H, Tail... T) {
cout << ' ' << to_string(H);
dbg_out(T...);
}
#ifdef DEBUG
#define dbg(...) cout << "(" << #__VA_ARGS__ << "):", dbg_out(__VA_ARGS__)
#else
#define dbg(...)
#endif
const int INF = 1e12;
struct _Line {
mutable int k, m, p;
bool operator<(const _Line& o) const { return k < o.k; }
bool operator<(int x) const { return p < x; }
};
struct _LineContainer : multiset<_Line, less<>> {
// (for doubles, use inf = 1/.0, div(a,b) = a/b)
static const int inf = LLONG_MAX;
int div(int a, int b) { // floored division
return a / b - ((a ^ b) < 0 && a % b); }
bool isect(iterator x, iterator y) {
if (y == end()) return x->p = inf, 0;
if (x->k == y->k) x->p = x->m > y->m ? inf : -inf;
else x->p = div(y->m - x->m, x->k - y->k);
return x->p >= y->p;
}
void add(int k, int m) {
auto z = insert({k, m, 0}), y = z++, x = y;
while (isect(y, z)) z = erase(z);
if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
while ((y = x) != begin() && (--x)->p >= y->p)
isect(x, erase(y));
}
int queryMax(int x, int& from) {
assert(!empty());
auto l = *lower_bound(x);
from = l.k;
return l.k * x + l.m;
}
};
struct LineContainer {
_LineContainer fs;
void add (int k, int m) { // kx+m
// -f(x) = -(kx+m) = (-k)x + (-m)
fs.add(-k, -m);
}
int min(int x, int& from) {
if (fs.empty()) return INF;
return -fs.queryMax(x, from);
}
};
int N, K;
string S;
// ferme[i] = nombre d'ouvrants avant Fi
vector<int> ouvre, ferme;
vector<int> cumuFerme;
int coutExclus(int left, int right) {
if (left >= right) {
return 0;
}
int projExclus = min(right, ouvre[right-1]);
if (projExclus <= left) return 0;
return (projExclus - left)*(right) - (cumuFerme[projExclus] - cumuFerme[left]);
}
signed main() {
ios::sync_with_stdio(false);
cin.tie(0);
cin >> N >> K >> S;
{
int curOuvre = 0, curFerme = 0;
cumuFerme.push_back(0);
for (char c : S) {
if (c == 'A') {
++curOuvre;
ouvre.push_back(curFerme);
} else {
++curFerme;
ferme.push_back(curOuvre);
cumuFerme.push_back(cumuFerme.back() + curOuvre);
}
}
}
auto calc = [&] (int lambda) -> pii {
vector<pii> dp(N+1, {INF, INF});
dp[N] = {0, 0};
LineContainer cont;
// [J EXCLUS]
// gright(left) = (projExclus - left)*(right) - (cumuFerme[projExclus] - cumuFerme[left])
// gj(x) = (pj - x)*j - (cf[pj] - cf[left])
// gj(x) = -jx + (j*pj - cf[pj]) + cf[x]
// mx + p + terme fixe
auto proj = [&] (int j) {
return min(j, ouvre[j-1]);
};
auto add = [&] (int j) {
int pj = proj(j);
cont.add(-j, dp[j].first + j*pj - cumuFerme[pj]);
};
int jToAdd = N;
for (int left = N-1; left >= 0; --left) {
while (jToAdd > 0 && left <= min(proj(jToAdd), jToAdd-1)) {
add(jToAdd--);
}
rep(right, left+1, N+1) {
int prop = dp[right].first + coutExclus(left, right) + lambda;
chmin(dp[left], pii {prop, dp[right].second + 1});
}
// if (true) {
// int from = -1;
// int prop = cont.min(left, from) + cumuFerme[left] + lambda;
// if (dp[left].first > prop) {
// dp[left] = {prop, dp[from].second + 1};
// }
// }
// if (jToAdd > 0) {
// int prop = dp[jToAdd].first + coutExclus(left, jToAdd) + lambda;
// if (dp[left].first > prop) {
// dp[left] = {prop, dp[jToAdd].second + 1};
// }
// }
}
return dp[0];
};
int lo = 0, hi = INF;
while (lo < hi) {
int mid = (lo+hi) / 2;
if(calc(mid).second > K) {
lo = mid+1;
} else {
hi = mid;
}
}
assert(lo == hi);
int lambda = lo;
auto [score, groupsMade] = calc(lambda);
assert(groupsMade <= K);
cout << score - lambda*groupsMade << '\n';
}
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
0 ms |
212 KB |
Output is correct |
| 2 |
Correct |
0 ms |
212 KB |
Output is correct |
| 3 |
Correct |
0 ms |
212 KB |
Output is correct |
| 4 |
Correct |
0 ms |
212 KB |
Output is correct |
| 5 |
Correct |
0 ms |
212 KB |
Output is correct |
| 6 |
Incorrect |
1 ms |
212 KB |
Output isn't correct |
| 7 |
Halted |
0 ms |
0 KB |
- |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
0 ms |
212 KB |
Output is correct |
| 2 |
Correct |
0 ms |
212 KB |
Output is correct |
| 3 |
Correct |
0 ms |
212 KB |
Output is correct |
| 4 |
Correct |
0 ms |
212 KB |
Output is correct |
| 5 |
Correct |
0 ms |
212 KB |
Output is correct |
| 6 |
Incorrect |
1 ms |
212 KB |
Output isn't correct |
| 7 |
Halted |
0 ms |
0 KB |
- |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
0 ms |
212 KB |
Output is correct |
| 2 |
Correct |
0 ms |
212 KB |
Output is correct |
| 3 |
Correct |
0 ms |
212 KB |
Output is correct |
| 4 |
Correct |
0 ms |
212 KB |
Output is correct |
| 5 |
Correct |
0 ms |
212 KB |
Output is correct |
| 6 |
Incorrect |
1 ms |
212 KB |
Output isn't correct |
| 7 |
Halted |
0 ms |
0 KB |
- |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
0 ms |
212 KB |
Output is correct |
| 2 |
Correct |
0 ms |
212 KB |
Output is correct |
| 3 |
Correct |
0 ms |
212 KB |
Output is correct |
| 4 |
Correct |
0 ms |
212 KB |
Output is correct |
| 5 |
Correct |
0 ms |
212 KB |
Output is correct |
| 6 |
Incorrect |
1 ms |
212 KB |
Output isn't correct |
| 7 |
Halted |
0 ms |
0 KB |
- |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
0 ms |
212 KB |
Output is correct |
| 2 |
Correct |
0 ms |
212 KB |
Output is correct |
| 3 |
Correct |
0 ms |
212 KB |
Output is correct |
| 4 |
Correct |
0 ms |
212 KB |
Output is correct |
| 5 |
Correct |
0 ms |
212 KB |
Output is correct |
| 6 |
Incorrect |
1 ms |
212 KB |
Output isn't correct |
| 7 |
Halted |
0 ms |
0 KB |
- |
