Pagini recente » Cod sursa (job #3179194) | Borderou de evaluare (job #2795689) | Borderou de evaluare (job #2611817) | Borderou de evaluare (job #2376675) | Cod sursa (job #1988312)
#include <vector>
#include <iostream>
#include <queue>
#include <set>
#include <cassert>
#include <limits>
#include <algorithm>
#include <map>
using namespace std;
class ConvexSet {
using T = long long;
struct SetElem {
T a, b;
mutable T ans;
bool is_query;
SetElem(T query_x) : b(query_x), ans(numeric_limits<T>::min()), is_query(true) {}
SetElem(T a, T b) : a(a), b(b), is_query(false) {}
T eval(T x) const {
return a * x + b;
}
bool operator< (const SetElem &rhs) const {
assert(!rhs.is_query);
if (is_query) {
// Upper bound operates from right to left
T now = rhs.eval(b);
if (ans < now) {
ans = now;
return true;
}
return false;
} else return (a != rhs.a) ? a > rhs.a : b > rhs.b;
}
};
set<SetElem> data;
bool is_bad(set<SetElem>::iterator it) {
if (it == data.begin() || next(it) == data.end())
return false;
auto prv = prev(it), nxt = next(it);
return (it->b - prv->b) * (nxt->a - it->a)
>= (it->b - nxt->b) * (prv->a - it->a);
}
public:
void Insert(T slope, T intercept) {
auto it = data.insert(SetElem(slope, intercept)).first;
if (is_bad(it)) data.erase(it);
else {
while (it != data.begin()) {
auto prv = prev(it);
if (is_bad(prv)) {
data.erase(prv);
} else break;
}
while (next(it) != data.end()) {
auto nxt = next(it);
if (is_bad(nxt)) {
data.erase(nxt);
} else break;
}
}
}
T EvaluateMax(T x) {
T ans = 0;
for (auto p : data)
ans = max(ans, p.eval(x));
return ans;
SetElem ret(x);
data.upper_bound(ret);
return ret.ans;
}
};
int main() {
freopen("euro.in", "r", stdin);
freopen("euro.out", "w", stdout);
int n, t;
cin >> n >> t;
// dp[i] = max_j(dp[j] + (gain[i] - gain[j]) * i - t)
// dp[i] = max_j(dp[j] - gain[j] * i + gain[i] * i - t)
// dp[i] = gain[i] * i - t + max_j(dp[j] - gain[j] * i)
// solution: keep stack of linear functions of type -gain[j] * X + dp[j]
// no monotony -> need set
ConvexSet fun_set;
fun_set.Insert(0, 0);
long long ans = 0, gain = 0;
for (int i = 1; i <= n; ++i) {
int x; cin >> x; gain += x;
ans = fun_set.EvaluateMax(i) + gain * i - t;
fun_set.Insert(-gain, ans);
}
cout << ans << endl;
return 0;
}