#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int N = 5e5+1;
const ll is_query = -(1LL<<62);
struct Line {
ll m, b;
mutable function<const Line*()> succ;
bool operator<(const Line& rhs) const {
if (rhs.b != is_query) return m < rhs.m;
const Line* s = succ();
if (!s) return 0;
ll x = rhs.m;
return b - s->b < (s->m - m) * x;
}
};
struct HullDynamic : public multiset<Line> { // will maintain upper hull for maximum
bool bad(iterator y) {
auto z = next(y);
if (y == begin()) {
if (z == end()) return 0;
return y->m == z->m && y->b <= z->b;
}
auto x = prev(y);
if (z == end()) return y->m == x->m && y->b <= x->b;
return (x->b - y->b)*(z->m - y->m) >= (y->b - z->b)*(y->m - x->m);
}
void update(ll m, ll b) {
auto y = insert({ m, b });
y->succ = [=] { return next(y) == end() ? 0 : &*next(y); };
if (bad(y)) { erase(y); return; }
while (next(y) != end() && bad(next(y))) erase(next(y));
while (y != begin() && bad(prev(y))) erase(prev(y));
}
ll query(ll x) {
auto l = *lower_bound((Line) { x, is_query });
return l.m * x + l.b;
}
} dp;
int n, h[N], res[N];
void solve() {
dp.clear();
dp.update(2*h[0], -1ll*h[0]*h[0]);
int mx = h[0];
for(int i = 1, x = 0; i < n; i++) {
while(x < mx || 1ll*x*x - i < dp.query(x)) ++x;
res[i] = max(x, res[i]);
mx = max(mx, h[i]);
dp.update(2*h[i], -1ll*h[i]*h[i] - i);
}
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
cin >> n;
for(int i = 0; i < n; i++) cin >> h[i];
solve();
reverse(h, h+n);
reverse(res, res+n);
solve();
reverse(h, h+n);
reverse(res, res+n);
// dp.update(2*h[n-1], -1ll*h[n-1]*h[n-1]);
// mx = h[n-1];
// for(int i = n-2, x = 0; i >= 0; i--) {
// cout << i << ' ' << x << ' ' << mx << ":" << endl;
// for(auto l: dp) cout << l.m*x + l.b << endl;
// while(x < mx || 1ll*x*x + i < dp.query(x)) ++x;
// res[i] = max(x, res[i]);
// mx = max(mx, h[i]);
// dp.update(2*h[i], -1ll*h[i]*h[i] + i);
// }
for(int i = 0; i < n; i++) cout << max(res[i] - h[i], 0) << '\n';
}
// h[j] <= x - sqrt(i - j)
// x - h[j] >= sqrt(i - j)
// x^2 - 2xh[j] + h[j]^2 >= i - j
// x^2 - i >= 2xh[j] - h[j]^2 - j
//
// x^2 - 2xh[j] + h[j]^2 >= j - i
// x^2 + i >= 2xh[j] - h[j]^2 + j
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
6084 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
6084 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
6084 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
956 ms |
6084 KB |
Execution killed because of forbidden syscall writev (20) |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
969 ms |
6084 KB |
Execution killed because of forbidden syscall writev (20) |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
306 ms |
6216 KB |
Execution killed because of forbidden syscall writev (20) |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
883 ms |
6084 KB |
Execution killed because of forbidden syscall writev (20) |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
1000 ms |
6084 KB |
Execution timed out |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
1000 ms |
6084 KB |
Execution timed out |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
1000 ms |
6084 KB |
Execution timed out |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
1000 ms |
6084 KB |
Execution timed out |
| 2 |
Halted |
0 ms |
0 KB |
- |
