// #pragma GCC optimize ("Ofast")
// #pragma GCC target ("avx2")
#include <bits/stdc++.h>
using namespace std;
#ifdef LOCAL
#include <debug.h>
#else
#define debug(...)
#endif
#define ft front
#define bk back
#define st first
#define nd second
#define ins insert
#define ers erase
#define pb push_back
#define pf push_front
#define _pb pop_back
#define _pf pop_front
#define lb lower_bound
#define ub upper_bound
#define mtp make_tuple
#define bg begin
#define ed end
#define all(x) (x).bg(), (x).ed()
#define sz(x) (int)(x).size()
// #define int long long
typedef long long ll; typedef unsigned long long ull;
typedef double db; typedef long double ldb;
typedef pair<int, int> pi; typedef pair<ll, ll> pll;
typedef vector<int> vi; typedef vector<ll> vll; typedef vector<pi> vpi; typedef vector<pll> vpll;
typedef string str;
#define FOR(i, l, r) for (int i = (l); i <= (r); ++i)
#define FOS(i, r, l) for (int i = (r); i >= (l); --i)
#define FRN(i, n) for (int i = 0; i < (n); ++i)
#define FSN(i, n) for (int i = (n) - 1; i >= 0; --i)
#define EACH(i, x) for (auto &i : (x))
#define WHILE while
template<typename T> T gcd(T a, T b) { T d2 = (a | b) & -(a | b); a /= d2; b /= d2; WHILE(b) { a = a % b; swap(a, b); } return a * d2; }
template<typename T> T lcm(T a, T b) { return a / gcd(a, b) * b; }
void _assert(bool statement) { if (statement) return; cerr << "\n>> Assertion failed!\n"; exit(0); }
void _assert(bool statement, const str &message) { if (statement) return; cerr << "\n>> Assertion failed: " << message << '\n'; exit(0); }
void _error(const str &message) { cerr << "\n>> Error: " << message << '\n'; exit(0); }
#define file "TEST"
mt19937 rd(chrono::steady_clock::now().time_since_epoch().count());
ll rand(ll l, ll r) { return uniform_int_distribution<ll>(l, r)(rd); }
/*
----------------------------------------------------------------
END OF TEMPLATE
----------------------------------------------------------------
Tran The Bao - ghostwriter
Training for VOI23 gold medal
----------------------------------------------------------------
GOAT
----------------------------------------------------------------
*/
struct Point {
ldb x, y;
Point() {}
Point(ldb x, ldb y) : x(x), y(y) {}
};
const int N = 2e5 + 5;
const int T = 8e5 + 5;
const ldb eps = 1e-6;
const ldb oo = sqrt(1e9) + 1;
int n, x[N], r[N], x1[N];
ldb ans[N];
Point tr[T];
void input(int test_id) {
cin >> n;
FOR(i, 1, n) {
cin >> x[i] >> r[i];
x1[i] = x[i];
}
sort(x1 + 1, x1 + 1 + n);
}
ldb f(const Point &a, ldb x) { return a.x * x + a.y; }
void upd(int i, int l, int r, Point v) {
int mid = l + (r - l) / 2, lv = x1[l], mv = x1[mid];
if (f(v, lv) < f(tr[i], lv)) swap(tr[i], v);
if (l == r) return;
if (f(tr[i], mv) < f(v, mv)) upd(i * 2 + 1, mid + 1, r, v);
else {
swap(tr[i], v);
upd(i * 2, l, mid, v);
}
}
ldb get(int i, int l, int r, int v) {
ldb rs = f(tr[i], x1[v]);
if (l == r) return rs;
int mid = l + (r - l) / 2;
if (v <= mid) rs = min(rs, get(i * 2, l, mid, v));
else rs = min(rs, get(i * 2 + 1, mid + 1, r, v));
return rs;
}
int getp(int v) { return lb(x1 + 1, x1 + 1 + n, v) - x1; }
void upd(int pos) {
ldb tmp = sqrt((ldb)ans[pos]);
tmp = max(tmp, (ldb)1 / oo);
upd(1, 1, n, Point((ldb)0.5 / tmp, (ldb)-0.5 * x[pos] / tmp));
}
void solve(int test_id) {
FOR(i, 1, n << 2) tr[i] = Point(0, oo + 1);
ans[1] = r[1];
upd(1);
FOR(i, 2, n) {
int cpos = getp(x[i]);
ans[i] = min(sqrt((ldb)r[i]), get(1, 1, n, cpos));
ans[i] *= ans[i];
upd(i);
}
FOR(i, 1, n) cout << setprecision(3) << fixed << ans[i] << '\n';
}
void reinit(int test_id) {
}
signed main() {
ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
// freopen(file".inp", "r", stdin);
// freopen(file".out", "w", stdout);
int test_num = 1;
// cin >> test_num; // comment if the problem does not requires multitest
FOR(i, 1, test_num) {
input(i); // input in noninteractive problems for case #i
solve(i); // main function to solve case #i
reinit(i); // reinit global data to default used in case #i
}
#ifdef LOCAL
cerr << "\nTime: " << setprecision(5) << fixed << (ldb)clock() / CLOCKS_PER_SEC << "ms.\n";
#endif
return 0;
}
/*
----------------------------------------------------------------
From Benq:
stuff you should look for
* int overflow, array bounds
* special cases (n=1?)
* do smth instead of nothing and stay organized
* WRITE STUFF DOWN
* DON'T GET STUCK ON ONE APPROACH
----------------------------------------------------------------
*/
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
340 KB |
10 numbers |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
340 KB |
2 numbers |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
332 KB |
505 numbers |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
604 KB |
2000 numbers |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
26 ms |
3768 KB |
20000 numbers |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
71 ms |
9060 KB |
50000 numbers |
| 2 |
Correct |
58 ms |
9216 KB |
49912 numbers |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
138 ms |
17828 KB |
100000 numbers |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
166 ms |
20580 KB |
115362 numbers |
| 2 |
Correct |
140 ms |
21684 KB |
119971 numbers |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
206 ms |
27516 KB |
154271 numbers |
| 2 |
Correct |
237 ms |
35916 KB |
200000 numbers |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
262 ms |
35032 KB |
200000 numbers |
| 2 |
Correct |
240 ms |
35980 KB |
199945 numbers |
