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>
#define Loop(x,l,r) for (ll x = (l); x < (ll)(r); ++x)
#define LoopR(x,l,r) for (ll x = (r)-1; x >= (ll)(l); --x)
typedef long long ll;
typedef std::pair<int, int> pii;
typedef std::pair<ll , ll > pll;
using namespace std;
typedef pair<double, double> pdd;
pdd in()
{
ll x, y;
cin >> x >> y;
return {x, y};
}
const int N = 200'010;
double a[N], b[N];
int len = 0;
void insert(pdd f)
{
a[len] = f.first;
b[len] = f.second;
++len;
}
__attribute__((optimize("Ofast,unroll-loops"),target("avx2,fma")))
double get_0(double x)
{
#define MIN(x, y) ((x)>(y)?(y):(x))
double ans = 1e30;
Loop (i,0,len) {
double tmp = a[i]*x + b[i];
ans = MIN(ans, tmp);
}
return ans;
#undef MIN
}
__attribute__((optimize("Ofast,unroll-loops"),target("avx2,fma")))
double get_1(double x)
{
#define MIN(x, y) ((x)>(y)?(y):(x))
double ans = 1e30;
Loop (i,len-len%4,len) {
double tmp = a[i]*x + b[i];
ans = MIN(ans, tmp);
}
typedef double ymm __attribute__((vector_size(32),aligned(32)));
ymm vans = {ans, ans, ans, ans};
LoopR (i,0,len/4) {
ymm tmp = ((ymm *)a)[i]*x + ((ymm *)b)[i];
vans = MIN(vans, tmp);
}
Loop (i,0,4)
ans = MIN(ans, vans[i]);
return ans;
#undef MIN
}
double (*get_ans[2])(double x) = {get_0, get_1};
int main()
{
cin.tie(0) -> sync_with_stdio(false);
cout << fixed << setprecision(3);
int n;
cin >> n;
Loop (i,0,n) {
auto [x, r] = in();
r = sqrt(r);
r = min(r, get_ans[i&1](x));
cout << r*r << '\n';
insert({0.5/r, -x*0.5/r});
}
}
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