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>
using namespace std;
void solve()
{
struct point
{
long x, y;
};
int n;
long l;
cin >> n >> l;
vector<point> coords(n);
for (int i = 0; i < n; i++)
cin >> coords[i].x >> coords[i].y;
auto valid = [&](const double &d) -> bool
{
vector<pair<double, double>> cov;
cov.reserve(2 * n);
for (const auto &[x, y] : coords)
{
if (y * y < d * d)
{
double h = sqrt(d * d - y * y);
while (!cov.empty() && cov.back().first > x - h)
cov.pop_back();
cov.emplace_back(x - h, x + h);
}
}
bool ended = 0;
double e = 0.0;
for (const auto &[x1, x2] : cov)
{
if (x1 <= e)
{
if (e = max(e, x2); e >= l)
{
ended = 1;
break;
}
}
else
break;
}
return ended;
};
double ans = 3e9;
for (double lo = 0.5; ans - lo > 1e-5;)
{
if (double mid = (lo + ans) / 2.0; valid(mid))
ans = mid;
else
lo = mid + 1e-4;
}
cout << fixed << setprecision(5) << ans << '\n';
}
int main()
{
ios_base::sync_with_stdio(false), cin.tie(NULL);
solve();
return 0;
}
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