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>
#include <ext/pb_ds/assoc_container.hpp>
using namespace std;
using namespace __gnu_pbds;
template <typename T1, typename T2>
using indexed_map = tree<T1, T2, less<T1>, rb_tree_tag, tree_order_statistics_node_update>;
template <typename T>
using indexed_set = indexed_map<T, null_type>;
#define loop(x, i) for (int i = 0; i < (x); i++)
#define loop1(x, i) for (int i = 1; i <= (x); i++)
#define rev(x, i) for (int i = (int)(x) - 1; i >= 0; i--)
#define itloop(x) for (auto it = begin(x); x != end(x); it++)
#define itrev(x) for (auto it = rbegin(x); x != rend(x); it++)
// #define int long long
#define INF ((int64_t)(4e18 + 1))
#define INF32 ((int32_t)(2e9 + 1))
#define ALL(x) begin(x), end(x)
#define RALL(x) rbegin(x), rend(x)
#define existsIn(x, l) (count(ALL(l), x) > 0)
#define removeIn(x, l) l.erase(find(ALL(l), x))
#define pb push_back
#define sz(x) (int)(x).size()
#define x first
#define y second
#define var const auto &
#define foreach(l) for (var e : l)
typedef pair<int, int> ii;
typedef tuple<int, int, int> iii;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ii> vii;
typedef vector<iii> viii;
typedef vector<vii> vvii;
typedef vector<viii> vviii;
typedef set<int> si;
typedef set<ii> sii;
typedef set<iii> siii;
typedef vector<si> vsi;
typedef vector<sii> vsii;
typedef vector<vsi> vvsi;
typedef vector<string> vstr;
typedef vector<vector<string>> vvstr;
typedef vector<bool> vb;
typedef vector<vb> vvb;
typedef vi::iterator viit;
typedef si::iterator siit;
typedef int8_t in8;
typedef int16_t in16;
typedef int32_t in32;
typedef int64_t in64;
typedef double ld;
typedef vector<pair<ld, ld>> vff;
// ld eps = 4e-4; // 13pt
ld eps = 1e-5; // 13pt
// ld eps = 1e-18; // 4pt: TLE
void solve()
{
int N;
ld L;
cin >> N >> L;
vff a(N);
loop(N, i)
{
cin >> a[i].x >> a[i].y;
}
ld lo = 0.0L, hi = 5e9L;
while (hi - lo > eps)
{
ld R = lo + (hi - lo) / 2.0L;
vff segments;
loop(N, i)
{
auto [x, y] = a[i];
ld D = (R * R) - ((ld)y * (ld)y);
if (D >= 0.0L)
{
ld l = x - sqrt(D);
ld r = x + sqrt(D);
segments.pb({l, r});
}
else if (D + eps >= 0.0L)
{
ld l = x;
ld r = x;
segments.pb({l, r});
}
}
if (segments.empty())
{
lo = R;
continue;
}
sort(ALL(segments));
bool highwayCovered = 1;
ld l = segments[0].first, r = segments[0].second;
if (l > eps)
highwayCovered = 0;
else
{
for (auto [l_i, r_i] : segments)
{
if (l_i > r + eps)
{
highwayCovered = 0;
break;
}
r = max(r, r_i);
}
}
if (r + eps < L)
highwayCovered = 0;
if (highwayCovered)
{
hi = R;
}
else
lo = R;
}
ld res = lo + (hi - lo) / 2.0L;
cout << fixed << setprecision(4) << res << endl;
}
signed main()
{
cin.tie(0)->sync_with_stdio(0);
solve();
}
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