Submission #854061

#	Time	Username	Problem	Language	Result	Execution time	Memory
854061		ventusliberum	Mobile (BOI12_mobile)	C++17	0 / 100	1066 ms	59412 KiB

mobile

/**
 *    title:  Mobile
**/
#include <bits/stdc++.h>
using namespace std;

template <class T> istream &operator>>(istream &is, vector<T> &v) { for (auto &x : v) is >> x; return is; }
template <class T> ostream &operator<<(ostream &os, const vector<T> &v) { auto sep = ""; for (auto &x : v) os << exchange(sep, " ") << x; return os; }
template <class T> vector<T> &operator+=(vector<T> &v, const T &a) { for (auto &x : v) x += a; return v; }
template <class T> vector<T> &operator-=(vector<T> &v, const T &a) { for (auto &x : v) x -= a; return v; }
template <class T, class U> inline bool chmax(T &a, const U &b) { return (a < b ? a = b, 1 : 0); }
template <class T, class U> inline bool chmin(T &a, const U &b) { return (b < a ? a = b, 1 : 0); }
#define si(x) int(x.size())
#define all(x) (x).begin(),(x).end()
#define rall(x) (x).rbegin(),(x).rend()
#define fi first
#define se second
using ll = long long;
using ld = long double;
constexpr int inf = 1001001001;
constexpr long long infll = 4004004004004004004LL;
constexpr long double eps = 1e-6;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    int N, L;
    cin >> N >> L;
    vector<int> X(N), Y(N);
    for (int i = 0; i < N; i++) {
        cin >> X[i] >> Y[i];
    }
    auto valid = [&](ld d) {
        vector<pair<ld, ld>> V;
        for (int i = 0; i < N; i++) {
            if (abs(Y[i]) > d) continue;
            ld t = sqrt(d * d - Y[i] * Y[i]);
            ld lhs = X[i] - t;
            chmax(lhs, 0);
            ld rhs = X[i] + t;
            chmin(rhs, L);
            V.emplace_back(lhs, rhs);
        }
        sort(all(V));
        if (V.empty()) return false;
        ld rhs = 0;
        for (int i = 0; i < si(V); i++) {
            if (rhs < V[i].fi) return false;
            chmax(rhs, V[i].se);
        }
        return rhs >= L;
    };
    ld l = 0, r = inf * 2;
    while (r - l > eps) {
        ld mid = (l + r) / 2;
        valid(mid) ? r = mid : l = mid;
    }
    cout << fixed << setprecision(6) << l << '\n';
}

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