Submission #1162073

#	Time	Username	Problem	Language	Result	Execution time	Memory
1162073		jared	Mobile (BOI12_mobile)	C++20	12 / 100	267 ms	8264 KiB

mobile

#include "bits/stdc++.h"
using namespace std;

int n, L;
// vector<pair<int, int> > p;
pair<int, int> p[1000000];

// bool ok(double radius) {
//     double end = 0;
//     for (auto [x, y]: p) {
//         // Equation of a circle: (X - x)^2 + (Y - y)^2 = r^2
//         // Want to find intersect with Y = 0,
//         // (X - x)^2 = r^2 - y^2
//         //         X = (+-) sqrt(r^2 - y^2) + x
//         double delta = sqrt(radius * radius - y * y);
//         double l_intercept = -delta + x, r_intercept = delta + x;
//         if (l_intercept <= end) end = max(end, r_intercept);
//     }
//     return end >= L;
// }

signed main() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);

    cin >> n >> L;
    // p.resize(n);
    // for (auto &i: p)
    //     cin >> i.first >> i.second;
    for (int i = 0; i < n; i++)
        cin >> p[i].first >> p[i].second;

    double l = 0, r = 1.5e9;
    while (r - l > 1e-3) {
        double mid = l + (r - l) / 2;

        double end = 0;
        // for (auto [x, y]: p) {
        for (int i = 0; i < n; i++) {
            auto x = p[i].first, y = p[i].second;
            // Equation of a circle: (X - x)^2 + (Y - y)^2 = r^2
            // Want to find intersect with Y = 0,
            // (X - x)^2 = r^2 - y^2
            //         X = (+-) sqrt(r^2 - y^2) + x
            double delta = sqrt(mid * mid - y * y);
            double l_intercept = -delta + x, r_intercept = delta + x;
            if (l_intercept <= end) end = max(end, r_intercept);
        }

        if (end >= L) r = mid;
        else l = mid;
    }
    cout << fixed << setprecision(6) << l << endl;
    return 0;
}

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