제출 #1093061

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
1093061		TommasoUlian	Mobile (BOI12_mobile)	C++17	100 / 100	412 ms	35408 KiB

mobile

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

typedef long long ll;

vector<pair<double, double>> torri;
ll n, L;

bool canCover(double r) {
    double curr = 0.0; // Current coverage along the highway

    for (int i = 0; i < n; i++) {
        double x = torri[i].first;
        double y = torri[i].second;

        // Calculate the horizontal coverage from the station
        if (abs(y) > r) continue; // Ignore stations that cannot reach the highway

        double dx = sqrt((r * r) - (y * y)); // Width of coverage
        double left = x - dx;  // Left end of coverage
        double right = x + dx; // Right end of coverage

        // If the current position is within the coverage
        if (left <= curr + 1e-6) {
            curr = max(curr, right); // Extend current coverage
        }

        // Early exit if the entire highway is covered
        if (curr >= L) return true;
    }

    return curr >= L; // Final check if we covered the highway
}

void solve() {
    cin >> n >> L;
    torri.resize(n);
    for (int i = 0; i < n; i++) {
        cin >> torri[i].first >> torri[i].second;
    }

    double l = 1.0, r = 2e9; // Reasonable bounds for binary search
    double ans = r;

    // Perform binary search
    while (r - l > 1e-4) {
        double mid = (l + r) / 2;
        if (canCover(mid)) {
            ans = mid; // Update best answer
            r = mid;   // Try for a smaller radius
        } else {
            l = mid; // Increase radius
        }
    }

    cout << setprecision(18) << ans << endl; // Output the result
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    
    solve();
    return 0;
}

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