Submission #1163537

#	Time	Username	Problem	Language	Result	Execution time	Memory
1163537		kedimestan	Mobile (BOI12_mobile)	C++20	0 / 100	114 ms	16096 KiB

mobile

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

// Function to calculate the Euclidean distance from a point (x, 0) on the highway to a BTS at (xi, yi)
long double distance(long double x, long double xi, long double yi) {
    return sqrt((x - xi) * (x - xi) + yi * yi);
}

// Function to find the nearest BTS to a point (x, 0) on the highway
long double nearestDistance(long double x, const vector<pair<long long int, long long int>>& stations) {
    // Use binary search to find the nearest BTS efficiently
    auto it = lower_bound(stations.begin(), stations.end(), make_pair((long long int)x, LLONG_MIN));
    long double minDist = 1e18;

    // Check the BTS at or after x
    if (it != stations.end()) {
        minDist = min(minDist, distance(x, it->first, it->second));
    }
    // Check the BTS before x
    if (it != stations.begin()) {
        --it;
        minDist = min(minDist, distance(x, it->first, it->second));
    }

    return minDist;
}

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

    long long int N, L;
    cin >> N >> L;

    vector<pair<long long int, long long int>> stations(N);
    for (long long int i = 0; i < N; ++i) {
        cin >> stations[i].first >> stations[i].second;
    }

    // Binary search to find the point x[q] that maximizes the distance to the nearest BTS
    long double left = 0.0, right = L;
    long double maxDist = 0.0;

    // Perform binary search until the search space is small enough
    while (right - left > 1e-9) {
        long double mid = (left + right) / 2.0;

        // Find the nearest distance at mid and mid + epsilon
        long double distMid = nearestDistance(mid, stations);
        long double distMidEpsilon = nearestDistance(mid + 1e-9, stations);

        // Update the maximum distance found so far
        maxDist = max(maxDist, distMid);

        // Adjust the search boundaries based on whether we are on the increasing or decreasing part
        if (distMid < distMidEpsilon) {
            left = mid;
        } else {
            right = mid;
        }
    }

    // Output the result with the required precision
    cout << fixed << setprecision(6) << maxDist << endl;

    return 0;
}

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