Submission #1267435

#	Time	Username	Problem	Language	Result	Execution time	Memory
1267435		pramad712	Mobile (BOI12_mobile)	C++17	100 / 100	387 ms	16096 KiB

mobile

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

struct Point {
    long long x, y;
};

int count_, length;
vector<Point> points;

pair<double, double> merge(pair<double, double> first, pair<double, double> second) {
    if (second < first) swap(first, second);

    if (first.second < second.first) {
        return make_pair(-1.0, -1.0);
    }

    return make_pair(first.first, max(first.second, second.second));
}

bool works(double distance) {
    stack<pair<double, double>> stack;

    for (Point point: points) {
        double x_change_squared = distance * distance - point.y * point.y;

        if (x_change_squared < 0) {
            continue;
        }

        pair<double, double> interval = make_pair(point.x - sqrt(x_change_squared), point.x + sqrt(x_change_squared));

        while (!stack.empty()) {
            pair<double, double> result = merge(stack.top(), interval);

            if (result == make_pair(-1.0, -1.0)) break;

            stack.pop();
            interval = result;
        }

        stack.emplace(interval);
    }

    while (!stack.empty()) {
        pair<double, double> interval = stack.top();
        stack.pop();

        if (interval.first <= 0 && length <= interval.second) {
            return true;
        }
    }

    return false;
}

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

    cin >> count_ >> length;

    points.resize(count_);

    for (int index = 0; index < count_; index++) cin >> points[index].x >> points[index].y;

    double left = 1, right = 1.5e9;

    while (right - left > 1e-3) {
        double middle = (left + right) / 2;

        if (works(middle)) {
            right = middle;
        }

        else {
            left = middle;
        }
    }

    cout << fixed << setprecision(4) << left << "\n";
    return 0;
}

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