Submission #477083

#	Time	Username	Problem	Language	Result	Execution time	Memory
477083		qwerty1234	Mobile (BOI12_mobile)	C++17	0 / 100	1091 ms	49972 KiB

mobile

#include <bits/stdc++.h>

#define ll long long

using namespace std;

bool check(double maxDist, vector<pair<double, double>> &transceivers, ll N, ll L) {
	vector<pair<double, double>> bounds;
	for (int i = 0; i < N; i++) {
		double ySquared = transceivers[i].second * transceivers[i].second;
		double hypoSquared = maxDist * maxDist;
		if (hypoSquared - ySquared < 0) {
			continue;
		}
		double x = sqrt(hypoSquared - ySquared);
		bounds.push_back({ max(transceivers[i].first - x, 0.0), min(transceivers[i].first + x, (double)L) });
	}
	if (bounds.size() == 0) {
		return false;
	}
	double covered = bounds[0].second - bounds[0].first;
	double right = bounds[0].second;
	for (int i = 1; i < (int)bounds.size(); i++) {
		double currBound = bounds[i].second - bounds[i].first;
		currBound -= max(0.0, right - bounds[i].first);
		covered += max(0.0, currBound);
		right = max(bounds[i].second, right);
	}

	return covered >= L;
}

int main() {
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	ll N, L;
	cin >> N >> L;
	vector<pair<double, double>> transceivers(N);
	for (int i = 0; i < N; i++) cin >> transceivers[i].first >> transceivers[i].second;
	double l = 0;
	double r = 1e18;
	double ans = 0;
	while (r - l >= 0.001) {
		double mid = l + (r - l) / 2;
		// cout << l << ' ' << r << ' ' << mid << '\n';
		if (check(mid, transceivers, N, L)) {
			r = mid;
			ans = mid;
		} else {
			l = mid;
		}
	}
	printf("%0.7lf\n", ans);
}

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