Submission #1116511

#	Time	Username	Problem	Language	Result	Execution time	Memory
1116511		vomanos	Mobile (BOI12_mobile)	C++14	100 / 100	824 ms	35412 KiB

mobile

// Source: https://usaco.guide/general/io

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

#define ll long long
#define pdd pair<double, double>

double dist2(pdd a, pdd b) {
	return (a.first - b.first) * (a.first - b.first)
	+ (a.second - b.second) * (a.second - b.second);
}

int main() {
	int N;
	ll L;
	cin >> N >> L;

	pdd s[N];
	for (int i = 0; i < N; i++) cin >> s[i].first >> s[i].second;

	double low = 0, high = 1e12;
	// double low = 6, high = 6.01;
	while (high - low > 0.000001) {
		double mid = low + (high - low) / 2;

		double x = 0;
		for (int i = 0; i < N; i++) {
			if (dist2({x, 0}, {s[i]}) > mid*mid) continue;

			// let x = s[i].first, y = s[i].second;
			// (x + d)^2 + y^2 = r^2
			// x + d = sqrt(r^2 - y^2)
			//d = sqrt(r^2 - y^2)

			x = s[i].first + sqrt(mid*mid - s[i].second * s[i].second);
		}

		// cout << mid << " " << x << endl;

		if (x >= L) high = mid;
		else low = mid;
	}

	cout << fixed << setprecision(10) << high;
}

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