Submission #829874

#	Time	Username	Problem	Language	Result	Execution time	Memory
829874		soumyojit_sen	Mobile (BOI12_mobile)	C++17	0 / 100	444 ms	18696 KiB

mobile

#include <bits/stdc++.h>
using namespace std;
vector<pair<double, double>> pts;
int n;
double L;

bool works(double d){
	// whether a radius of d is enough to intersect all the circles
	double currDistCovered = 0.0;
	for(int i = 0; i < n; i++){
		// find the segment covered by ith circle on the highway
		// radius^2 = yi^2 + dist^2
		double dist = sqrt(d*d - pts[i].second*pts[i].second);
		double start = pts[i].first - dist;
		double end = pts[i].first + dist;

		if(start <= currDistCovered){
			currDistCovered = max(currDistCovered, end);
		}
	}
	return currDistCovered >= L;
}

int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(nullptr);
	cin >> n >> L;
	pts.resize(n);
	for(int i = 0; i < n; i++) cin >> pts[i].first >> pts[i].second;

	double good = 1.5e9;
	double bad = 1.0;
	
	while(bad + 1 - good < 1e-3){
		double mid = bad + (good - bad)/2;
		//cout << fixed << setprecision(6) << i << " " << mid <<"\n" ;
		if(works(mid)){
			good = mid;
		} else {
			bad = mid;
		}
	}
	cout << fixed << setprecision(12) << good;
}

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