Submission #1073861

#	Time	Username	Problem	Language	Result	Execution time	Memory
1073861		vjudge1	Mobile (BOI12_mobile)	C++17	0 / 100	1044 ms	27572 KiB

mobile

#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
typedef long double ld;

ld dist(ld x1, ld y1, ld x2, ld y2){
	return (x1-x2)*(x1-x2)+(y1-y2)*(y1-y2);
}

int main(){
	ios_base::sync_with_stdio(0); cin.tie(0);

	int n;
	ll L;
	cin >> n >> L;
	
	vector <pair<ll,ll>> pts;
	for(int i=0; i<n; i++){
		ll x, y;
		cin >> x >> y;
		if(!pts.empty() && x == pts.back().first){
			pts.back().second = min(pts.back().second, abs(y));
		}
		else{
			pts.push_back({x,abs(y)});
		}
	}
	n = pts.size();

	ld ans = 0.0;
	ld ans_start = dist(pts[0].first, pts[0].second, 0,0);
	for(int i=0; i<n; i++){
		ans_start = min(ans_start, dist(pts[i].first,pts[i].second,0,0));
	}
	ld ans_end = dist(pts[0].first, pts[0].second, L,0);
	for(int i=0; i<n; i++){
		ans_end = min(ans_end, dist(pts[i].first,pts[i].second,L,0));
	}
	ans = max(ans_start,ans_end);

	const ld EPS = 1e-8;

	auto f = [&](ld x, int i){
		return max(
				dist(x,0,pts[i-1].first,pts[i-1].second),
				dist(x,0,pts[i].first,pts[i].second));
	};

	for(int i=1; i<n; i++){
		// ternary search x* between pts[i-1], pts[i]
		
		ld l=max(0LL, pts[i-1].first);
		ld r=min(L, pts[i].first);

		/*
		for(ld xt = l; xt <= r; xt+=0.5){
			cout << "xt: " << xt << ' ' << f(xt, i) << endl;
		}
		*/

		while(r-l > EPS){
			ld mid1 = l+(r-l)/3;
			ld mid2 = l+2*(r-l)/3;
			
			if(f(mid2,i)-f(mid1,i) >= 0) r = mid2;
			else l = mid1;
		}
		ans = max(ans, f(l,i));
	}

	ans = sqrt(ans);
	cout << fixed << setprecision(6) << ans << '\n';
	return 0;
}

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