Submission #445957

#	Time	Username	Problem	Language	Result	Execution time	Memory
445957		Qw3rTy	Mobile (BOI12_mobile)	C++11	0 / 100	671 ms	33532 KiB

mobile

#pragma GCC optimize(2)
#pragma GCC optimize(3)
#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
#define int long long
#define db double
#define delta 1e-6
#define INF 1e9+5
#define pi pair<int,int>
#define pb pair<db,db>
#define fi first
#define se second
using namespace std;

const int maxN = 1e6+5;

int N,L;
pi tower[maxN];
pb inter[maxN]; //intersections

bool cmp(pb a, pb b){
	if(abs(a.fi - b.fi) < delta)return a.se < b.se;
	return a.fi < b.fi;
}

bool works(db r){
	for(int i = 1; i <= N; ++i)inter[i].fi = inter[i].se = -INF;
	for(int i = 1; i <= N; ++i) {
		//Can't reach any point on the highway
		if (r * r - tower[i].se * tower[i].se < 0)continue;
		inter[i].fi = tower[i].fi - sqrt(r*r - tower[i].se*tower[i].se);
		inter[i].se = tower[i].fi + sqrt(r*r + tower[i].se*tower[i].se);
		inter[i].fi = (inter[i].fi < 0)?0:inter[i].fi;
		inter[i].se = (inter[i].se > L)?L:inter[i].se;
	}
	//sort(inter+1,inter+N+1,cmp);
	db a = 0; db b = 0;
	for(int i = 1; i <= N; ++i){
		//Invalid intersections
		if(inter[i].fi > inter[i].se)continue;
		//Merge intervals
		if(inter[i].fi <= b)b = (inter[i].se > b)?inter[i].se:b;
		else return false;
	}

	if(abs(a-0) < delta && abs(b-L) < delta)return true;
	return false;
}

signed main(){
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	//freopen("../test.in","r",stdin);
	cin >> N >> L;
	for(int i = 1; i <= N; ++i)cin >> tower[i].fi >> tower[i].se;
	db low = 1; db high = 2e9;
	while(abs(high-low) > delta){
		db mid = (low+high)/2;
		if(works(mid))high = mid;
		else low = mid + delta;
	}
	cout << setprecision(6) << low  << '\n';
	return 0;
}

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