Submission #1136619

#	Time	Username	Problem	Language	Result	Execution time	Memory
1136619		concua	Mobile (BOI12_mobile)	C++20	0 / 100	430 ms	31760 KiB

mobile

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

const int N = 1e6 + 1;
pair<long double, long double> p[N];

long long n, L;

bool check(long double x){
    long double pre = 0.0; 
    for (int i = 1; i <= n; i++){
        if (x * x < (long double)p[i].second * p[i].second){
            return false; 
        }
        
        long double po = p[i].second * p[i].second;
        
        long double delta = sqrt(x * x - po);
        long double left = p[i].first - delta;
        long double right = p[i].first + delta;

        if (pre >= left){
            pre = max(pre, right);
        }
    }
    return pre >= L;
}

int main(){
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    
    cin >> n >> L;
    for (int i = 1; i <= n; i++){
        cin >> p[i].first >> p[i].second;
    }

    long double l = 0, r = 2e9;

    while (r - l > 1e-4) { 
        long double mid = (r + l) / 2.0;
        if (check(mid)){
            r = mid;
        } 
        else{
            l = mid;
        }
    }

    cout << fixed << setprecision(6) << r << "\n"; 

    return 0;
}

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