Submission #1166146

#	Time	Username	Problem	Language	Result	Execution time	Memory
1166146		fryingduc	Mobile (BOI12_mobile)	C++20	0 / 100	1099 ms	70852 KiB

mobile

#include "bits/stdc++.h"

using namespace std;

#ifdef duc_debug
#include "bits/debug.h"
#else
#define debug(...)
#endif

const int maxn = 1e6 + 6;
const double eps = 1e-3;
int n, L;
pair<int, int> a[maxn];
map<double, int> mp;

bool check(double mid) {
  mp.clear();
  for (int i = 1; i <= n; ++i) { 
    if (a[i].second > mid) continue;
    auto calc = [&](double a, double c) {
      return sqrtl(c * c - a * a);
    };
    double len = calc(a[i].second, mid);
    double l = (a[i].first - len);
    double r = (a[i].first + len);
    debug(mid, l, r);
    if (l > L || r < 0) continue;
    l = max(l, 0.0);
    r = min(r, L * 1.0);
    ++mp[l], --mp[r];
  }
  debug(mp);
  int dlt = 0;
  if (mp.begin()->first != 0) return 0;
  if (mp.rbegin()->first != L) return 0;
  for (auto i : mp) { 
    dlt += i.second;
    if (dlt == 0 and i.first < L) return 0;
  }
  return 1;
}

void solve() {
  cin >> n >> L;
  for (int i = 1; i <= n; ++i) {
    cin >> a[i].first >> a[i].second;
  }
  double l = 0, r = 1e18;
  for (int ite = 0; ite < 80; ++ite) {
    if (r - l > eps) {
      double mid = (l + r) / 2;
      if (check(mid)) {
        r = mid;
      } else {
        l = mid;
      }
    }
  }
  
  cout << fixed << setprecision(12) << r;
}

signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  
  solve();
  
  return 0;
}

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