Problem p02764 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <algorithm>
#include <cmath>
#include <complex>
#include <functional>
#include <iostream>
#include <limits>
#include <sstream>
#include <string>

#include <queue>
#include <vector>

using namespace std;

int N, K;
vector<tuple<int, int, int>> info;

double nth_distance(double x, double y) {
  vector<double> dist(N);
  for (int i = 0; i < N; i++) {
    dist[i] = get<2>(info[i]) * hypot(x - get<0>(info[i]), y - get<1>(info[i]));
  }

  nth_element(dist.begin(), dist.begin() + K - 1, dist.end());
  return dist[K - 1];
}

double nth_distance_lb(double x, double y, double r) {
  vector<double> dist(N);
  for (int i = 0; i < N; i++) {
    dist[i] = get<2>(info[i]) * hypot(max(abs(x - get<0>(info[i])) - r, 0.0),
                                      max(abs(y - get<1>(info[i])) - r, 0.0));
  }

  nth_element(dist.begin(), dist.begin() + K - 1, dist.end());
  return dist[K - 1];
}

const double eps = 1e-6;

int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);

  cin >> N >> K;

  for (int i = 0; i < N; i++) {
    int x, y, c;
    cin >> x >> y >> c;

    info.emplace_back(x, y, c);
  }

  double result = 1e9;

  queue<tuple<double, double, double>> q;
  q.emplace(0, 0, 1000);
  while (!q.empty()) {
    double x, y, r;
    tie(x, y, r) = q.front();
    q.pop();

    double lb = nth_distance_lb(x, y, r);
    if (result - lb > eps) {
      result = min(result, nth_distance(x, y));

      for (double dx : {-0.5, 0.5}) {
        for (double dy : {-0.5, 0.5}) {
          q.emplace(x + dx * r, y + dy * r, r / 2.0);
        }
      }
    }
  }

  cout.setf(ios::fixed);
  cout.precision(15);
  cout << result;

  return 0;
}


Fixed submission:
#include <algorithm>
#include <cmath>
#include <complex>
#include <functional>
#include <iostream>
#include <limits>
#include <sstream>
#include <string>

#include <queue>
#include <vector>

using namespace std;

int N, K;
vector<tuple<int, int, int>> info;

double nth_distance(double x, double y) {
  vector<double> dist(N);
  for (int i = 0; i < N; i++) {
    dist[i] = get<2>(info[i]) * hypot(x - get<0>(info[i]), y - get<1>(info[i]));
  }

  nth_element(dist.begin(), dist.begin() + K - 1, dist.end());
  return dist[K - 1];
}

double nth_distance_lb(double x, double y, double r) {
  vector<double> dist(N);
  for (int i = 0; i < N; i++) {
    dist[i] = get<2>(info[i]) * hypot(max(abs(x - get<0>(info[i])) - r, 0.0),
                                      max(abs(y - get<1>(info[i])) - r, 0.0));
  }

  nth_element(dist.begin(), dist.begin() + K - 1, dist.end());
  return dist[K - 1];
}

const double eps = 1e-6;

int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);

  cin >> N >> K;

  for (int i = 0; i < N; i++) {
    int x, y, c;
    cin >> x >> y >> c;

    info.emplace_back(x, y, c);
  }

  double result = 1e9;

  queue<tuple<double, double, double>> q;
  q.emplace(0, 0, 1000);
  while (!q.empty()) {
    double x, y, r;
    tie(x, y, r) = q.front();
    q.pop();

    double lb = nth_distance_lb(x, y, r);
    if (result - lb > eps * max(1.0, lb)) {
      result = min(result, nth_distance(x, y));

      for (double dx : {-0.5, 0.5}) {
        for (double dy : {-0.5, 0.5}) {
          q.emplace(x + dx * r, y + dy * r, r / 2.0);
        }
      }
    }
  }

  cout.setf(ios::fixed);
  cout.precision(15);
  cout << result;

  return 0;
}