Submission #966224

#	Time	Username	Problem	Language	Result	Execution time	Memory
966224		duckindog	Aliens (IOI16_aliens)	C++17	100 / 100	148 ms	9208 KiB

aliens

#include <bits/stdc++.h>
 
using namespace std;
 
#ifndef LOCAL
#include "aliens.h"
#endif
 
struct Line { 
  long long a, b;
  int idx;
  double x(const auto& rhs) { return 1.0 * (rhs.b - b) / (a - rhs.a); };
  long long cal(const auto& x) { return a * x + b; }
}; 

struct CHT {
  Line s[100'000 + 10];
  int st = 1, ed = 0;

  void add(Line nline) {
    while (ed - st + 1 >= 2 && s[ed - 1].x(s[ed]) > s[ed - 1].x(nline)) ed -= 1;
    s[++ed] = nline;
  }
 
  Line get(long long x) {
    while (ed - st + 1 >= 2 && s[st].cal(x) > s[st + 1].cal(x)) st += 1;
    return s[st];
  }
};

long long take_photos(int n, int m, int k, vector<int> row, vector<int> column) { 
  using pii = pair<int, int>;
  vector<pii> p(n);
 
  for (int i = 0; i < n; ++i) {
    if (row[i] > column[i]) swap(row[i], column[i]);
    p[i] = {row[i], column[i]};
  }
 
  auto dis = [&](pii a) { return abs(a.first - a.second) + 1; };
  
  { //sort_the_points
    sort(p.begin(), p.end(), [&](const auto& a, const auto& b) { 
      return make_pair(a.first, -dis(a)) < make_pair(b.first, -dis(b)); 
    });
    vector<bool> mk(n, true);
    pii point = {-1, -1};
    for (int i = 0; i < n; ++i) { 
      if (point.first <= p[i].first && p[i].second <= point.second) mk[i] = false;
      else point = p[i];
    }
    
    int cnt = 0;
    for (int i = 0; i < n; ++i) { 
      cnt += mk[i];
      if (mk[i]) p.push_back(p[i]);
    }
    p.erase(p.begin(), p.begin() + n);
    
    p.push_back({-1, -1});
    k = min(k, n = cnt);
    sort(p.begin(), p.end(), [&](const auto& a, const auto& b) { return a.first < b.first; });
  }
 
  auto cost = [&](const auto& C) { 
    vector<long long> f(n + 1, 1'000'000'000'000'000), g(n + 1);
    CHT hull;
    f[0] = 0;
    for (int i = 1; i <= n; ++i) { 
      long long pl = -p[i].first + 1;
      long long pre = max(0ll, p[i - 1].second + pl); pre *= pre;
      Line nline = {2 * pl, f[i - 1] + pl * pl - pre, i - 1};
      hull.add(nline);

      Line opt = hull.get(p[i].second);
      g[i] = g[opt.idx] + 1;
      f[i] = opt.cal(p[i].second) + 1ll * p[i].second * p[i].second + C;
    }
    
    return make_pair(f[n], g[n]);
  };

  long long l = 0, r = 1'000'000'000'000'000'000;
  long long answer = 1'000'000'000'000'000'000;
  while (l <= r) { 
    long long mid = l + r >> 1;
    
    auto [val, cnt] = cost(mid);
    if (cnt <= k) {
      r = mid - 1;
      answer = val - k * mid;
    } else l = mid + 1;
  }
 
  return answer;
}
 
#ifdef LOCAL
int32_t main() { 
  cin.tie(0)->sync_with_stdio(0);
 
  int n, m, k; cin >> n >> m >> k;
  vector<int> r(n), c(n);
  for (int i = 0; i < n; ++i) cin >> r[i] >> c[i];
 
  cout << take_photos(n, m, k, r, c) << "\n";
}
#endif

Compilation message (stderr)

aliens.cpp:12:18: warning: use of 'auto' in parameter declaration only available with '-fconcepts-ts'
   12 |   double x(const auto& rhs) { return 1.0 * (rhs.b - b) / (a - rhs.a); };
      |                  ^~~~
aliens.cpp:13:23: warning: use of 'auto' in parameter declaration only available with '-fconcepts-ts'
   13 |   long long cal(const auto& x) { return a * x + b; }
      |                       ^~~~
aliens.cpp: In function 'long long int take_photos(int, int, int, std::vector<int>, std::vector<int>)':
aliens.cpp:86:23: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
   86 |     long long mid = l + r >> 1;
      |                     ~~^~~

• Subtask 1: 4 / 4
• Subtask 2: 12 / 12
• Subtask 3: 9 / 9
• Subtask 4: 16 / 16
• Subtask 5: 19 / 19
• Subtask 6: 40 / 40