Submission #172276

#	Time	Username	Problem	Language	Result	Execution time	Memory
172276		golikovnik	Aliens (IOI16_aliens)	C++14	0 / 100	2 ms	380 KiB

aliens

#include <bits/stdc++.h>

using namespace std;

using i64 = long long;
using real_t = long double;

template <typename T>
struct line {
  T k, b;

  [[nodiscard]] T apply(T x) const {
    return k * x + b;
  }
};

template <typename T>
real_t inter(line<T> const& a, line<T> const& b) {
  return static_cast<real_t>(a.b - b.b) / (b.k - a.k);
}

template <typename T>
struct hull {
  struct item {
    line<T> l;
    real_t from;
    real_t to;
    int cnt;

    item(line<T> l_, real_t from_, real_t to_, int cnt_) : l(l_), from(from_)
    , to(to_), cnt(cnt_) {}
  };
  vector<item> lines;
  real_t const inf = 1e20;
  int ptr = 0;

  void add_line(line<T> const& l, int cnt) {
    while ((int) lines.size() >= 2 &&
           inter(l, lines.back().l) <=
           inter(lines.back().l, lines[lines.size() - 2].l)) {
      lines.pop_back();
    }
    if (lines.empty()) {
      lines.emplace_back(l, -inf, inf, cnt);
    } else {
      auto x = inter(l, lines.back().l);
      lines.back().to = x;
      lines.emplace_back(l, x, inf, cnt);
    }
  }

  pair<T, int> get(T x) {
    ptr = min(ptr, (int) lines.size() - 1);
    while (x > lines[ptr].to) {
      ++ptr;
    }
    return {lines[ptr].l.apply(x), lines[ptr].cnt};
  }
};

i64 take_photos(int n, int, int mx, vector<int> r, vector<int> c) {
  struct cell {
    int r, c;

    cell(int r_, int c_) : r(r_), c(c_) {}
  };
  vector<cell> a;
  {
    for (int i = 0; i < n; ++i) {
      if (r[i] < c[i]) {
        swap(r[i], c[i]);
      }
    }
    vector<int> p(n);
    iota(p.begin(), p.end(), 0);
    sort(p.begin(), p.end(), [&](int i, int j) {
      if (r[i] != r[j]) {
        return r[i] < r[j];
      }
      return c[i] > c[j];
    });
    for (int i = 0; i < n; ++i) {
      while (!a.empty() && a.back().c >= c[p[i]]) {
        a.pop_back();
      }
      a.emplace_back(r[p[i]], c[p[i]]);
    }
  }
  n = (int) a.size();
  auto calc = [&](real_t lam) -> pair<real_t, int> {
    auto sqr = [](auto x) {
      return x * x;
    };
    hull<real_t> cht;
    real_t cur = 0;
    int cnt = 0;
    for (int i = 0; i < n; ++i) {
      auto ci = !i ? 0 : sqr(
              max<i64>(0, a[i - 1].r - a[i].c + 1));
      cht.add_line({(long double) (-2 * a[i].c), sqr(a[i].c) + cur - ci},
              cnt);
      auto res = cht.get(a[i].r + 1);
      cnt = res.second + 1;
      cur = sqr(a[i].r + 1) + res.first + lam;
    }
    return {cur, cnt};
  };
  real_t left = -1e18;
  real_t right = 1e18;
  for (int it = 0; it < 200; ++it) {
    auto middle = (left + right) / 2;
    if (calc(middle).second > mx) {
      left = middle;
    } else {
      right = middle;
    }
  }
  auto lam = (left + right) / 2;
  auto res = calc(lam);
  return (i64) roundl(res.first - res.second * lam);
}

//int main() {
//  vector<int> r{0, 4, 4, 4, 4};
//  vector<int> c{3, 4, 6, 5, 6};
//  int n = (int) r.size();
//  int m = -1;
//  int k = n;
//  cout << take_photos(n, m, k, r, c) << '\n';
//}

• Subtask 1: 0 / 4
• Subtask 2: 0 / 12
• Subtask 3: 0 / 9
• Subtask 4: 0 / 16
• Subtask 5: 0 / 19
• Subtask 6: 0 / 40