Submission #259212

#	Time	Username	Problem	Language	Result	Execution time	Memory
259212		EntityIT	Split the sequence (APIO14_sequence)	C++14	100 / 100	995 ms	87472 KiB

sequence

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

#define ALL(x) (x).begin(), (x).end()
#define SZ(x) static_cast<int>((x).size())

template<class T, size_t D>
struct vec : vector<vec<T, D - 1>> {
  template<class... Args>
  vec(size_t n = 0, Args... args)
      : vector<vec<T, D - 1>>(n, vec<T, D - 1>(args...)) {}
};
template<class T>
struct vec<T, 1> : vector<T> {
  template<class... Args>
  vec(Args... args)
      : vector<T>(args...) {}
};

template<class T>
inline bool Minimize(T& a, const T& b) { return a > b ? a = b, true : false; }
template<class T>
inline bool Maximize(T& a, const T& b) { return a < b ? a = b, true : false; }
inline int Next(int i, int n) { return i == n - 1 ? 0 : i + 1; }
inline int Prev(int i, int n) { return !i ? n - 1 : i - 1; }

mt19937 rng(static_cast<uint32_t>(chrono::steady_clock::now().time_since_epoch().count()));

struct Line {
  int a;
  int64_t b;
  int label;
  Line(int t_a = 0, int64_t t_b = 0, int t_label = 0)
      : a(t_a),
        b(t_b),
        label(t_label) {}
  int64_t y(int x) { return static_cast<int64_t>(a) * x + b; }
};

struct ConvexHullTrick {
  vector<Line> lines;
  int index_line;
  ConvexHullTrick()
      : lines(),
        index_line(-1) {}

  bool Bad(Line line_1, Line line_2, Line line_3) {
    return static_cast<double>(line_1.b - line_3.b) / (line_3.a - line_1.a) <= static_cast<double>(line_1.b - line_2.b) / (line_2.a - line_1.a);
  }

  void AddLine(Line line) {
    if (SZ(lines) && line.a == lines.back().a) {
      if (line.b <= lines.back().b) {
        return;
      }
      lines.pop_back();
      Minimize(index_line, SZ(lines) - 1);
    }

    while (SZ(lines) > 1 && Bad(lines.rbegin()[1], lines.back(), line)) {
      lines.pop_back();
      Minimize(index_line, SZ(lines) - 1);
    }
    lines.emplace_back(line);
  }

  int Get(int x) {
    for (; index_line + 1 < SZ(lines) && (!~index_line || lines[index_line].y(x) < lines[index_line + 1].y(x)); ++index_line);
    return index_line;
  }
};

int main() {
  ios_base::sync_with_stdio(0); cin.tie(0);

  int n, n_cuts; cin >> n >> n_cuts;
  vec<int, 1> prefix_sums(n + 1);
  for (int i = 0; i < n; ++i) {
    int a; cin >> a;
    prefix_sums[i + 1] = prefix_sums[i] + a;
  }

  vec<int64_t, 1> f(n + 1), next_f(n + 1);
  vec<int, 2> trace(n_cuts + 1, n + 1);
  for (int i = 1; i <= n_cuts; ++i) {
    ConvexHullTrick cht;
    for (int j = i + 1; j <= n; ++j) {
      cht.AddLine(Line(prefix_sums[j - 1], f[j - 1] - static_cast<int64_t>(prefix_sums[j - 1]) * prefix_sums[j - 1], j - 1));
      int index_line = cht.Get(prefix_sums[j]);
      assert(~index_line);
      next_f[j] = cht.lines[index_line].y(prefix_sums[j]);
      trace[i][j] = cht.lines[index_line].label;
    }
    f.swap(next_f);
  }

  cout << f[n] << '\n';
  vec<int, 1> positions;
  for (int i = n_cuts, j = n; i; --i) {
    positions.emplace_back((j = trace[i][j]));
  }
  reverse(ALL(positions));
  for (auto& position : positions) {
    cout << position << ' ';
  }
  cout << '\n';

  return 0;
}

• Subtask 1: 11 / 11
• Subtask 2: 11 / 11
• Subtask 3: 11 / 11
• Subtask 4: 17 / 17
• Subtask 5: 21 / 21
• Subtask 6: 29 / 29