Submission #372333

#	Time	Username	Problem	Language	Result	Execution time	Memory
372333		toitoi	Split the sequence (APIO14_sequence)	C++14	100 / 100	1259 ms	82900 KiB

sequence

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

class SeqGame {
  typedef pair<int, int64_t> Line;

private:
  vector<int64_t> sum;
  vector<int64_t> points;
  vector<vector<int>> log;
  deque<Line> convhull;

  void split();
  void update_convhull(Line line);
  Line query_convhull(int64_t x);

  int64_t intersec(Line line1, Line line2);

public:
  SeqGame(vector<int> seq);
  pair<int64_t, vector<int>> get_max_point(int k);
};

SeqGame::SeqGame(vector<int> seq) {
  int n = seq.size();

  sum.resize(n);
  sum[0] = seq[0];
  for (int i = 1; i < n; i++) {
    sum[i] = seq[i] + sum[i - 1];
  }
}

pair<int64_t, vector<int>> SeqGame::get_max_point(int k) {
  for (int i = 0; i < k; i++) {
    split();
  }

  int64_t max_point = -1;
  int max_point_idx = 0;
  vector<int> max_point_log;

  for (int i = k - 1; i < points.size() - 1; i++) {
    if (max_point < points[i]) {
      max_point = points[i];
      max_point_idx = i;
    }
  }

  max_point_log.push_back(max_point_idx);
  for (int k = log.size() - 1; k >= 0; k--) {
    max_point_idx = log[k][max_point_idx];
    max_point_log.push_back(max_point_idx);
  }

  reverse(max_point_log.begin(), max_point_log.end());

  return {max_point, max_point_log};
}

void SeqGame::split() {
  int n = sum.size();
  int k = log.size();

  if (points.empty()) {
    points.resize(n);
    for (int i = 0; i < n - 1; i++) {
      points[i] = sum[i] * (sum[n - 1] - sum[i]);
    }
    return;
  }

  vector<int64_t> new_points(n);
  vector<int> new_log(n);

  for (int i = k + 1; i < n - 1; i++) {
    update_convhull({i - 1, points[i - 1] - sum[n - 1] * sum[i - 1]});
    auto res = query_convhull(sum[i]);
    int j = res.first;

    new_points[i] = res.second + (sum[j] + sum[n - 1] - sum[i]) * sum[i];
    new_log[i] = j;
  }

  points = new_points;
  log.push_back(new_log);

  convhull.clear();
}

pair<int, int64_t> SeqGame::query_convhull(int64_t x) {
  while (convhull.size() >= 2) {
    if (intersec(convhull[0], convhull[1]) <= x) {
      convhull.pop_front();
    } else {
      break;
    }
  }
  return convhull.front();
}

void SeqGame::update_convhull(Line line) {
  if (convhull.empty()) {
    convhull.push_back(line);
    return;
  }

  while (convhull.size() >= 2) {
    int n = convhull.size();
    if (intersec(convhull[n - 2], convhull[n - 1]) >=
        intersec(convhull[n - 1], line)) {
      convhull.pop_back();
    } else {
      break;
    }
  }

  if (sum[convhull.back().first] != sum[line.first]) {
    convhull.push_back(line);
  } else {
    if (convhull.back().second < line.second) {
      convhull.pop_back();
      convhull.push_back(line);
    }
  }
}

int64_t SeqGame::intersec(Line line1, Line line2) {
  int64_t a = sum[line1.first] - sum[line2.first];
  int64_t b = line2.second - line1.second;

  if (a == 0) {
    return (1LL << 62);
  } else if (b % a == 0) {
    return b / a;
  } else {
    return b / a + 1;
  }
}

int main() {
  int n, k;
  scanf("%d %d", &n, &k);

  vector<int> seq(n);
  for (int i = 0; i < n; i++) {
    scanf("%d", &seq[i]);
  }

  auto game = SeqGame(seq);
  auto ans = game.get_max_point(k);

  printf("%lld\n", ans.first);
  for (int i = 0; i < ans.second.size(); i++) {
    printf("%d ", ans.second[i] + 1);
  }

  return 0;
}

Compilation message (stderr)

sequence.cpp: In member function 'std::pair<long int, std::vector<int> > SeqGame::get_max_point(int)':
sequence.cpp:43:25: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   43 |   for (int i = k - 1; i < points.size() - 1; i++) {
      |                       ~~^~~~~~~~~~~~~~~~~~~
sequence.cpp: In function 'int main()':
sequence.cpp:153:14: warning: format '%lld' expects argument of type 'long long int', but argument 2 has type 'long int' [-Wformat=]
  153 |   printf("%lld\n", ans.first);
      |           ~~~^     ~~~~~~~~~
      |              |         |
      |              |         long int
      |              long long int
      |           %ld
sequence.cpp:154:21: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  154 |   for (int i = 0; i < ans.second.size(); i++) {
      |                   ~~^~~~~~~~~~~~~~~~~~~
sequence.cpp:143:8: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  143 |   scanf("%d %d", &n, &k);
      |   ~~~~~^~~~~~~~~~~~~~~~~
sequence.cpp:147:10: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  147 |     scanf("%d", &seq[i]);
      |     ~~~~~^~~~~~~~~~~~~~~

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