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Submission #372333

# Submission time Handle Problem Language Result Execution time Memory
372333 2021-02-27T16:54:58 Z toitoi Split the sequence (APIO14_sequence) C++14
100 / 100
 1259 ms 82900 KB 
#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

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
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 364 KB contestant found the optimal answer: 108 == 108
2 Correct 1 ms 364 KB contestant found the optimal answer: 999 == 999
3 Correct 1 ms 364 KB contestant found the optimal answer: 0 == 0
4 Correct 1 ms 364 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 1 ms 364 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 1 ms 364 KB contestant found the optimal answer: 1 == 1
7 Correct 1 ms 364 KB contestant found the optimal answer: 1 == 1
8 Correct 1 ms 364 KB contestant found the optimal answer: 1 == 1
9 Correct 1 ms 364 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 1 ms 364 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 1 ms 364 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 1 ms 364 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 1 ms 364 KB contestant found the optimal answer: 140072 == 140072
14 Correct 1 ms 364 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 1 ms 364 KB contestant found the optimal answer: 805 == 805
16 Correct 1 ms 364 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 1 ms 364 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 364 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 1 ms 364 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 1 ms 364 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 364 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 1 ms 364 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 1 ms 492 KB contestant found the optimal answer: 933702 == 933702
7 Correct 1 ms 384 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 1 ms 364 KB contestant found the optimal answer: 687136 == 687136
9 Correct 1 ms 364 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 1 ms 364 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 364 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 364 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 2 ms 492 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 364 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 2 ms 492 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 2 ms 492 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 2 ms 492 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 1 ms 364 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 1 ms 364 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 1 ms 364 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 364 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 364 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 11 ms 1132 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 364 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 10 ms 1132 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 9 ms 1004 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 12 ms 1132 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 10 ms 1152 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 3 ms 492 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 5 ms 620 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 748 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 3 ms 876 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 117 ms 8684 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 4 ms 876 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 78 ms 5484 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 94 ms 6124 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 105 ms 6636 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 74 ms 5484 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 86 ms 6124 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 112 ms 7788 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 25 ms 5076 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 25 ms 5204 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 1220 ms 82900 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 28 ms 5588 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 1259 ms 82088 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 881 ms 58708 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 1069 ms 62804 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 783 ms 52052 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 876 ms 59092 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 1118 ms 74708 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845