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Submission #971192

# Submission time Handle Problem Language Result Execution time Memory
971192 2024-04-28T06:18:15 Z kilkuwu Split the sequence (APIO14_sequence) C++17
71 / 100
 2000 ms 91476 KB 
#include <bits/stdc++.h>

#define nl '\n'

struct Line {
  mutable int64_t k, m, p;
  int id;

  bool operator<(const Line& o) const { return k < o.k; }
  bool operator<(int64_t x) const { return p < x; }
};

struct LineContainer : std::multiset<Line, std::less<>> {
  // (for doubles, use inf = 1/.0, div(a,b) = a/b)
  static const int64_t inf = LLONG_MAX;
  int64_t div(int64_t a, int64_t b) {  // floored division
    return a / b - ((a ^ b) < 0 && a % b);
  }

  bool isect(iterator x, iterator y) {
    if (y == end()) return x->p = inf, 0;
    if (x->k == y->k)
      x->p = x->m > y->m ? inf : -inf;
    else
      x->p = div(y->m - x->m, x->k - y->k);
    return x->p >= y->p;
  }
  void add(int64_t k, int64_t m, int id) {
    auto z = insert({k, m, 0, id}), y = z++, x = y;
    while (isect(y, z)) z = erase(z);
    if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
    while ((y = x) != begin() && (--x)->p >= y->p) isect(x, erase(y));
  }
  std::pair<int64_t, int> query(int64_t x) {
    assert(!empty());
    auto l = *lower_bound(x);
    return {l.k * x + l.m, l.id};
  }
};

const int mxN = 1e5 + 5, mxK = 205;
int way[mxN][mxK];
int N, K;

signed main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);

  std::cin >> N >> K;

  std::vector<int> A(N + 1);
  std::vector<int64_t> pref(N + 1);
  for (int i = 1; i <= N; i++) {
    std::cin >> A[i];
    pref[i] = pref[i - 1] + A[i];
  }
  std::vector<int64_t> dp(N + 1, -1e18);
  std::vector<int64_t> ndp(N + 1, -1e18);
  dp[0] = 0;

  for (int j = 1; j <= K + 1; j++) {
    LineContainer lines;

    lines.add(pref[0], dp[0] - pref[0] * pref[0], 0);

    ndp[0] = -1e18;
    for (int i = 1; i <= N; i++) {

      auto line = lines.query(pref[i]);
      ndp[i] = line.first;
      way[i][j] = line.second;
      lines.add(pref[i], dp[i] - pref[i] * pref[i], i);
    }

    std::swap(dp, ndp);
  }

  std::cout << dp[N] << nl;
  std::vector<int> ans;

  int x = N;
  int y = K + 1;
  while (x > 0 && y > 1) {
    ans.push_back(way[x][y]);
    x = way[x][y];
    y--;
  }

  for (int i : ans) std::cout << i << " ";
  std::cout << nl;
}

/*
7 3
4 1 3 4 0 2 3
*/

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 600 KB contestant found the optimal answer: 108 == 108
2 Correct 0 ms 348 KB contestant found the optimal answer: 999 == 999
3 Correct 0 ms 348 KB contestant found the optimal answer: 0 == 0
4 Correct 0 ms 348 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 0 ms 348 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 0 ms 348 KB contestant found the optimal answer: 1 == 1
7 Correct 1 ms 536 KB contestant found the optimal answer: 1 == 1
8 Correct 1 ms 348 KB contestant found the optimal answer: 1 == 1
9 Correct 1 ms 348 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 0 ms 348 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 0 ms 348 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 0 ms 348 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 0 ms 348 KB contestant found the optimal answer: 140072 == 140072
14 Correct 0 ms 348 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 0 ms 348 KB contestant found the optimal answer: 805 == 805
16 Correct 0 ms 348 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 1 ms 348 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 0 ms 416 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 1 ms 348 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 0 ms 348 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 1 ms 344 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 1 ms 348 KB contestant found the optimal answer: 933702 == 933702
7 Correct 0 ms 348 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 0 ms 348 KB contestant found the optimal answer: 687136 == 687136
9 Correct 0 ms 348 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 0 ms 348 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 604 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 0 ms 604 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 4 ms 604 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 0 ms 616 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 3 ms 644 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 3 ms 604 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 4 ms 856 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 1 ms 604 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 1 ms 604 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 2 ms 604 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2652 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 2652 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 20 ms 2788 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 2652 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 24 ms 2776 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 18 ms 2652 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 21 ms 2652 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 20 ms 2652 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 5 ms 2652 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 9 ms 2652 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 7 ms 9564 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 7 ms 9564 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 304 ms 9900 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 7 ms 9816 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 166 ms 9564 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 188 ms 9956 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 211 ms 9816 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 173 ms 9924 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 198 ms 9820 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 249 ms 9816 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 96 ms 89692 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 84 ms 89944 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Execution timed out 2031 ms 91476 KB Time limit exceeded
4 Halted 0 ms 0 KB -