Submission #971192

#	Time	Username	Problem	Language	Result	Execution time	Memory
971192		kilkuwu	Split the sequence (APIO14_sequence)	C++17	71 / 100	2031 ms	91476 KiB

sequence

#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 / 11
• Subtask 2: 11 / 11
• Subtask 3: 11 / 11
• Subtask 4: 17 / 17
• Subtask 5: 21 / 21
• Subtask 6: 0 / 29