Submission #989252

#	Time	Username	Problem	Language	Result	Execution time	Memory
989252		OAleksa	Split the sequence (APIO14_sequence)	C++14	0 / 100	46 ms	131072 KiB

sequence

#include <bits/stdc++.h>
#define f first
#define s second
#define int long long
using namespace std;
const int N = 1e5 + 69;
const int K = 220;
int n, a[N], dp[N][K], p[N], k;
struct line {
  int n, k;
  int val(int x) {
    return k * x + n;
  }
};
deque<line> dq[K];
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int tt = 1;
  //cin >> tt;
  while (tt--) {
    cin >> n >> k;
    for (int i = 1;i <= n;i++)
      cin >> a[i];
    for (int i = 1;i <= n;i++)
      p[i] = p[i - 1] + a[i];
    auto Get = [&](int l, int r) {
      return p[r] - p[l - 1];
    };
    for (int i = 1;i <= n;i++) {
      for (int j = 1;j <= k;j++)
        dp[i][j] = -1e9;
    }
    dq[0].push_back({0, 0});
    for (int i = 1;i < n;i++) {
      for (int j = 1;j <= min(i, k);j++) {  
        int x = p[n] - p[i], m = dq[j - 1].size();
        while (m > 1 && dq[j - 1][m - 1].val(x) < dq[j - 1][m - 2].val(x)) {
          dq[j - 1].pop_back();
          --m;
        }
        dp[i][j] = dq[j - 1][m - 1].val(x) + p[i] * (p[n] - p[i]);
        line t = {dp[i][j], -p[i]};
        while (m > 1 && (dq[j][0].k - t.k) * (dq[j][1].n - dq[j][0].n) > (t.n - dq[j][0].n) * (dq[j][0].k - dq[j][1].k)) 
          dq[j].pop_front();
        dq[j].push_front(t);
      }
    }
    int ans = 0;
    for (int i = 1;i < n;i++)
      ans = max(ans, dp[i][k]);
    vector<int> res;
    int t = -1;
    for (int i = 1;i < n;i++) {
      if (ans == dp[i][k])
        t = i;
    }
    assert(t != -1);
    res.push_back(t);
    for (int j = t - 1;j >= 1 && k > 0;j--) {
      int dd = dp[j][k - 1] + Get(j + 1, t) * Get(t + 1, n);
      if (dd == dp[t][k]) {
        res.push_back(j);
        --k;
        t = j;
      }
    }
    cout << ans << '\n';
    reverse(res.begin(), res.end());
    for (auto j : res) 
      cout << j << ' ';
  }
  return 0; 
}

• Subtask 1: 0 / 11
• Subtask 2: 0 / 11
• Subtask 3: 0 / 11
• Subtask 4: 0 / 17
• Subtask 5: 0 / 21
• Subtask 6: 0 / 29