Submission #838510

#	Time	Username	Problem	Language	Result	Execution time	Memory
838510		tch1cherin	Split the sequence (APIO14_sequence)	C++17	100 / 100	1309 ms	85352 KiB

sequence

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

const int64_t INF = 1ll << 60;
const int MAX_N = 100005, MAX_K = 205;
vector<int64_t> dp, new_dp;
vector<int64_t> pref, pref_sq;
int path[MAX_N][MAX_K];

int64_t get_weight(int l, int r) {
  int64_t sum = pref[r] - pref[l];
  int64_t sum_sq = pref_sq[r] - pref_sq[l];
  return sum * sum - sum_sq;
}

void divide(int ki, int l, int r, int optl, int optr) {
  if (l >= r) {
    return;
  }
  int mid = (l + r) / 2;
  int opt = optl;
  for (int i = optl; i < min(mid, optr); i++) {
    int64_t value = dp[i] + get_weight(i, mid);
    if (new_dp[mid] > value) {
      new_dp[mid] = value;
      opt = i;
    }
  }
  path[mid][ki] = opt;
  divide(ki, l, mid, optl, opt + 1);
  divide(ki, mid + 1, r, opt, optr);
}

int main() {
  cin.tie(nullptr)->sync_with_stdio(false);
  int N, K;
  cin >> N >> K;
  vector<int> A(N);
  for (int &v : A) {
    cin >> v;
  }
  K++;
  pref = pref_sq = vector<int64_t>(N + 1);
  for (int i = 0; i < N; i++) {
    pref[i + 1] = pref[i] + A[i];
    pref_sq[i + 1] = pref_sq[i] + A[i] * A[i];
  }
  memset(path, -1, sizeof path);
  dp = vector<int64_t>(N + 1, INF);
  dp[0] = 0;
  for (int i = 0; i < K; i++) {
    new_dp = vector<int64_t>(N + 1, INF);
    divide(i + 1, 0, N + 1, 0, N + 1);
    dp = new_dp;
  }
  cout << (get_weight(0, N) - dp[N]) / 2 << "\n";
  int pos = N, ki = K;
  vector<int> ans;
  while (pos > 0) {
    ans.push_back(pos = path[pos][ki--]);
  }
  ans.pop_back();
  reverse(ans.begin(), ans.end());
  for (int i = 0; i < K - 1; i++) {
    cout << ans[i] << " \n"[i + 1 == K - 1];
  }
}

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