Submission #208850

#	Time	Username	Problem	Language	Result	Execution time	Memory
208850		baohiep	Split the sequence (APIO14_sequence)	C++14	100 / 100	688 ms	85860 KiB

sequence

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int N = 1e5 + 5, K = 205;

struct Line {
  ll a, b;
  int id;
  Line(ll _a, ll _b, int _id): a(_a), b(_b - _a * _a), id(_id) {}

  ll calc(ll x) {
    return a * x + b;
  }
};

int n, k, a[N], trace[N][K];
ll sum[N], pre[N], dp[N];
vector<Line> dq;

double intersect(const Line &p, const Line &q) {
  return (double)(p.b - q.b) / (double)(q.a - p.a);
}

int main() {
  ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
  cin >> n >> k;
  for (int i = 1; i <= n; ++i) {
    cin >> a[i];
    sum[i] = sum[i - 1] + a[i];
  }

  for (int i = 1; i <= k; ++i) {
    int seen = 0;
    dq.clear();
    fill(dp + 1, dp + 1 + n, 0);
    for (int j = 1; j <= n; ++j) {
      while (seen + 1 < (int)dq.size() && dq[seen].calc(sum[j]) <= dq[seen + 1].calc(sum[j]))
        ++seen;
      if (seen < (int)dq.size()) {
        dp[j] = dq[seen].calc(sum[j]);
        trace[j][i] = dq[seen].id;
      }
      Line newLine = Line(sum[j], pre[j], j);
      while ((int)dq.size() > 1 && intersect(dq[(int)dq.size() - 2], newLine) <= intersect(dq[(int)dq.size() - 2], dq.back()))
        dq.pop_back();
      dq.push_back(newLine);
    }
    for (int j = 1; j <= n; ++j) pre[j] = dp[j];
  }

  int cur = n;
  vector<int> pos;
  while (k) {
    cur = trace[cur][k--];
    pos.emplace_back(cur);
  }
  reverse(pos.begin(), pos.end());

  cout << dp[n] << "\n";
  for (int x: pos) cout << x << " ";
  return 0;
}

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