Submission #208839

#	Time	Username	Problem	Language	Result	Execution time	Memory
208839		baohiep	Split the sequence (APIO14_sequence)	C++14	0 / 100	60 ms	84336 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), id(_id) {}

  ll calc(ll x) {
    return a * (x - a) + 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();
    dq.emplace_back(sum[1], 0, 1);
    for (int j = 2; j <= n; ++j) {
      while (seen + 1 < (int)dq.size() && dq[seen].calc(sum[j]) <= dq[seen + 1].calc(sum[j]))
        ++seen;
      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() > seen + 1 && intersect(dq[(int)dq.size() - 2], dq.back()) >= intersect(dq.back(), newLine))
        dq.pop_back();
      dq.push_back(newLine);
    }
    for (int j = 2; j <= n; ++j) pre[j] = dp[j];
  }
  cout << dp[n] << "\n";
  int cur = n;
  while (k) {
    cur = trace[cur][k--];
    cout << cur << " ";
  }
  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