Submission #971200

#	Time	Username	Problem	Language	Result	Execution time	Memory
971200		kilkuwu	Split the sequence (APIO14_sequence)	C++17	100 / 100	827 ms	84824 KiB

sequence

#include <bits/stdc++.h>

#define nl '\n'

struct Line {
  int64_t a, b;
  int id;

  double intersect(const Line& l) const {
    auto nume = b - l.b;
    auto deno = l.a - a;
    return (double) nume / deno;
  }

  int64_t eval(int64_t x) const {
    return a * x + b;
  }
};

struct DoubleEndedLineContainer : std::deque<Line> {
  void add(const Line& l) {
    if (empty()) {
      push_back(l);
      return;
    }

    while (size() >= 2 && at(size() - 1).intersect(at(size() - 2)) >= at(size() - 2).intersect(l)) {
      pop_back();
    }

    if (back().a == l.a) {
      if (l.b > back().b) {
        back() = l;
      }
    } else {
      push_back(l);
    }
  }

  std::pair<int64_t, int> query(int64_t x) {
    while (size() >= 2 && at(0).intersect(at(1)) <= x) {
      pop_front();
    }
    return {front().eval(x), front().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++) {
    DoubleEndedLineContainer 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: 29 / 29