Submission #259095

#	Time	Username	Problem	Language	Result	Execution time	Memory
259095		KoD	Split the sequence (APIO14_sequence)	C++17	71 / 100	110 ms	131076 KiB

sequence

#line 1 "main.cpp"

/**
 * @title Template
 */

#include <iostream>
#include <algorithm>
#include <utility>
#include <numeric>
#include <vector>
#include <array>
#include <cassert>
#include <deque>

#line 2 "/Users/kodamankod/Desktop/Programming/Library/other/chmin_chmax.cpp"

template <class T, class U>
constexpr bool chmin(T &lhs, const U &rhs) {
  if (lhs > rhs) { 
    lhs = rhs; 
    return true; 
  }
  return false;
}

template <class T, class U>
constexpr bool chmax(T &lhs, const U &rhs) {
  if (lhs < rhs) { 
    lhs = rhs; 
    return true; 
  }
  return false;
}

/**
 * @title Chmin/Chmax
 */
#line 2 "/Users/kodamankod/Desktop/Programming/Library/other/range.cpp"

#line 4 "/Users/kodamankod/Desktop/Programming/Library/other/range.cpp"

class range {
public:
  class iterator {
  private:
    int64_t M_position;

  public:
    constexpr iterator(int64_t position) noexcept: M_position(position) { }
    constexpr void operator ++ () noexcept { ++M_position; }
    constexpr bool operator != (iterator other) const noexcept { return M_position != other.M_position; }
    constexpr int64_t operator * () const noexcept { return M_position; }

  };

  class reverse_iterator {
  private:
    int64_t M_position;
  
  public:
    constexpr reverse_iterator(int64_t position) noexcept: M_position(position) { }
    constexpr void operator ++ () noexcept { --M_position; }
    constexpr bool operator != (reverse_iterator other) const noexcept { return M_position != other.M_position; }
    constexpr int64_t operator * () const noexcept { return M_position; }

  };
  
private:
  const iterator M_first, M_last;

public:
  constexpr range(int64_t first, int64_t last) noexcept: M_first(first), M_last(std::max(first, last)) { }
  constexpr iterator begin() const noexcept { return M_first; }
  constexpr iterator end() const noexcept { return M_last; }
  constexpr reverse_iterator rbegin() const noexcept { return reverse_iterator(*M_last - 1); } 
  constexpr reverse_iterator rend() const noexcept { return reverse_iterator(*M_first - 1); } 

};

/**
 * @title Range
 */
#line 2 "/Users/kodamankod/Desktop/Programming/Library/other/rev.cpp"

#include <type_traits>
#include <iterator>
#line 6 "/Users/kodamankod/Desktop/Programming/Library/other/rev.cpp"

template <class T>
class rev_impl {
public:
  using iterator = typename std::decay<T>::type::reverse_iterator;

private:
  const iterator M_begin;
  const iterator M_end;

public:
  constexpr rev_impl(T &&cont) noexcept: M_begin(std::rbegin(cont)), M_end(std::rend(cont)) { }
  constexpr iterator begin() const noexcept { return M_begin; }
  constexpr iterator end() const noexcept { return M_end; }

};

template <class T>
constexpr decltype(auto) rev(T &&cont) {
  return rev_impl<T>(std::forward<T>(cont));
}

/**
 * @title Reverser
 */
#line 18 "main.cpp"

using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;

constexpr i32 inf32 = (i32(1) << 30) - 1;
constexpr i64 inf64 = (i64(1) << 62) - 1;

struct line_t {
  i64 a, b;
  i64 val(i64 x) const {
    return a * x + b;
  }
};

struct convex_hull_trick {
  std::deque<line_t> lines;
  bool need(line_t a, line_t b, line_t c) const {
    i64 x1 = (c.b - b.b) * (a.a - b.a);
    i64 x2 = (b.b - a.b) * (b.a - c.a);
    return x1 < x2;
  }
  void add_line(line_t l) {
    i32 size = lines.size();
    while (size >= 2 && !need(l, lines[size - 1], lines[size - 2])) {
      lines.pop_back();
      --size;
    }
    lines.push_back(l);
  }
  i64 min(i64 x) {
    i32 size = lines.size();
    if (size == 0) {
      return inf64;
    }
    while (size >= 2 && lines[0].val(x) > lines[1].val(x)) {
      lines.pop_front();
      --size;
    }
    return lines[0].val(x);
  }
};

int main() {
  i32 N, K;
  std::cin >> N >> K;
  ++K;
  std::vector<i32> A(N);
  for (auto &x: A) {
    std::cin >> x;
  }
  std::vector<i64> sum(N + 1);
  for (auto i: range(0, N)) {
    sum[i + 1] = sum[i] + A[i];
  }
  std::vector<std::vector<i64>> dp(N + 1, std::vector<i64>(K + 1, inf64));
  dp[0][0] = 0;
  for (auto k: range(1, K + 1)) {
    convex_hull_trick cht;
    for (auto i: range(1, N + 1)) {
      if (dp[i - 1][k - 1] != inf64) {
        cht.add_line(line_t{ -2 * sum[i - 1], sum[i - 1] * sum[i - 1] + dp[i - 1][k - 1] });
      }
      chmin(dp[i][k], cht.min(sum[i]) + sum[i] * sum[i]);
    }
  }
  std::cout << ((sum[N] - sum[0]) * (sum[N] - sum[0]) - dp[N][K]) / 2 << '\n';
  std::vector<i32> step;
  {
    i32 r = N, k = K;
    while (r > 0) {
      for (auto l: rev(range(0, r))) {
        if (dp[r][k] == dp[l][k - 1] + (sum[r] - sum[l]) * (sum[r] - sum[l])) {
          step.push_back(l);
          r = l;
          --k;
          break;
        }
      }
    }
  }
  step.pop_back();
  for (auto i: range(0, step.size())) {
    std::cout << step[i] << (i + 1 == step.size() ? '\n' : ' ');
  }
  return 0;
}

Compilation message (stderr)

main.cpp: In function 'int main()':
main.cpp:102:36: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]

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