Submission #1090870

#	Time	Username	Problem	Language	Result	Execution time	Memory
1090870		vjudge1	Safety (NOI18_safety)	C++17	100 / 100	73 ms	3792 KiB

safety

#include <functional>
#include <iostream>
#include <queue>
#include <vector>

int main() {
  std::cin.tie(NULL)->sync_with_stdio(false);
  
  int n;
  long long h;
  std::cin >> n >> h;

  // dp[0][x]: y = |x - a[0]|
  // dp[i+1][x] = min(dp[i][y], x - h <= y <= x + h) + |x - a[i+1]|
  // inductively: dp[i] is a convex linear piecewise lines
  // min x-h <= y <= x+h --> shift minimum range (xL, xR) -> (xL - h, xR + h)

  int m = 0;
  long long shift = -h, c = 0;
  std::priority_queue<long long> pq_l;
  std::priority_queue<long long, std::vector<long long>, std::greater<long long>> pq_r;
  for (int i = 0; i < n; i++) {
    long long x;
    std::cin >> x;

    // shift by h
    shift += h;
    c -= h * m;

    // append to line
    pq_l.push(x + shift);
    pq_r.push(x - shift);
    
    // normalize
    while (true) {
      long long x_l = pq_l.top();
      long long x_r = pq_r.top();
      if (x_l - shift <= x_r + shift) {
        break;
      }

      pq_l.pop();
      pq_r.pop();
      x_l -= shift;
      x_r += shift;
      pq_l.push(x_r + shift);
      pq_r.push(x_l - shift);
    }

    // m*x + c + (x - x0) = (m+1)*x + (c - x0)
    m++;
    c -= x;
  }

  while (!pq_r.empty()) {
    // pop largest
    long long x = pq_r.top();
    pq_r.pop();

    // apply shift
    x += shift;

    // m*x + c = (m-1)*x + (x + c)
    m--;
    c += x;
  }

  std::cout << c << std::endl;

  return 0;
}

• Subtask 1: 3 / 3
• Subtask 2: 4 / 4
• Subtask 3: 9 / 9
• Subtask 4: 5 / 5
• Subtask 5: 6 / 6
• Subtask 6: 11 / 11
• Subtask 7: 11 / 11
• Subtask 8: 22 / 22
• Subtask 9: 29 / 29