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Submission #1090870

# Submission time Handle Problem Language Result Execution time Memory
1090870 2024-09-19T01:14:32 Z vjudge1 Safety (NOI18_safety) C++17
100 / 100
 73 ms 3792 KB 
#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
3.0 / 3.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct

Subtask #2
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct

Subtask #3
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct

Subtask #4
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 43 ms 3520 KB Output is correct
2 Correct 63 ms 3740 KB Output is correct
3 Correct 69 ms 3780 KB Output is correct

Subtask #5
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 1 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 0 ms 348 KB Output is correct

Subtask #6
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 1 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 0 ms 344 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 0 ms 348 KB Output is correct
24 Correct 0 ms 348 KB Output is correct
25 Correct 0 ms 344 KB Output is correct
26 Correct 0 ms 348 KB Output is correct
27 Correct 0 ms 348 KB Output is correct

Subtask #7
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 1 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 0 ms 344 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 0 ms 348 KB Output is correct
24 Correct 0 ms 348 KB Output is correct
25 Correct 0 ms 344 KB Output is correct
26 Correct 0 ms 348 KB Output is correct
27 Correct 0 ms 348 KB Output is correct
28 Correct 2 ms 604 KB Output is correct
29 Correct 1 ms 604 KB Output is correct
30 Correct 1 ms 604 KB Output is correct
31 Correct 1 ms 348 KB Output is correct
32 Correct 1 ms 604 KB Output is correct
33 Correct 1 ms 604 KB Output is correct
34 Correct 1 ms 604 KB Output is correct

Subtask #8
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 1 ms 348 KB Output is correct
20 Correct 0 ms 348 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 0 ms 348 KB Output is correct
24 Correct 0 ms 348 KB Output is correct
25 Correct 0 ms 348 KB Output is correct
26 Correct 0 ms 344 KB Output is correct
27 Correct 0 ms 348 KB Output is correct
28 Correct 0 ms 348 KB Output is correct
29 Correct 0 ms 348 KB Output is correct
30 Correct 0 ms 348 KB Output is correct
31 Correct 0 ms 344 KB Output is correct
32 Correct 0 ms 348 KB Output is correct
33 Correct 0 ms 348 KB Output is correct
34 Correct 2 ms 604 KB Output is correct
35 Correct 1 ms 604 KB Output is correct
36 Correct 1 ms 604 KB Output is correct
37 Correct 1 ms 348 KB Output is correct
38 Correct 1 ms 604 KB Output is correct
39 Correct 1 ms 604 KB Output is correct
40 Correct 1 ms 604 KB Output is correct
41 Correct 2 ms 604 KB Output is correct
42 Correct 1 ms 348 KB Output is correct
43 Correct 1 ms 604 KB Output is correct
44 Correct 1 ms 604 KB Output is correct
45 Correct 1 ms 604 KB Output is correct
46 Correct 1 ms 604 KB Output is correct

Subtask #9
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 43 ms 3520 KB Output is correct
20 Correct 63 ms 3740 KB Output is correct
21 Correct 69 ms 3780 KB Output is correct
22 Correct 1 ms 348 KB Output is correct
23 Correct 0 ms 348 KB Output is correct
24 Correct 0 ms 348 KB Output is correct
25 Correct 0 ms 348 KB Output is correct
26 Correct 0 ms 348 KB Output is correct
27 Correct 0 ms 348 KB Output is correct
28 Correct 0 ms 348 KB Output is correct
29 Correct 0 ms 344 KB Output is correct
30 Correct 0 ms 348 KB Output is correct
31 Correct 0 ms 348 KB Output is correct
32 Correct 0 ms 348 KB Output is correct
33 Correct 0 ms 348 KB Output is correct
34 Correct 0 ms 344 KB Output is correct
35 Correct 0 ms 348 KB Output is correct
36 Correct 0 ms 348 KB Output is correct
37 Correct 2 ms 604 KB Output is correct
38 Correct 1 ms 604 KB Output is correct
39 Correct 1 ms 604 KB Output is correct
40 Correct 1 ms 348 KB Output is correct
41 Correct 1 ms 604 KB Output is correct
42 Correct 1 ms 604 KB Output is correct
43 Correct 1 ms 604 KB Output is correct
44 Correct 2 ms 604 KB Output is correct
45 Correct 1 ms 348 KB Output is correct
46 Correct 1 ms 604 KB Output is correct
47 Correct 1 ms 604 KB Output is correct
48 Correct 1 ms 604 KB Output is correct
49 Correct 1 ms 604 KB Output is correct
50 Correct 73 ms 3792 KB Output is correct
51 Correct 56 ms 3520 KB Output is correct
52 Correct 27 ms 3784 KB Output is correct
53 Correct 30 ms 3528 KB Output is correct
54 Correct 54 ms 3728 KB Output is correct
55 Correct 27 ms 3528 KB Output is correct
56 Correct 29 ms 3780 KB Output is correct
57 Correct 28 ms 3780 KB Output is correct
58 Correct 30 ms 3780 KB Output is correct
59 Correct 35 ms 3528 KB Output is correct