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Submission #1091918

# Submission time Handle Problem Language Result Execution time Memory
1091918 2024-09-22T15:02:33 Z vjudge1 Potatoes and fertilizers (LMIO19_bulves) C++17
100 / 100
 217 ms 19124 KB 
#include <climits>
#include <functional>
#include <iostream>
#include <queue>
#include <set>
#include <vector>

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

  int n;
  std::cin >> n;

  // ans = sum abs(prefix(a - c, i)) where c[] = final configuration
  // c[i] = b[i] + x[i], where x[i] = some fertilizers we remove from position i
  // so ans = sum abs(prefix(a - b, i) - prefix(x, i)) and we want to minimize this
  // DP[i][x] = minimize ans with x = prefix(x, i)
  // DP[i][x] = min(DP[i-1][y] + abs(prefix(a - b, i) - x, 0 <= x - y <= a[i]) 
  //  - here x = prefix(x, i) and y = prefix(x, i-1), and x[i] = x - y
  //  - range x[i] is [0, a[i]] -> 0 <= x - y <= a[i]
  // Transform DP: DP[i][x] = min(DP[i-1][y], max(0, x-a[i]) <= y <= x) + abs(prefix(a - b, i) - x)
  // we can do slope trick here as inductively it is convex linear
  long long total = 0;
  long long m = 0, c = 0; // leftmost m & c
  long long shift = 0;
  std::priority_queue<long long> pq_neg;
  std::priority_queue<long long, std::vector<long long>, std::greater<long long>> pq_pos;
  for (int i = 0; i < n; i++) {
    long long a, b;
    std::cin >> a >> b;

    total += a - b;

    // take min: shift positive grad all by a
    if (!pq_pos.empty()) {
      shift += a;
    }

    // insert
    if (total > 0) {
      // combine with y = total - x
      m--;
      c += total;
      pq_neg.push(total);
      pq_pos.push(total - shift);
    } else {
      // combine with y = x + (-total) if x >= 0, else -x -total
      m--;
      c += -total;
      pq_neg.push(0);
      pq_pos.push(-shift);
    }

    // normalize
    while (pq_neg.top() > pq_pos.top() + shift) {
      long long x_neg = pq_neg.top();
      long long x_pos = pq_pos.top() + shift;
      pq_neg.pop();
      pq_pos.pop();

      pq_neg.push(x_pos);
      pq_pos.push(x_neg - shift);
    }
  }

  // reorder pq_neg
  std::vector<long long> xs(pq_neg.size());
  while (!pq_neg.empty()) {
    long long x = pq_neg.top();
    pq_neg.pop();
    xs[pq_neg.size()] = x;
  }
  for (long long x: xs) {
    if (x > total) {
      std::cout << m * total + c << std::endl;
      return 0;
    }
    m++;
    c -= x;
  }

  while (!pq_pos.empty()) {
    long long x = pq_pos.top() + shift;
    pq_pos.pop();
    if (x > total) {
      std::cout << m * total + c << std::endl;
      return 0;
    }
    m++;
    c -= x;
  }

  std::cout << m * total + c << std::endl;

  return 0;
}

Subtask #1
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 1 ms 468 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 14 ms 1976 KB Output is correct
5 Correct 32 ms 3520 KB Output is correct
6 Correct 95 ms 9904 KB Output is correct
7 Correct 109 ms 19060 KB Output is correct
8 Correct 141 ms 17064 KB Output is correct
9 Correct 126 ms 16496 KB Output is correct
10 Correct 114 ms 14236 KB Output is correct
11 Correct 114 ms 14248 KB Output is correct

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 1 ms 468 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 14 ms 1976 KB Output is correct
5 Correct 32 ms 3520 KB Output is correct
6 Correct 95 ms 9904 KB Output is correct
7 Correct 109 ms 19060 KB Output is correct
8 Correct 141 ms 17064 KB Output is correct
9 Correct 126 ms 16496 KB Output is correct
10 Correct 114 ms 14236 KB Output is correct
11 Correct 114 ms 14248 KB Output is correct
12 Correct 44 ms 5056 KB Output is correct
13 Correct 115 ms 11692 KB Output is correct
14 Correct 113 ms 19108 KB Output is correct
15 Correct 149 ms 17060 KB Output is correct
16 Correct 191 ms 16528 KB Output is correct
17 Correct 104 ms 14280 KB Output is correct
18 Correct 1 ms 348 KB Output is correct

Subtask #3
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 1 ms 468 KB Output is correct
3 Correct 1 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 1 ms 348 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 2 ms 472 KB Output is correct
9 Correct 1 ms 344 KB Output is correct
10 Correct 1 ms 348 KB Output is correct

Subtask #4
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 1 ms 468 KB Output is correct
3 Correct 1 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 1 ms 348 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 2 ms 472 KB Output is correct
9 Correct 1 ms 344 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 1 ms 348 KB Output is correct
13 Correct 1 ms 604 KB Output is correct
14 Correct 1 ms 604 KB Output is correct
15 Correct 1 ms 540 KB Output is correct
16 Correct 1 ms 600 KB Output is correct
17 Correct 1 ms 348 KB Output is correct
18 Correct 2 ms 564 KB Output is correct

Subtask #5
36.0 / 36.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 1 ms 468 KB Output is correct
3 Correct 1 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 1 ms 348 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 2 ms 472 KB Output is correct
9 Correct 1 ms 344 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 14 ms 1976 KB Output is correct
12 Correct 32 ms 3520 KB Output is correct
13 Correct 95 ms 9904 KB Output is correct
14 Correct 109 ms 19060 KB Output is correct
15 Correct 141 ms 17064 KB Output is correct
16 Correct 126 ms 16496 KB Output is correct
17 Correct 114 ms 14236 KB Output is correct
18 Correct 114 ms 14248 KB Output is correct
19 Correct 44 ms 5056 KB Output is correct
20 Correct 115 ms 11692 KB Output is correct
21 Correct 113 ms 19108 KB Output is correct
22 Correct 149 ms 17060 KB Output is correct
23 Correct 191 ms 16528 KB Output is correct
24 Correct 104 ms 14280 KB Output is correct
25 Correct 1 ms 348 KB Output is correct
26 Correct 1 ms 604 KB Output is correct
27 Correct 1 ms 604 KB Output is correct
28 Correct 1 ms 540 KB Output is correct
29 Correct 1 ms 600 KB Output is correct
30 Correct 1 ms 348 KB Output is correct
31 Correct 2 ms 564 KB Output is correct
32 Correct 1 ms 348 KB Output is correct
33 Correct 48 ms 5196 KB Output is correct
34 Correct 135 ms 11684 KB Output is correct
35 Correct 217 ms 19124 KB Output is correct
36 Correct 206 ms 16556 KB Output is correct
37 Correct 133 ms 17060 KB Output is correct
38 Correct 201 ms 19096 KB Output is correct
39 Correct 116 ms 15256 KB Output is correct
40 Correct 138 ms 13976 KB Output is correct
41 Correct 114 ms 14352 KB Output is correct
42 Correct 118 ms 14188 KB Output is correct
43 Correct 113 ms 14240 KB Output is correct
44 Correct 119 ms 14168 KB Output is correct
45 Correct 191 ms 19108 KB Output is correct
46 Correct 96 ms 14500 KB Output is correct
47 Correct 130 ms 12440 KB Output is correct