Submission #844907

#	Time	Username	Problem	Language	Result	Execution time	Memory
844907		nskybytskyi	Potatoes and fertilizers (LMIO19_bulves)	C++17	100 / 100	179 ms	27332 KiB

bulves

#include <bits/stdc++.h>
using namespace std;

// dp[i][j] = min cost to get a[k] >= b[k] for all k <= i
// and (sum (a[k] - b[k]) over k <= i) <= j
// f_i(j) := dp[i][j] is decreasing and convex in j

int main() {
  cin.tie(0)->sync_with_stdio(0);

  int n;
  cin >> n;

  vector<pair<int, int>> ab(n);
  for (auto& [a, b] : ab) {
    cin >> a >> b;
  }

  vector<int> differences(n);
  for (int i = 0; i < n; ++i) {
    const auto& [a, b] = ab[i];
    differences[i] = a - b;
  }

  vector<int64_t> prefix_sums(n + 1);
  for (int i = 0; i < n; ++i) {
    prefix_sums[i + 1] = prefix_sums[i] + differences[i];
  }

  // looking for a non-decreasing sequence of prefix sums
  // with smallest possible sum of absolute differences
  // same problem but cannot modify prefix_sums[0]=0 and prefix_sums[n]
  // same as saying there are infinitely many breakpoints at 0

  int64_t value{0};
  priority_queue<int64_t> slope;

  for (int i = 1; i < n; ++i) {
    slope.push(prefix_sums[i]);
    slope.push(prefix_sums[i]);
    value += max<int64_t>(0, slope.top()) - prefix_sums[i];
    if (slope.top() > 0) {
      slope.pop();
    }
  }

  while (!slope.empty()) {
    value += max<int64_t>(0, slope.top() - prefix_sums[n]);
    slope.pop();
  }

  cout << value << '\n';
}

• Subtask 1: 24 / 24
• Subtask 2: 10 / 10
• Subtask 3: 20 / 20
• Subtask 4: 10 / 10
• Subtask 5: 36 / 36