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Submission #582834

# Submission time Handle Problem Language Result Execution time Memory
582834 2022-06-24T13:36:39 Z 600Mihnea Building Bridges (CEOI17_building) C++17
0 / 100
 57 ms 3700 KB 
#include <bits/stdc++.h>

using namespace std;
typedef long double ld;
typedef long long ll;

struct T {
  ll a;
  ll b;
};

const int N = (int) 1e5 + 7;
const ll INF = (ll) 1e18 + 7;
int n;
ll h[N];
ll sum[N];
ll dp[N];
T coef[N];

/**

T first
T second
T third

T ff, ss, tt

ff.a * x + ff.b = ss.a * x + ss.b
ff.b - ss.b = x * (ss.a - ff.a)

(ff.b - ss.b) / (ss.a - ff.a) < (ss.b - tt.b) / (tt.a - ss.a)
(ff.b - ss.b) * (tt.a - ss.a) < (ss.b - tt.b) * (ss.a - ff.a)

**/

signed main() {
  ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);

  cin >> n;
  for (int i = 1; i <= n; i++) {
    int x;
    cin >> x;
    h[i] = x;
  }
  for (int i = 1; i <= n; i++) {
    int x;
    cin >> x;
    sum[i] = sum[i - 1] + x;
  }

  dp[1] = 0;
  for (int i = 2; i <= n; i++) {
    dp[i] = INF;
  }

  vector<T> all;

  for (int r = 2; r <= n; r++) {
    T p3 = {- 2 * h[r - 1], dp[r - 1] + h[r - 1] * h[r - 1] - sum[r - 1]};

    while ((int) all.size() >= 2) {
      T p1 = all[(int) all.size() - 2];
      T p2 = all[(int) all.size() - 1];
      if ((ld) (p3.b - p1.b) / (ld) (p1.a - p3.a) > (ld) (p2.b - p1.b) / (ld) (p1.a - p2.a)) {
        all.pop_back();
      } else {
        break;
      }
    }

    all.push_back(p3);



    ll x = h[r];
    for (auto &ln : all) {
      dp[r] = min(dp[r], ln.a * x + ln.b);
    }
    dp[r] += h[r] * h[r] + sum[r - 1];
  }

  cout << dp[n] << "\n";

}

Subtask #1
0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Incorrect 1 ms 340 KB Output isn't correct
3 Halted 0 ms 0 KB -

Subtask #2
0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 57 ms 2680 KB Output is correct
2 Incorrect 49 ms 3700 KB Output isn't correct
3 Halted 0 ms 0 KB -

Subtask #3
0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Incorrect 1 ms 340 KB Output isn't correct
3 Halted 0 ms 0 KB -