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Submission #698515

# Submission time Handle Problem Language Result Execution time Memory
698515 2023-02-13T16:35:29 Z dattranxxx Building Bridges (CEOI17_building) C++11
100 / 100
 79 ms 66404 KB 
#include<bits/stdc++.h>
using namespace std;
using ll = long long;
 
const int N = 1e5 + 5;
const ll INF = 1e12;
const ll LLINF = 1e18;
ll h[N], w[N];
int n;
 
ll dp[N];
 
ll sqr(ll x) {
  return x * x;
}
 
namespace task1 {
  void solve() {
    dp[1] = 0;
    for (int i = 2; i <= n; ++i) {
      dp[i] = LLINF;
      for (int j = i - 1; j; --j) {
        dp[i] = min(dp[i], dp[j] + sqr(h[i] - h[j]) + (w[i - 1] - w[j]));
      }
    }
    cout << dp[n];
  }
}
 
namespace task2 {
  const int C = 1e6;
  
  struct Line {
    ll a, b;
    Line(ll a = INF, ll b = INF): a(a), b(b) {}
    ll get(ll x) {
      return a * x + b;
    }
  };
  
  struct LichaoTree {
    // vector<Line> cont;
    // void update(ll a, ll b) {
      // cont.emplace_back(a, b);
    // }
//     
    // ll get(ll x) {
      // ll res = INF;
      // for (auto& l : cont)
        // res = min(res, l.get(x));
      // return res;
    // }
    Line v; ll x, res;
    Line lct[(C + 1) * 4];
    void update(int i, int l, int r) {
      if (l == r) {
        if (v.get(l) < lct[i].get(l)) {
          lct[i] = v;
        }
        return;
      }
      int m = (l + r) / 2;
      if (v.a < lct[i].a) swap(v, lct[i]);
      if (v.get(m) < lct[i].get(m)) {
        swap(v, lct[i]);
        update(i * 2 + 1, m + 1, r);
      } else {
        update(i * 2, l, m);
      }
    }
    
    void get(int i, int l, int r) {
      res = min(res, lct[i].get(x));
      if (l == r) return;
      int m = (l + r) / 2;
      if (x <= m) get(i * 2, l, m);
      else get(i * 2 + 1, m + 1, r);
    }
    
    void update(ll a, ll b) {
      v = Line(a, b);
      update(1, 0, C);
    }
    
    ll get(ll x) {
      res = LLINF;
      this->x = x;
      get(1, 0, C);
      return res;
    }
    
  } lct;
  
  void solve() {
    dp[1] = 0;
    lct.update(-2 * h[1], dp[1] + sqr(h[1]) - w[1]);
    for (int i = 2; i <= n; ++i) {
      // dp[i] = h[i]^2 + w[i-1] + MIN[(-2h[j]) * h[i] + dp[j] + h[j]^2 - w[j]]
      dp[i] = sqr(h[i]) + w[i-1] + lct.get(h[i]);
      lct.update(-2 * h[i], dp[i] + sqr(h[i]) - w[i]);
    }
    cout << dp[n];
  }
}
 
 
int main() {
  cin.tie(0)->sync_with_stdio(0); cout.tie(0);
  cin >> n;
  for (int i = 1; i <= n; ++i)
    cin >> h[i];
  for (int i = 1; i <= n; ++i)
    cin >> w[i],
    w[i] += w[i - 1];
    
  if (n <= 1000) task1::solve();
  else task2::solve();
  
	return 0;
}

Subtask #1
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 24 ms 62908 KB Output is correct
2 Correct 25 ms 62928 KB Output is correct
3 Correct 25 ms 62932 KB Output is correct
4 Correct 25 ms 62960 KB Output is correct
5 Correct 33 ms 62852 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 66 ms 66260 KB Output is correct
2 Correct 63 ms 66252 KB Output is correct
3 Correct 65 ms 66224 KB Output is correct
4 Correct 62 ms 66156 KB Output is correct
5 Correct 57 ms 66124 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 24 ms 62908 KB Output is correct
2 Correct 25 ms 62928 KB Output is correct
3 Correct 25 ms 62932 KB Output is correct
4 Correct 25 ms 62960 KB Output is correct
5 Correct 33 ms 62852 KB Output is correct
6 Correct 66 ms 66260 KB Output is correct
7 Correct 63 ms 66252 KB Output is correct
8 Correct 65 ms 66224 KB Output is correct
9 Correct 62 ms 66156 KB Output is correct
10 Correct 57 ms 66124 KB Output is correct
11 Correct 79 ms 66404 KB Output is correct
12 Correct 73 ms 66232 KB Output is correct
13 Correct 62 ms 66380 KB Output is correct
14 Correct 71 ms 66384 KB Output is correct
15 Correct 58 ms 66128 KB Output is correct
16 Correct 59 ms 66264 KB Output is correct
17 Correct 50 ms 66268 KB Output is correct
18 Correct 50 ms 66288 KB Output is correct