oj.uz

Submission #890125

# Submission time Handle Problem Language Result Execution time Memory
890125 2023-12-20T15:07:40 Z khohoc Knapsack (NOI18_knapsack) C++14
100 / 100
 46 ms 7260 KB 
#include <bits/stdc++.h>
 
using namespace std;
 
typedef vector<pair<long long, long long>> vii;
 
#define pb push_back
#define all(x) x.begin(), x.end()
 
const int V = 1e6 + 7;
const int N = 1e5 + 7;
const int S = 2e3 + 7;
const int inf = 1e9;
 
long long s, n, v[N], w[N], k[N];
 
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
 
  #ifndef ONLINE_JUDGE
  // freopen("test.inp", "r", stdin);
  //freopen("test.out", "w", stdout);
  #endif
 
  cin >> s >> n;
  for (int i = 1; i <= n; i++) cin >> v[i] >> w[i] >> k[i];
 
  int mx = *max_element(k, k + n);
  // Subtask 1
  if (n == 1) {
    cout << v[1] * min(s / w[1], k[1]) << endl;
  }
  // Subtask 2 & 3: Normal knapsack
  else if (1 <= n && n <= 100 && mx <= 10) {
    long long dp[2001];
    memset(dp, 0, sizeof dp);
    for (int i = 1; i <= n; i++) 
      for (int j = s; j >= w[i]; j--)
        for (int t = 0; t <= k[i]; t++)
          if (j >= w[i] * t) {
            dp[j] = max(dp[j], dp[j - w[i] * t] + v[i] * t);
          }
    cout << dp[s] << endl;
  }
  // Subtask 4 & 5: knapsack with observation
  else if (1 <= n && n <= 1e5 && mx <= 1e9) {
 
    /*
      Observation: The numbers of taken product must less than S since 1 <= Wi <= S -> maximum taken product: S / W[i]
      -> consider the top valued S/W[i] items for each W[i]
    */
    vii obj[S];
    long long dp[2001];
    memset(dp, 0, sizeof dp);
    for (int i = 1; i <= n; i++) {
      obj[w[i]].pb({v[i], k[i]});
    }
 
    for (int i = 0; i <= s; i++) {
      if (obj[i].size() == 0) continue;
      sort(all(obj[i]), greater<pair<int, int>>());
 
      int id = 0;
      for (int j = 0; j * i < s; j++) {
        if (id >= obj[i].size()) break;
        for (int k = s; k >= i; k--) {
          dp[k] = max(dp[k], dp[k - i] + obj[i][id].first);
        }
        --obj[i][id].second;
        if (obj[i][id].second == 0) ++id;
      }
    }
    cout << dp[s] << endl;
  } 
}

Compilation message

knapsack.cpp: In function 'int main()':
knapsack.cpp:66:16: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<long long int, long long int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   66 |         if (id >= obj[i].size()) break;
      |             ~~~^~~~~~~~~~~~~~~~

Subtask #1
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2396 KB Output is correct
2 Correct 0 ms 2396 KB Output is correct
3 Correct 1 ms 2396 KB Output is correct
4 Correct 1 ms 2396 KB Output is correct

Subtask #2
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2396 KB Output is correct
2 Correct 1 ms 2396 KB Output is correct
3 Correct 1 ms 2568 KB Output is correct
4 Correct 1 ms 2396 KB Output is correct
5 Correct 1 ms 2396 KB Output is correct
6 Correct 1 ms 2396 KB Output is correct
7 Correct 2 ms 2648 KB Output is correct
8 Correct 1 ms 2396 KB Output is correct
9 Correct 1 ms 2396 KB Output is correct
10 Correct 1 ms 2648 KB Output is correct

Subtask #3
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2396 KB Output is correct
2 Correct 1 ms 2396 KB Output is correct
3 Correct 1 ms 2568 KB Output is correct
4 Correct 1 ms 2396 KB Output is correct
5 Correct 1 ms 2396 KB Output is correct
6 Correct 1 ms 2396 KB Output is correct
7 Correct 2 ms 2648 KB Output is correct
8 Correct 1 ms 2396 KB Output is correct
9 Correct 1 ms 2396 KB Output is correct
10 Correct 1 ms 2648 KB Output is correct
11 Correct 1 ms 2396 KB Output is correct
12 Correct 3 ms 2396 KB Output is correct
13 Correct 1 ms 2396 KB Output is correct
14 Correct 1 ms 2396 KB Output is correct
15 Correct 1 ms 2396 KB Output is correct
16 Correct 1 ms 2396 KB Output is correct
17 Correct 1 ms 2396 KB Output is correct
18 Correct 1 ms 2396 KB Output is correct
19 Correct 1 ms 2396 KB Output is correct
20 Correct 1 ms 2396 KB Output is correct

Subtask #4
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2396 KB Output is correct
2 Correct 0 ms 2396 KB Output is correct
3 Correct 1 ms 2396 KB Output is correct
4 Correct 1 ms 2396 KB Output is correct
5 Correct 1 ms 2396 KB Output is correct
6 Correct 1 ms 2396 KB Output is correct
7 Correct 1 ms 2568 KB Output is correct
8 Correct 1 ms 2396 KB Output is correct
9 Correct 1 ms 2396 KB Output is correct
10 Correct 1 ms 2396 KB Output is correct
11 Correct 2 ms 2648 KB Output is correct
12 Correct 1 ms 2396 KB Output is correct
13 Correct 1 ms 2396 KB Output is correct
14 Correct 1 ms 2648 KB Output is correct
15 Correct 1 ms 2396 KB Output is correct
16 Correct 3 ms 2396 KB Output is correct
17 Correct 1 ms 2396 KB Output is correct
18 Correct 1 ms 2396 KB Output is correct
19 Correct 1 ms 2396 KB Output is correct
20 Correct 1 ms 2396 KB Output is correct
21 Correct 1 ms 2396 KB Output is correct
22 Correct 1 ms 2396 KB Output is correct
23 Correct 1 ms 2396 KB Output is correct
24 Correct 1 ms 2396 KB Output is correct
25 Correct 1 ms 2396 KB Output is correct
26 Correct 3 ms 2396 KB Output is correct
27 Correct 1 ms 2396 KB Output is correct
28 Correct 1 ms 2396 KB Output is correct
29 Correct 1 ms 2396 KB Output is correct
30 Correct 2 ms 2580 KB Output is correct
31 Correct 1 ms 2392 KB Output is correct
32 Correct 1 ms 2396 KB Output is correct
33 Correct 1 ms 2568 KB Output is correct
34 Correct 1 ms 2396 KB Output is correct

Subtask #5
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2396 KB Output is correct
2 Correct 0 ms 2396 KB Output is correct
3 Correct 1 ms 2396 KB Output is correct
4 Correct 1 ms 2396 KB Output is correct
5 Correct 1 ms 2396 KB Output is correct
6 Correct 1 ms 2396 KB Output is correct
7 Correct 1 ms 2568 KB Output is correct
8 Correct 1 ms 2396 KB Output is correct
9 Correct 1 ms 2396 KB Output is correct
10 Correct 1 ms 2396 KB Output is correct
11 Correct 2 ms 2648 KB Output is correct
12 Correct 1 ms 2396 KB Output is correct
13 Correct 1 ms 2396 KB Output is correct
14 Correct 1 ms 2648 KB Output is correct
15 Correct 1 ms 2396 KB Output is correct
16 Correct 3 ms 2396 KB Output is correct
17 Correct 1 ms 2396 KB Output is correct
18 Correct 1 ms 2396 KB Output is correct
19 Correct 1 ms 2396 KB Output is correct
20 Correct 1 ms 2396 KB Output is correct
21 Correct 1 ms 2396 KB Output is correct
22 Correct 1 ms 2396 KB Output is correct
23 Correct 1 ms 2396 KB Output is correct
24 Correct 1 ms 2396 KB Output is correct
25 Correct 1 ms 2396 KB Output is correct
26 Correct 3 ms 2396 KB Output is correct
27 Correct 1 ms 2396 KB Output is correct
28 Correct 1 ms 2396 KB Output is correct
29 Correct 1 ms 2396 KB Output is correct
30 Correct 2 ms 2580 KB Output is correct
31 Correct 1 ms 2392 KB Output is correct
32 Correct 1 ms 2396 KB Output is correct
33 Correct 1 ms 2568 KB Output is correct
34 Correct 1 ms 2396 KB Output is correct
35 Correct 23 ms 6100 KB Output is correct
36 Correct 29 ms 6348 KB Output is correct
37 Correct 26 ms 6100 KB Output is correct
38 Correct 23 ms 6104 KB Output is correct
39 Correct 33 ms 6816 KB Output is correct
40 Correct 46 ms 6992 KB Output is correct
41 Correct 33 ms 6488 KB Output is correct
42 Correct 34 ms 6488 KB Output is correct
43 Correct 43 ms 6488 KB Output is correct
44 Correct 42 ms 6492 KB Output is correct
45 Correct 27 ms 7192 KB Output is correct
46 Correct 27 ms 6944 KB Output is correct
47 Correct 29 ms 7260 KB Output is correct
48 Correct 37 ms 7008 KB Output is correct
49 Correct 25 ms 7020 KB Output is correct
50 Correct 39 ms 6484 KB Output is correct