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Submission #646540

# Submission time Handle Problem Language Result Execution time Memory
646540 2022-09-30T02:37:40 Z alvinpiter Knapsack (NOI18_knapsack) C++17
100 / 100
 57 ms 17364 KB 
/*
Observations:
* Since the weight of each item is >= 1, we can take at most 2000 items.
* The weight of each item is <= 2000. This allow us to group the items and only take the top 2000 most expensive ones.
  We can have tighter bound tho, for example, when considering items with weight x, we can take at most 2000/x items.

Dynamic programming solution:
dp[w][c] -> maximum price achievable if we only consider items whose weight is between 1..w and our
bag capacity is c.

The complexity of the solution is around W^2 log W.
The log factor comes from the second observation.
*/

#include<bits/stdc++.h>
using namespace std;
#define MAXW 2000

int S, N, dp[MAXW + 3][MAXW + 3];
vector<pair<int, int> > itemsWithWeight[MAXW + 3];
vector<int> itemPricesWithWeight[MAXW + 3];

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);

  cin >> S >> N;
  for (int i = 1; i <= N; i++) {
    int v, w, k;
    cin >> v >> w >> k;

    itemsWithWeight[w].push_back({v, k});
  }

  for (int w = 1; w <= MAXW; w++) {
    sort(itemsWithWeight[w].rbegin(), itemsWithWeight[w].rend());
    for (auto [price, count]: itemsWithWeight[w]) {
      for (int i = 0; i < count && itemPricesWithWeight[w].size() * w <= MAXW; i++) {
        itemPricesWithWeight[w].push_back(price);
      }
    }
  }

  memset(dp, 0, sizeof(dp));
  for (int w = 1; w <= MAXW; w++) {
    for (int cap = 1; cap <= S; cap++) {
      // Skip all items with weight w.
      dp[w][cap] = dp[w - 1][cap];

      int sumPrice = 0;
      int sumWeight = 0;
      for (auto price: itemPricesWithWeight[w]) {
        sumPrice += price;
        sumWeight += w;

        if (sumWeight <= cap) {
          dp[w][cap] = max(dp[w][cap], sumPrice + dp[w - 1][cap - sumWeight]);
        } else {
          break;
        }
      }
    }
  }

  cout << dp[MAXW][S] << endl;
}

Subtask #1
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 16084 KB Output is correct
2 Correct 9 ms 16112 KB Output is correct
3 Correct 9 ms 16084 KB Output is correct
4 Correct 10 ms 16120 KB Output is correct

Subtask #2
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 7 ms 16092 KB Output is correct
2 Correct 11 ms 16084 KB Output is correct
3 Correct 11 ms 16092 KB Output is correct
4 Correct 12 ms 16084 KB Output is correct
5 Correct 11 ms 16116 KB Output is correct
6 Correct 11 ms 16084 KB Output is correct
7 Correct 15 ms 16084 KB Output is correct
8 Correct 11 ms 16120 KB Output is correct
9 Correct 11 ms 16116 KB Output is correct
10 Correct 10 ms 16084 KB Output is correct

Subtask #3
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 7 ms 16092 KB Output is correct
2 Correct 11 ms 16084 KB Output is correct
3 Correct 11 ms 16092 KB Output is correct
4 Correct 12 ms 16084 KB Output is correct
5 Correct 11 ms 16116 KB Output is correct
6 Correct 11 ms 16084 KB Output is correct
7 Correct 15 ms 16084 KB Output is correct
8 Correct 11 ms 16120 KB Output is correct
9 Correct 11 ms 16116 KB Output is correct
10 Correct 10 ms 16084 KB Output is correct
11 Correct 6 ms 16084 KB Output is correct
12 Correct 13 ms 16084 KB Output is correct
13 Correct 11 ms 16092 KB Output is correct
14 Correct 10 ms 16084 KB Output is correct
15 Correct 10 ms 16084 KB Output is correct
16 Correct 11 ms 16084 KB Output is correct
17 Correct 13 ms 16012 KB Output is correct
18 Correct 13 ms 16016 KB Output is correct
19 Correct 11 ms 16120 KB Output is correct
20 Correct 12 ms 16120 KB Output is correct

Subtask #4
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 16084 KB Output is correct
2 Correct 9 ms 16112 KB Output is correct
3 Correct 9 ms 16084 KB Output is correct
4 Correct 10 ms 16120 KB Output is correct
5 Correct 7 ms 16092 KB Output is correct
6 Correct 11 ms 16084 KB Output is correct
7 Correct 11 ms 16092 KB Output is correct
8 Correct 12 ms 16084 KB Output is correct
9 Correct 11 ms 16116 KB Output is correct
10 Correct 11 ms 16084 KB Output is correct
11 Correct 15 ms 16084 KB Output is correct
12 Correct 11 ms 16120 KB Output is correct
13 Correct 11 ms 16116 KB Output is correct
14 Correct 10 ms 16084 KB Output is correct
15 Correct 6 ms 16084 KB Output is correct
16 Correct 13 ms 16084 KB Output is correct
17 Correct 11 ms 16092 KB Output is correct
18 Correct 10 ms 16084 KB Output is correct
19 Correct 10 ms 16084 KB Output is correct
20 Correct 11 ms 16084 KB Output is correct
21 Correct 13 ms 16012 KB Output is correct
22 Correct 13 ms 16016 KB Output is correct
23 Correct 11 ms 16120 KB Output is correct
24 Correct 12 ms 16120 KB Output is correct
25 Correct 7 ms 16000 KB Output is correct
26 Correct 13 ms 16084 KB Output is correct
27 Correct 14 ms 16084 KB Output is correct
28 Correct 11 ms 16084 KB Output is correct
29 Correct 10 ms 16084 KB Output is correct
30 Correct 11 ms 16084 KB Output is correct
31 Correct 11 ms 16084 KB Output is correct
32 Correct 11 ms 16116 KB Output is correct
33 Correct 11 ms 16084 KB Output is correct
34 Correct 11 ms 16084 KB Output is correct

Subtask #5
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 16084 KB Output is correct
2 Correct 9 ms 16112 KB Output is correct
3 Correct 9 ms 16084 KB Output is correct
4 Correct 10 ms 16120 KB Output is correct
5 Correct 7 ms 16092 KB Output is correct
6 Correct 11 ms 16084 KB Output is correct
7 Correct 11 ms 16092 KB Output is correct
8 Correct 12 ms 16084 KB Output is correct
9 Correct 11 ms 16116 KB Output is correct
10 Correct 11 ms 16084 KB Output is correct
11 Correct 15 ms 16084 KB Output is correct
12 Correct 11 ms 16120 KB Output is correct
13 Correct 11 ms 16116 KB Output is correct
14 Correct 10 ms 16084 KB Output is correct
15 Correct 6 ms 16084 KB Output is correct
16 Correct 13 ms 16084 KB Output is correct
17 Correct 11 ms 16092 KB Output is correct
18 Correct 10 ms 16084 KB Output is correct
19 Correct 10 ms 16084 KB Output is correct
20 Correct 11 ms 16084 KB Output is correct
21 Correct 13 ms 16012 KB Output is correct
22 Correct 13 ms 16016 KB Output is correct
23 Correct 11 ms 16120 KB Output is correct
24 Correct 12 ms 16120 KB Output is correct
25 Correct 7 ms 16000 KB Output is correct
26 Correct 13 ms 16084 KB Output is correct
27 Correct 14 ms 16084 KB Output is correct
28 Correct 11 ms 16084 KB Output is correct
29 Correct 10 ms 16084 KB Output is correct
30 Correct 11 ms 16084 KB Output is correct
31 Correct 11 ms 16084 KB Output is correct
32 Correct 11 ms 16116 KB Output is correct
33 Correct 11 ms 16084 KB Output is correct
34 Correct 11 ms 16084 KB Output is correct
35 Correct 32 ms 16968 KB Output is correct
36 Correct 39 ms 16968 KB Output is correct
37 Correct 38 ms 17104 KB Output is correct
38 Correct 41 ms 16956 KB Output is correct
39 Correct 43 ms 16944 KB Output is correct
40 Correct 57 ms 17320 KB Output is correct
41 Correct 46 ms 17232 KB Output is correct
42 Correct 50 ms 17280 KB Output is correct
43 Correct 52 ms 17332 KB Output is correct
44 Correct 56 ms 17332 KB Output is correct
45 Correct 44 ms 17364 KB Output is correct
46 Correct 43 ms 16964 KB Output is correct
47 Correct 44 ms 17320 KB Output is correct
48 Correct 49 ms 17228 KB Output is correct
49 Correct 39 ms 17356 KB Output is correct
50 Correct 47 ms 17128 KB Output is correct