Problem p02320 - Generation 2

Orig Description

Knapsack Problem with Limitations
You have N items that you want to put them into a knapsack. Item i has value vi, weight wi and limitation mi.
You want to find a subset of items to put such that:
The total value of the items is as large as possible.
The items have combined weight at most W, that is capacity of the knapsack.
You can select at most mi items for ith item.
Find the maximum total value of items in the knapsack.
Input
N W
v1 w1 m1
v2 w2 m2
:
vN wN mN
The first line consists of the integers N and W. In the following N lines, the value, weight and limitation of the i-th item are given.
Output
Print the maximum total values of the items in a line.
Constraints
 1 ≤ N ≤ 100
 1 ≤ vi ≤ 1,000
 1 ≤ wi ≤ 1,000
 1 ≤ mi ≤ 10,000
 1 ≤ W ≤ 10,000
Sample Input 1
4 8
4 3 2
2 1 1
1 2 4
3 2 2
Sample Output 1
12
Sample Input 2
2 100
1 1 100
2 1 50
Sample Output 2
150

Extracted Specification

An integer N (1 ≤ N ≤ 100) and an integer W (1 ≤ W ≤ 10,000), representing some quantities or sizes.
A list of N tuples, where each tuple contains:
    - An integer vi (1 ≤ vi ≤ 1,000)
    - An integer wi (1 ≤ wi ≤ 1,000)
    - An integer mi (1 ≤ mi ≤ 10,000)

### Example Input:

```
4 8
4 3 2
2 1 1
1 2 4
3 2 2
```

### Function Signature:
Write a function f(N, W, items) that takes in the input.
def f(N: int, W: int, items: List[Tuple[int, int, int]]):
    '''
    N: an integer
    W: an integer
    items: a list of tuples, where each tuple contains three integers
    '''

Test Case Generator

Certainly! Here is a Python function to generate test cases for the "Knapsack Problem with Limitations" problem statement you provided:

```python
import random

def generate_knapsack_test_case():
    # Generate values for the constraints
    N = random.randint(1, 100)
    W = random.randint(1, 10000)
    
    # List to store item details
    items = []
    for _ in range(N):
        vi = random.randint(1, 1000)
        wi = random.randint(1, 1000)
        mi = random.randint(1, 10000)
        items.append((vi, wi, mi))
    
    # Format the input as specified in the problem statement
    input_data = f"{N} {W}\n"
    for vi, wi, mi in items:
        input_data += f"{vi} {wi} {mi}\n"

    return input_data.strip()

# Example usage
print(generate_knapsack_test_case())
```

This function generates random test cases for the "Knapsack Problem with Limitations" problem. Each test case is formatted as specified in the problem statement. The function ensures that the constraints are respected:

1. \(1 \leq N \leq 100\)
2. \(1 \leq v_i \leq 1000\)
3. \(1 \leq w_i \leq 1000\)
4. \(1 \leq m_i \leq 10000\)
5. \(1 \leq W \leq 10000\)

The output of the function is a string that can be directly used as input for testing the problem.

Extract Arguments

def extract_arguments(fh):
    N, W = map(int, fh.readline().strip().split())
    items = []
    for _ in range(N):
        v, w, m = map(int, fh.readline().strip().split())
        items.append((v, w, m))
    return N, W, items

# if __name__ == "__main__":
#     input_path = sys.argv[1]
#     with open(input_path, 'r') as fh: 
#     N, W, items = extract_arguments(fh)
#     f(N, W, items)