Problem p02320 - Generation 1

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), representing some quantity or size.
An integer W (1 ≤ W ≤ 10,000), representing some capacity.
A list of tuples of form (vi, wi, mi) of size N, 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.
```python
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

Sure! Here is a test case generator for the given Knapsack Problem with Limitations:

```python
import random

def tcgen():
    N = random.randint(1, 100)
    W = random.randint(1, 10000)
    
    items = []
    for _ in range(N):
        v = random.randint(1, 1000)
        w = random.randint(1, 1000)
        m = random.randint(1, 10000)
        items.append((v, w, m))
    
    return (N, W, items)

def format_test_case(N, W, items):
    test_case = f"{N} {W}\n"
    for (v, w, m) in items:
        test_case += f"{v} {w} {m}\n"
    return test_case

# Example usage
N, W, items = tcgen()
test_case = format_test_case(N, W, items)
print(test_case)
```

This generator will produce random test cases for the knapsack problem with limitations, adhering to the constraints specified in the problem statement. Here is how it works:

1. It randomly selects the number of items \(N\) between 1 and 100.
2. It randomly selects the maximum weight \(W\) of the knapsack between 1 and 10000.
3. For each item, it randomly selects the value \(v\) between 1 and 1000, weight \(w\) between 1 and 1000, and limitation \(m\) between 1 and 10000.
4. The `format_test_case` function formats the generated test case into the required input format.

You can use the `tcgen` and `format_test_case` functions to generate and format test cases for your problem.

Extract Arguments

def extract_arguments(fh):
    # Read the first line for N and W
    N, W = map(int, fh.readline().strip().split())
    # Initialize the list to hold the tuples (value, weight, limit) for each item
    items = []
    # Read the next N lines for the 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)