Problem p02320 - Generation 3

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 or limit.
N lines each containing three integers v, w, and m, where 1 ≤ v ≤ 1,000, 1 ≤ w ≤ 1,000, and 1 ≤ m ≤ 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 N tuples, where each tuple contains three integers
    '''

Test Case Generator

Certainly! Here is a test case generator for the given Knapsack problem with limitations:

```python
import random

def tcgen():
    # Constraints
    N = random.randint(1, 100)  # Number of items
    W = random.randint(1, 10000)  # Capacity of the knapsack
    
    items = []
    for _ in range(N):
        v = random.randint(1, 1000)  # Value of item
        w = random.randint(1, 1000)  # Weight of item
        m = random.randint(1, 10000)  # Limitation of item
        items.append((v, w, m))
    
    return N, W, items

# Example usage
N, W, items = tcgen()
print(N, W)
for item in items:
    print(item[0], item[1], item[2])
```

### Explanation
- **N**: Number of items, randomly chosen between 1 and 100.
- **W**: Capacity of the knapsack, randomly chosen between 1 and 10,000.
- **items**: List of tuples where each tuple contains:
  - **v**: Value of the item, randomly chosen between 1 and 1,000.
  - **w**: Weight of the item, randomly chosen between 1 and 1,000.
  - **m**: Limitation on the number of that item, randomly chosen between 1 and 10,000.

This generator will create a variety of test cases within the constraints provided by the problem statement. You can use this to generate multiple test cases to thoroughly test your solution to 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