Problem p02733 - Generation 1

Orig Description

Score : 500 points
Problem StatementWe have a chocolate bar partitioned into H horizontal rows and W vertical columns of squares.
The square (i, j) at the i-th row from the top and the j-th column from the left is dark if S_{i,j} is 0, and white if S_{i,j} is 1.
We will cut the bar some number of times to divide it into some number of blocks. In each cut, we cut the whole bar by a line running along some boundaries of squares from end to end of the bar.
How many times do we need to cut the bar so that every block after the cuts has K or less white squares?
Constraints
1 \leq H \leq 10
1 \leq W \leq 1000
1 \leq K \leq H \times W
S_{i,j} is 0 or 1.
InputInput is given from Standard Input in the following format:
H W K
S_{1,1}S_{1,2}...S_{1,W}
:
S_{H,1}S_{H,2}...S_{H,W}
OutputPrint the number of minimum times the bar needs to be cut so that every block after the cuts has K or less white squares.
Sample Input 13 5 4
11100
10001
00111
Sample Output 12
For example, cutting between the 1-st and 2-nd rows and between the 3-rd and 4-th columns - as shown in the figure to the left - works.
Note that we cannot cut the bar in the ways shown in the two figures to the right.
Sample Input 23 5 8
11100
10001
00111
Sample Output 20
No cut is needed.
Sample Input 34 10 4
1110010010
1000101110
0011101001
1101000111
Sample Output 33

Extracted Specification

An integer H (1 ≤ H ≤ 10), representing some quantity or size.
An integer W (1 ≤ W ≤ 1000), representing some quantity or size.
An integer K (1 ≤ K ≤ H * W), representing some quantity or size.
A matrix S of size H x W, where each element S[i][j] is either 0 or 1.

### Example Input:

```
3 5 4
11100
10001
00111
```

### Function Signature:
Write a function f(H, W, K, S) that takes in the input.
def f(H: int, W: int, K: int, S: List[List[int]]):
    '''
    H: an integer
    W: an integer
    K: an integer
    S: a list of lists of integers
    '''

Test Case Generator

To create a test case generator for the given problem, we need to generate random values for the parameters \( H \), \( W \), \( K \), and the grid \( S \). Here's the Python code that generates such test cases:

```python
import random

def tcgen():
    H = random.randint(1, 10)
    W = random.randint(1, 1000)
    K = random.randint(1, H * W)
    
    S = []
    for i in range(H):
        row = ''.join(random.choice(['0', '1']) for _ in range(W))
        S.append(row)
    
    return H, W, K, S

def print_test_case():
    H, W, K, S = tcgen()
    
    print(H, W, K)
    for row in S:
        print(row)

# To generate and print a test case
print_test_case()
```

### Explanation:

1. **Random Values Generation**:
   - `H` is chosen randomly between 1 and 10.
   - `W` is chosen randomly between 1 and 1000.
   - `K` is chosen randomly between 1 and \( H \times W \).

2. **Grid Generation**:
   - The grid \( S \) is generated by creating a list of strings, where each string represents a row of the grid.
   - Each character in the row is either '0' (dark square) or '1' (white square), randomly chosen.

3. **Output**:
   - The function `print_test_case()` prints the generated test case in the required format.

You can call `print_test_case()` to generate and print a test case. This will help in generating multiple test cases for thorough testing of your solution.

Extract Arguments

def extract_arguments(fh):
    H, W, K = map(int, fh.readline().strip().split())
    S = [fh.readline().strip() for _ in range(H)]
    return H, W, K, S

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