Problem p02357 - Generation 1

Orig Description

Sliding Minimum Element
  For a given array $a_1, a_2, a_3, ... , a_N$ of $N$ elements and an integer $L$, find the minimum of each possible sub-arrays with size $L$ and print them from the beginning. For example, for an array $\{1, 7, 7, 4, 8, 1, 6\}$ and $L = 3$, the possible sub-arrays with size $L = 3$ includes $\{1, 7, 7\}$, $\{7, 7, 4\}$, $\{7, 4, 8\}$, $\{4, 8, 1\}$, $\{8, 1, 6\}$ and the minimum of each sub-array is 1, 4, 4, 1, 1 respectively.
Constraints
 $1 \leq N \leq 10^6$ 
 $1 \leq L \leq 10^6$
 $1 \leq a_i \leq 10^9$
 $L \leq N$ 
Input
The input is given in the following format.
$N$ $L$
$a_1$ $a_2$ ... $a_N$
Output
  Print a sequence of the minimum in a line. Print a space character between adjacent elements.
Sample Input 1
7 3
1 7 7 4 8 1 6
Sample Output 1
1 4 4 1 1

Extracted Specification

An integer N (1 ≤ N ≤ 10^6), representing some quantity or size.
An integer L (1 ≤ L ≤ 10^6), representing some quantity or size.
A list of integers A of size N, where each integer is between 1 and 1e9.

### Example Input:

```
7 3
1 7 7 4 8 1 6
```

### Function Signature:
Write a function f(N, L, A) that takes in the input.
```python
def f(N: int, L: int, A: List[int]):
    ''' 
    N: an integer 
    L: an integer
    A: a list of integers
    '''
```

Test Case Generator

Sure! Below is the Python code for a test case generator for the "Sliding Minimum Element" problem:

```python
import random

def tcgen():
    # Generate a random value for N within the constraints
    N = random.randint(1, 10**6)
    
    # Generate a random value for L such that 1 <= L <= N
    L = random.randint(1, N)
    
    # Generate the array A with N elements, each element in the range [1, 10**9]
    A = [random.randint(1, 10**9) for _ in range(N)]
    
    return N, L, A

# Example usage
N, L, A = tcgen()
print(N, L)
print(" ".join(map(str, A)))
```

### Explanation:

1. **Generating \( N \)**:
   - A random integer \( N \) is generated between 1 and \( 10^6 \), which specifies the number of elements in the array.

2. **Generating \( L \)**:
   - A random integer \( L \) is generated between 1 and \( N \), ensuring that the length of the sub-arrays is valid.

3. **Generating Array \( A \)**:
   - An array \( A \) of size \( N \) is generated, where each element is a random integer between 1 and \( 10^9 \).

4. **Returning the test case**:
   - The function returns \( N \), \( L \), and the array \( A \).

5. **Example Usage**:
   - The example usage shows how to call the `tcgen` function and output the generated test case in the required format.

This code ensures that all constraints are respected, and it provides a random but valid test case for the "Sliding Minimum Element" problem.

Extract Arguments

def extract_arguments(fh):
    N, L = map(int, fh.readline().strip().split())
    A = list(map(int, fh.readline().strip().split()))
    return N, L, A