Problem p02357 - Generation 3

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), another quantity with a constraint relative to N.
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.
def f(N: int, L: int, A: List[int]):
    '''
    N: an integer
    L: an integer
    A: a list of integers
    '''

Test Case Generator

Sure, I can help you write a test case generator for the "Sliding Minimum Element" problem. Below is a Python function to generate random test cases for this problem:

```python
import random

def tcgen():
    N = random.randint(1, 10**6)
    L = random.randint(1, N)
    
    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. **N (number of elements)**: The function uses `random.randint(1, 10**6)` to generate a random integer between 1 and 1,000,000 (inclusive) for the number of elements in the array.
   
2. **L (size of sub-arrays)**: The function ensures that the size of the sub-arrays is at most `N` by generating a random integer between 1 and `N`.

3. **A (array elements)**: The function generates an array `A` of size `N` with random integers, each between 1 and 1,000,000,000 (inclusive).

### Example Usage:

```python
N, L, A = tcgen()
print(N, L)
print(" ".join(map(str, A)))
```

This code snippet will generate a random test case and print it in the format specified in the problem statement.

### Note:
Due to the constraints (with `N` up to 10^6 and `a_i` up to 10^9), the generated test cases can be quite large. If you want to test the generator for smaller values or specific scenarios, you can adjust the ranges accordingly. For example, you can set `N = random.randint(1, 100)` for smaller arrays during testing.

Extract Arguments

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