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