Problem p00374 - Generation 3

Orig Description

Iron Bars
A boy PCK had N straight iron bars, which were serially indexed. Unfortunately, the first M bars (0 ≤ M ≤ N) among them were bent during transportation. They all suffered a perpendicular bend at one point.
  He is planning to make a cube using a set of bars selected using the following rules: X bars from bent ones, Y bars from straight ones, where 2X + Y = 12. Any two bars can be jointed only at the apexes of the cube. He wants to count how many types of rectangular parallelepipeds (hereafter RP) he can make using these bars.
Make a program to count out types (different shapes) of RPs that PCK can make using the following information: the number of bars and length of each one, position of the bend, and the number of bars to be used to construct an RP. Note that any two RPs similar in shape are considered identical: namely if the length of three defining sides of two RPs coincide if arranged in increasing/decreasing order (e.g., three sides of RP i and j are A_i, B_i, C_i, and A_j, B_j and C_j in increasing order, then the relations A_i = A_j, B_i = B_j, and C_i = C_j hold. Note also that the bars are sufficiently thin to allow you to consider them as idealized lines.
  
Input
  The input is given in the following format.
N M X Y
a_1
a_2
:
a_N
b_1
b_2
:
b_M
The first line provides the total number of iron bars and bent bars, and those straight and bent bars used to construct an RP: N (6 ≤ N ≤ 6000), M (0 ≤ M ≤ N), X (0 ≤ X ≤ 6), and Y (0 ≤ Y ≤ 12). The following relations always hold for them: 2X+Y=12, X+Y ≤ N, X ≤ M. Each of the subsequent N lines provides the length of the i-th bar a_i (1 ≤ a_i ≤ 6000) in integers. Furthermore, each of the subsequent M lines provides the location at which the i-th bent bar suffered a perpendicular bend b_i (1 ≤ b_i ≤ 3000) in centimeters from one end of the bar (note: 1 ≤ a_i-b_i ≤ 3000).
  
Output
  Output the number of constructible rectangular parallelepipeds.
Sample Input 1
18 8 3 6
4
3
3
3
3
2
2
2
1
1
1
1
1
2
2
3
3
3
1
1
1
1
1
1
1
1
Sample Output 1
3

Extracted Specification

Canonicalized Input Description:

An integer N (6 ≤ N ≤ 6000), representing some quantity or size.
An integer M (0 ≤ M ≤ N), representing some quantity or size.
An integer X (0 ≤ X ≤ 6), representing some quantity or size.
An integer Y (0 ≤ Y ≤ 12), representing some quantity or size.
A list of N integers, where each integer is between 1 and 6000.
A list of M integers, where each integer is between 1 and 3000.

### Example Input:

```
18 8 3 6
4
3
3
3
3
2
2
2
1
1
1
1
1
2
2
3
3
3
1
1
1
1
1
1
1
1
```

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

Test Case Generator

Sure, I can help you with a test case generator for the "Iron Bars" problem. Here is the Python code to generate random test cases for this problem:

```python
import random

def generate_test_case():
    # Constants based on the problem constraints
    N = random.randint(6, 6000)
    M = random.randint(0, N)
    X = random.randint(0, 6)
    Y = 12 - 2 * X
    
    while X + Y > N or X > M:
        X = random.randint(0, 6)
        Y = 12 - 2 * X

    a = [random.randint(1, 6000) for _ in range(N)]
    b = [random.randint(1, min(3000, a[i] - 1)) for i in range(M)]
    
    # Ensuring the condition 1 ≤ a_i - b_i ≤ 3000 for bent bars
    for i in range(M):
        while a[i] - b[i] > 3000:
            b[i] = random.randint(1, min(3000, a[i] - 1))
    
    return N, M, X, Y, a, b

def format_test_case(N, M, X, Y, a, b):
    test_case = f"{N} {M} {X} {Y}\n"
    test_case += "\n".join(map(str, a)) + "\n"
    test_case += "\n".join(map(str, b))
    return test_case

# Example usage
N, M, X, Y, a, b = generate_test_case()
print(format_test_case(N, M, X, Y, a, b))
```

### Explanation:
1. **Constants**: We set the constants for the constraints as specified in the problem.
2. **Random Values**: Generate random values for \(N\), \(M\), \(X\), and \(Y\) based on the constraints.
   - \(N\) is the total number of bars.
   - \(M\) is the number of bent bars.
   - \(X\) and \(Y\) are chosen in such a way that \(2X + Y = 12\) and other constraints are satisfied.
3. **Lengths of Bars**: Generate a list of lengths for each of the \(N\) bars.
4. **Positions of Bends**: Generate positions of bends for each of the \(M\) bent bars such that they adhere to the constraints.
5. **Formatting**: Format the test case in the required input format.

This code generates random test cases that you can use to test your solution for the "Iron Bars" problem. You can run the code multiple times to generate different test cases.

Extract Arguments

def extract_arguments(fh):
    N, M, X, Y = map(int, fh.readline().strip().split())
    lengths = [int(fh.readline().strip()) for _ in range(N)]
    bends = [int(fh.readline().strip()) for _ in range(M)]
    return N, M, X, Y, lengths, bends

# Example usage:
# with open('input.txt', 'r') as fh:
#     N, M, X, Y, lengths, bends = extract_arguments(fh)
#     print(N, M, X, Y, lengths, bends)