Problem p02556 - Generation 1

Orig Description

Score : 500 points
Problem StatementThere are N points on the 2D plane, i-th of which is located on (x_i, y_i).
There can be multiple points that share the same coordinate.
What is the maximum possible Manhattan distance between two distinct points?
Here, the Manhattan distance between two points (x_i, y_i) and (x_j, y_j) is defined by |x_i-x_j| + |y_i-y_j|.
Constraints
2 \leq N \leq 2 \times 10^5
1 \leq x_i,y_i \leq 10^9
All values in input are integers.
InputInput is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
:
x_N y_N
OutputPrint the answer.
Sample Input 13
1 1
2 4
3 2
Sample Output 14
The Manhattan distance between the first point and the second point is |1-2|+|1-4|=4, which is maximum possible.
Sample Input 22
1 1
1 1
Sample Output 20

Extracted Specification

An integer N (2 ≤ N ≤ 2 × 10^5), representing some quantity or size.
N pairs of integers (x_i, y_i) where each integer is between 1 and 10^9.

### Example Input:

```
3
1 1
2 4
3 2
```

### Function Signature:
Write a function f(N, points) that takes in the input.
```python
def f(N: int, points: List[Tuple[int, int]]):
    '''
    N: an integer
    points: a list of tuples, each containing two integers
    '''
```

Test Case Generator

Sure! Here's a Python function that generates test cases for the given problem statement about calculating the maximum possible Manhattan distance between two points on a 2D plane.

```python
import random

def tcgen():
    # Number of points on the 2D plane
    N = random.randint(2, 2 * 10**5)
    
    # Generate the list of points
    points = [(random.randint(1, 10**9), random.randint(1, 10**9)) for _ in range(N)]
    
    return N, points

# Example usage
if __name__ == "__main__":
    N, points = tcgen()
    
    print(N)
    for x, y in points:
        print(x, y)
```

### Explanation:

1. **N**: This is generated randomly within the given constraints, i.e., between 2 and 200,000.
2. **Points**: Each point (x_i, y_i) is generated such that both x_i and y_i are random integers between 1 and \(10^9\).

### Example Output:

Upon running the `tcgen` function, you may get an output like:
```
4
123456789 987654321
135792468 246813579
102938475 564738291
192837465 564738291
```

This provides a valid input for the problem statement.

Feel free to adjust the random seed (using `random.seed()`) if you need reproducible test cases.

Extract Arguments

def extract_arguments(fh):
    N = int(fh.readline().strip())
    points = []
    for _ in range(N):
        x, y = map(int, fh.readline().strip().split())
        points.append((x, y))
    return N, points

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