Problem p03802 - Generation 3

Orig Description

Score : 1200 points
Problem StatementSnuke loves flags.
Snuke is placing N flags on a line.
The i-th flag can be placed at either coordinate x_i or coordinate y_i.
Snuke thinks that the flags look nicer when the smallest distance between two of them, d, is larger. Find the maximum possible value of d.
Constraints
2 ≤ N ≤ 10^{4}
1 ≤ x_i, y_i ≤ 10^{9}
x_i and y_i are integers.
InputThe input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
OutputPrint the answer.
Sample Input 13
1 3
2 5
1 9
Sample Output 14
The optimal solution is to place the first flag at coordinate 1, the second flag at coordinate 5 and the third flag at coordinate 9. The smallest distance between two of the flags is 4 in this case.
Sample Input 25
2 2
2 2
2 2
2 2
2 2
Sample Output 20
There can be more than one flag at the same position.
Sample Input 322
93 6440
78 6647
862 11
8306 9689
798 99
801 521
188 206
6079 971
4559 209
50 94
92 6270
5403 560
803 83
1855 99
42 504
75 484
629 11
92 122
3359 37
28 16
648 14
11 269
Sample Output 317

Extracted Specification

An integer N (2 ≤ N ≤ 10^4), representing some quantity or size.
A list of N tuples, where each tuple contains two integers (1 ≤ x_i, y_i ≤ 10^9).

### Example Input:

```
3
1 3
2 5
1 9
```

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

Test Case Generator

Certainly! Here is the test case generator for the given problem statement:

```python
import random

def tcgen():
    # Generate a random number of flags within the given constraints
    N = random.randint(2, 10**4)
    
    # Generate N pairs of coordinates (x_i, y_i) within the given constraints
    coordinates = [(random.randint(1, 10**9), random.randint(1, 10**9)) for _ in range(N)]
    
    return N, coordinates

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

**Explanation:**

1. **Number of Flags:** The number of flags \( N \) is generated randomly between 2 and \( 10^4 \) (inclusive) to meet the problem's constraints.
2. **Coordinates:** For each flag, two possible coordinates \( x_i \) and \( y_i \) are generated randomly between 1 and \( 10^9 \) (inclusive).

This script generates a test case, prints the number of flags, and then prints each pair of possible coordinates. You can run this script to generate a new test case each time.

Extract Arguments

def extract_arguments(fh):
    N = int(fh.readline().strip())
    coordinates = [tuple(map(int, fh.readline().strip().split())) for _ in range(N)]
    return N, coordinates

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