Problem p03686 - Generation 3

Orig Description

Score : 1000 points
Problem StatementThere are M chairs arranged in a line. The coordinate of the i-th chair (1 ≤ i ≤ M) is i.
N people of the Takahashi clan played too much games, and they are all suffering from backaches. They need to sit in chairs and rest, but they are particular about which chairs they sit in. Specifically, the i-th person wishes to sit in a chair whose coordinate is not greater than L_i, or not less than R_i. Naturally, only one person can sit in the same chair.
It may not be possible for all of them to sit in their favorite chairs, if nothing is done.
Aoki, who cares for the health of the people of the Takahashi clan, decides to provide additional chairs so that all of them can sit in chairs at their favorite positions.
Additional chairs can be placed at arbitrary real coordinates. Find the minimum required number of additional chairs.
Constraints
1 ≤ N,M ≤ 2 × 10^5
0 ≤ L_i < R_i ≤ M + 1(1 ≤ i ≤ N)
All input values are integers.
InputInput is given from Standard Input in the following format:
N M
L_1 R_1
:
L_N R_N
OutputPrint the minimum required number of additional chairs.
Sample Input 14 4
0 3
2 3
1 3
3 4
Sample Output 10
The four people can sit in chairs at the coordinates 3, 2, 1 and 4, respectively, and no more chair is needed.
Sample Input 27 6
0 7
1 5
3 6
2 7
1 6
2 6
3 7
Sample Output 22
If we place additional chairs at the coordinates 0 and 2.5, the seven people can sit at coordinates 0, 5, 3, 2, 6, 1 and 2.5, respectively.
Sample Input 33 1
1 2
1 2
1 2
Sample Output 32
Sample Input 46 6
1 6
1 6
1 5
1 5
2 6
2 6
Sample Output 42

Extracted Specification

An integer N (1 ≤ N ≤ 2 × 10^5), representing some quantity or size.
An integer M (1 ≤ M ≤ 2 × 10^5), representing some quantity or size.
N pairs of integers (L_i, R_i), where 0 ≤ L_i < R_i ≤ M + 1.

### Example Input:

```
4 4
0 3
2 3
1 3
3 4
```

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

Test Case Generator

Sure, I can help you write a test case generator for the given problem statement. Here's a Python function that generates test cases based on the constraints provided:

```python
import random

def tcgen():
    # Number of people and chairs
    N = random.randint(1, 2 * 10**5)
    M = random.randint(1, 2 * 10**5)
    
    # Generate L and R values for each person
    LR = []
    for _ in range(N):
        L = random.randint(0, M)
        R = random.randint(L + 1, M + 1)
        LR.append((L, R))
    
    return N, M, LR

def format_input(N, M, LR):
    input_str = f"{N} {M}\n"
    for L, R in LR:
        input_str += f"{L} {R}\n"
    return input_str.strip()

# Example usage
if __name__ == "__main__":
    N, M, LR = tcgen()
    test_case = format_input(N, M, LR)
    print(test_case)
```

This script will generate random test cases based on the constraints given in the problem statement. Here's a breakdown of the code:

1. **tcgen function**:
   - Randomly generates `N`, the number of people, and `M`, the number of chairs, within the specified constraints.
   - For each person, it generates random values for `L` and `R` such that `0 ≤ L < R ≤ M + 1`.
   - Collects all these `(L, R)` pairs in the list `LR`.

2. **format_input function**:
   - Takes the generated values (`N`, `M`, and `LR`) and formats them into the input format expected by the problem.
   - Returns the formatted string.

3. **Example usage**:
   - Calls the `tcgen` function to generate a test case.
   - Formats the generated test case using `format_input`.
   - Prints the test case.

You can run the script multiple times to generate different test cases, or you can modify it to generate a specific number of test cases and write them to files for further testing.

Extract Arguments

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