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
Canonicalized Input Description:
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.
A list of N tuples (L_i, R_i), where each tuple consists of two integers 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, each containing an integer, an integer, and a list of tuples of integers
'''
Test Case Generator
Sure! Based on the problem statement you provided, here is a test case generator for the problem:
```python
import random
def tcgen():
# Constraints
N = random.randint(1, 200000)
M = random.randint(1, 200000)
# Generating L and R values within the constraints
L = []
R = []
for _ in range(N):
Li = random.randint(0, M)
Ri = random.randint(Li + 1, M + 1)
L.append(Li)
R.append(Ri)
return N, M, L, R
# Example usage
N, M, L, R = tcgen()
print(N, M)
for Li, Ri in zip(L, R):
print(Li, Ri)
```
This function generates a random test case based on the constraints provided in the problem statement. Here is what the function does step-by-step:
1. It randomly selects the number of people \(N\) and the number of chairs \(M\) within the given constraints.
2. It generates random pairs of coordinates \(L_i\) and \(R_i\) for each person, ensuring that \(0 \leq L_i < R_i \leq M + 1\).
3. It returns the generated values so they can be used to create a test case.
You can run the example usage to see a randomly generated test case printed in the required format.
Extract Arguments
def extract_arguments(fh):
N, M = map(int, fh.readline().strip().split())
preferences = []
for _ in range(N):
L, R = map(int, fh.readline().strip().split())
preferences.append((L, R))
return N, M, preferences