Orig Description
Score : 300 points
Problem StatementWe have N ID cards, and there are M gates.
We can pass the i-th gate if we have one of the following ID cards: the L_i-th, (L_i+1)-th, ..., and R_i-th ID cards.
How many of the ID cards allow us to pass all the gates alone?
Constraints
All values in input are integers.
1 \leq N \leq 10^5
1 \leq M \leq 10^5
1 \leq L_i \leq R_i \leq N
InputInput is given from Standard Input in the following format:
N M
L_1 R_1
L_2 R_2
\vdots
L_M R_M
OutputPrint the number of ID cards that allow us to pass all the gates alone.
Sample Input 14 2
1 3
2 4
Sample Output 12
Two ID cards allow us to pass all the gates alone, as follows:
The first ID card does not allow us to pass the second gate.
The second ID card allows us to pass all the gates.
The third ID card allows us to pass all the gates.
The fourth ID card does not allow us to pass the first gate.
Sample Input 210 3
3 6
5 7
6 9
Sample Output 21
Sample Input 3100000 1
1 100000
Sample Output 3100000
Extracted Specification
Canonicalized Input Description:
An integer N (1 ≤ N ≤ 10^5), representing some quantity or size.
An integer M (1 ≤ M ≤ 10^5), representing some other quantity or size.
M pairs of integers (L_i, R_i) where 1 ≤ L_i ≤ R_i ≤ N.
### Example Input:
```
4 2
1 3
2 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 contains:
- an integer N
- an integer M
- a list of M tuples, each containing two integers (L_i, R_i)
'''
Test Case Generator
Certainly! Here’s a test case generator for the given problem involving ID cards and gates:
```python
import random
def tcgen():
# Generate N and M within their respective constraints
N = random.randint(1, 10**5)
M = random.randint(1, 10**5)
# Generate M pairs of (L_i, R_i) such that 1 <= L_i <= R_i <= N
gates = []
for _ in range(M):
L_i = random.randint(1, N)
R_i = random.randint(L_i, N)
gates.append((L_i, R_i))
return N, M, gates
def format_tc(N, M, gates):
output = []
output.append(f"{N} {M}")
for L_i, R_i in gates:
output.append(f"{L_i} {R_i}")
return "\n".join(output)
# Example usage
N, M, gates = tcgen()
formatted_tc = format_tc(N, M, gates)
print(formatted_tc)
```
This `tcgen` function generates random values for \( N \) and \( M \) within their respective constraints and then generates \( M \) pairs of \( (L_i, R_i) \). The `format_tc` function formats these values into the required input format.
### Explanation:
1. **N**: Number of ID cards, randomly chosen between 1 and 100,000.
2. **M**: Number of gates, randomly chosen between 1 and 100,000.
3. **gates**: A list of \( M \) pairs \((L_i, R_i)\) where \( 1 \leq L_i \leq R_i \leq N \).
The test case generator ensures that each pair \((L_i, R_i)\) satisfies the constraints \( 1 \leq L_i \leq R_i \leq N \).
You can use the function `tcgen` to generate random test cases for this problem and `format_tc` to format the output in the correct input format for testing purposes.
Extract Arguments
def extract_arguments(fh):
N, M = map(int, fh.readline().strip().split())
gates = []
for _ in range(M):
L, R = map(int, fh.readline().strip().split())
gates.append((L, R))
return N, M, gates