Problem p03037 - Generation 1

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 quantity or size.
A list of M tuples, each tuple containing two integers L_i and R_i (1 ≤ L_i ≤ R_i ≤ N).

### Example Input:

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

### Function Signature:

Write a function f(N, M, intervals) that takes in the input.

```python
def f(N: int, M: int, intervals: List[Tuple[int, int]]):
    '''
    N: an integer
    M: an integer
    intervals: a list of tuples, each containing two integers
    '''
```

Test Case Generator

Sure, here is a test case generator for the given problem statement:

```python
import random

def tcgen():
    # Define the constraints
    N = random.randint(1, 10**5)
    M = random.randint(1, 10**5)
    
    # Generate the list of (L_i, R_i) pairs
    LR = []
    for _ in range(M):
        L = random.randint(1, N)
        R = random.randint(L, N)  # Ensure L_i <= R_i
        LR.append((L, R))
    
    return N, M, LR

# This function will print the test case in the required format
def print_test_case():
    N, M, LR = tcgen()
    print(N, M)
    for L, R in LR:
        print(L, R)

# Example usage
print_test_case()
```

This code generates a random test case according to the constraints specified in the problem statement. The function `tcgen` produces random valid values for \(N\) and \(M\), and then generates \(M\) pairs of \((L_i, R_i)\) such that \(1 \leq L_i \leq R_i \leq N\).

The `print_test_case` function prints the generated test case in the required format. You can call `print_test_case()` to generate and print a random test case.

This should help you test your solution with various inputs!

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