Problem p01559 - Generation 1

Orig Description

MinimumCostPath
There is an NxN square grid.
(Figure for the case of N=3)
The cost to move to an adjacent square is 1. However, diagonal movement is not allowed.
Also, there are M squares with obstacles, and it is not allowed to enter those squares.
How many ways are there to move from square (1,1) to square (N,N) with the minimum cost?
Since the answer can be large, output it by taking the MOD of 1000000009 (=109+9).
Input
The input is given in the following format:
N MX1 Y1X2 Y2……XM YM
Xi, Yi indicate that there is an obstacle at (Xi, Yi).
Constraints
2 ≤ N ≤ 106
 0 ≤ M ≤ 50
 1 ≤ Xi , Yi ≤ N
 i ≠ j implies (Xi, Yi) ≠ (Xj, Yj)
 (Xi, Yi) ≠ (1, 1)
 (Xi, Yi) ≠ (N, N)
Output
Output the total number of routes in one line. If there is no route to move from square (1,1) to square (N,N), output 0.
Sample Input 1
3 0
Output for the Sample Input 1
6
Corresponds to the following figure.
Sample Input 2
3 1
2 2
Output for the Sample Input 2
2
Corresponds to the following figure.
Sample Input 3
5 8
4 3
2 1
4 2
4 4
3 4
2 2
2 4
1 4
Output for the Sample Input 3
1
Corresponds to the following figure.
Sample Input 4
1000 10
104 87
637 366
393 681
215 604
707 876
943 414
95 327
93 415
663 596
661 842
Output for the Sample Input 4
340340391
Sample Input 5
2 2
1 2
2 1
Output for the Sample Input 5
0

Extracted Specification

An integer N (2 ≤ N ≤ 10^6), representing some quantity or size.
An integer M (0 ≤ M ≤ 50), representing another quantity.
M pairs of integers (Xi, Yi) where 1 ≤ Xi, Yi ≤ N and all pairs are distinct.

### Example Input:

```
3 1
2 2
```

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

Test Case Generator

Certainly! Below is a Python test case generator for the "MinimumCostPath" problem statement.

```python
import random

def tcgen():
    # Constants
    MOD = 1000000009
    
    # Randomly generate N within the given constraint
    N = random.randint(2, 10**6)
    
    # Randomly generate M within the given constraint
    M = random.randint(0, 50)
    
    obstacle_positions = set()
    
    # Generate unique obstacle coordinates
    while len(obstacle_positions) < M:
        x = random.randint(1, N)
        y = random.randint(1, N)
        
        # Ensure the position is not (1,1) or (N,N) and not already taken
        if (x, y) != (1, 1) and (x, y) != (N, N):
            obstacle_positions.add((x, y))
    
    obstacles = list(obstacle_positions)
    
    # Return the generated test case
    return N, obstacles

def format_test_case(N, obstacles):
    M = len(obstacles)
    obstacles_str = ' '.join(f'{x} {y}' for x, y in obstacles)
    return f"{N} {M}\n{obstacles_str}"

# Example of generating and formatting a test case
if __name__ == "__main__":
    N, obstacles = tcgen()
    test_case = format_test_case(N, obstacles)
    print(test_case)
```

### Explanation:
1. **Generating `N`**: 
    - We generate `N` randomly within the constraints (2 ≤ N ≤ 10^6).
2. **Generating `M`**: 
    - We generate `M` randomly within the constraints (0 ≤ M ≤ 50).
3. **Generating Obstacles**: 
    - We use a set to store unique obstacle positions.
    - We ensure that no obstacle is placed at the start (1, 1) or the end (N, N) and that all positions are unique.
4. **Formatting the Test Case**: 
    - We create a function to convert the generated data into the expected input format.

This generator will produce random test cases that adhere to the problem constraints. You can run the script to produce different test cases.

Extract Arguments

def extract_arguments(fh):
    N, M = map(int, fh.readline().strip().split())
    obstacles = []
    for _ in range(M):
        xi, yi = map(int, fh.readline().strip().split())
        obstacles.append((xi, yi))
    return N, obstacles