Problem p00764 - Generation 3

Orig Description

Chain-Confined Path
There is a chain consisting of multiple circles on a plane.
The first (last) circle of the chain only intersects with the next (previous) circle,
and each intermediate circle intersects only with the two neighboring circles.
Your task is to find the shortest path that satisfies the following conditions.
The path connects the centers of the first circle and the last circle.
The path is confined in the chain, that is, all the points on the path are located within or on at least one of the circles.
Figure E-1 shows an example of such a chain and the corresponding shortest path.
Figure E-1: An  example chain and the corresponding shortest path
Input
The input consists of multiple datasets.
Each dataset represents the shape of a chain in the following format.
n
x1 y1 r1 
x2 y2 r2 
...
xn yn rn 
The first line of a dataset contains an integer n (3 ≤ n ≤ 100) 
representing the number of the circles.
Each of the following n lines contains three integers separated by a single space.
(xi, yi) 
and ri represent 
the center position and the radius of the i-th circle Ci.
You can assume that 0 ≤ xi ≤ 1000, 
0 ≤ yi ≤ 1000, and
1 ≤ ri ≤ 25.
You can assume that Ci  and 
Ci+1  (1 ≤ i ≤ n−1) intersect at two separate points.
When j ≥ i+2, Ci  and Cj  are apart and either of them does not contain the other.
In addition, you can assume that any circle does not contain the center of any other circle.
The end of the input is indicated by a line containing a zero. 
Figure E-1 corresponds to the first dataset of Sample Input below.
Figure E-2 shows the shortest paths for the subsequent datasets of Sample Input. 
Figure E-2: Example chains and the corresponding shortest paths
Output
For each dataset, output a single line containing the length of the shortest chain-confined path between the centers of the first circle and the last circle.
The value should not have an error greater than 0.001.
No extra characters should appear in the output. 
Sample Input
10
802 0 10
814 0 4
820 1 4
826 1 4
832 3 5
838 5 5
845 7 3
849 10 3
853 14 4
857 18 3
3
0 0 5
8 0 5
8 8 5
3
0 0 5
7 3 6
16 0 5
9
0 3 5
8 0 8
19 2 8
23 14 6
23 21 6
23 28 6
19 40 8
8 42 8
0 39 5
11
0 0 5
8 0 5
18 8 10
8 16 5
0 16 5
0 24 5
3 32 5
10 32 5
17 28 8
27 25 3
30 18 5
0
Output for the Sample Input
58.953437
11.414214
16.0
61.874812
63.195179

Extracted Specification

An integer n (3 ≤ n ≤ 100), representing some quantity or size.
A list of n tuples where each tuple contains three integers (x, y, r).
For each tuple: 
- x (0 ≤ x ≤ 1000), an integer representing a coordinate.
- y (0 ≤ y ≤ 1000), an integer representing a coordinate.
- r (1 ≤ r ≤ 25), an integer representing a size.

### Example Input:

```
10
802 0 10
814 0 4
820 1 4
826 1 4
832 3 5
838 5 5
845 7 3
849 10 3
853 14 4
857 18 3
```

### Function Signature:
Write a function f(inputs) that takes in the input.
```python
def f(inputs: List[Tuple[int, int, int]]):
    ''' 
    inputs: a list of tuples, each containing three integers
    '''
```

Test Case Generator

Certainly! Based on the problem statement for the "Chain-Confined Path," here is the test case generator in Python:

```python
import random

def generate_test_case():
    # Number of circles, must be between 3 and 100 inclusive
    n = random.randint(3, 100)
    
    # Generate n circles
    circles = []
    for _ in range(n):
        x = random.randint(0, 1000)  # x-coordinate of the center
        y = random.randint(0, 1000)  # y-coordinate of the center
        r = random.randint(1, 25)    # radius of the circle
        circles.append((x, y, r))
    
    # Ensure the circles follow the problem constraints
    # Note: This is a simplified version and does not guarantee all the constraints are met.
    # In a real scenario, you might need a more sophisticated method to ensure all constraints are satisfied.
    
    # Print the test case
    print(n)
    for x, y, r in circles:
        print(f"{x} {y} {r}")

# Generate multiple test cases
def generate_multiple_test_cases(num_cases=5):
    for _ in range(num_cases):
        generate_test_case()
        print()  # Add a blank line between test cases

# Main function to generate the test cases and add the terminating zero
def main():
    generate_multiple_test_cases()
    print(0)  # Terminating zero to indicate end of input

if __name__ == "__main__":
    main()
```

### Explanation:

1. **Random Generation**:
   - `n` is randomly selected between 3 and 100 to represent the number of circles.
   - For each circle, the coordinates (`x`, `y`) are randomly chosen between 0 and 1000, and the radius (`r`) is chosen between 1 and 25.

2. **Constraints**:
   - The generator does not enforce all constraints explicitly (e.g., ensuring each circle intersects only its neighbors and does not contain the center of another circle). For a competitive programming problem, this might need a more sophisticated approach to ensure all constraints are fully satisfied.

3. **Output**:
   - Each test case is printed in the required format, followed by a blank line to separate multiple test cases.
   - The main function generates a specified number of test cases (`num_cases`) and appends a terminating zero to indicate the end of input.

This generator provides a basic implementation to create random test cases for the problem. For more complex constraints, additional logic would need to be incorporated.

Extract Arguments

def extract_arguments(fh):
    inputs = []
    while True:
        n = int(fh.readline().strip())
        if n == 0:
            break
        dataset = []
        for _ in range(n):
            x, y, r = map(int, fh.readline().strip().split())
            dataset.append((x, y, r))
        inputs.append(dataset)
    return inputs

# if __name__ == "__main__":
#     input_path = sys.argv[1]
#     with open(input_path, 'r') as fh: 
#         inputs = extract_arguments(fh)
#         f(inputs)