Problem p00625 - Generation 3

Orig Description

Problem E: Frisbee Dogs
Crane is trying to enter her beloved dog, Jack, into a Frisbee Dog competition. However, she is not confident that Jack will perform well. She would like you to create a program that simulates the competition and estimates Jack's performance.
The competition is held by N dogs on a two-dimensional plane. At the start of the competition, the i-th dog is at position (Dix, Diy). The i-th dog can run at a speed of Vi [m/s], and all dogs are small enough to be considered as points. At any time, two or more dogs can be in the same position.
The competition starts with the launch of the first Frisbee, and from that moment on, the dogs are allowed to move. The Frisbee can also be considered as a point, and the i-th Frisbee is launched from the position (FPix, FPin) with a velocity vector of (FVix, FViy) [m/s], and continues to move at constant speed in a straight line. When the position of a dog and the position of a Frisbee are the same, the dog can acquire the Frisbee.
When the first Frisbee is acquired by a dog, the second Frisbee is launched. When the second Frisbee is acquired, the third is launched, and so on, with the next Frisbee launched immediately after it is acquired. The competition ends when M Frisbees are acquired.
Needless to say, the goal of the dogs is to acquire as many Frisbees as possible. The dogs take the following strategy:
When a Frisbee is launched, a dog moves to be able to acquire it as soon as possible, and acquires the Frisbee. However, if the dog cannot acquire the Frisbee, it waits at its current location.
Whether a dog can acquire a Frisbee is determined independently of the actions of other dogs. That is, even if a dog moves to acquire a Frisbee, it may be acquired by another dog first. When a Frisbee is acquired by any dog and a new Frisbee is launched, the dogs take the above strategy for the new Frisbee.
Your program should output the number of Frisbees acquired by each dog.
Input
The input file consists of multiple datasets.
The first line of each dataset gives the number of dogs N (1 ≤ N ≤ 10) and the number of Frisbees M (1 ≤ M ≤ 1000).
The following N lines give the initial position and speed of the dogs, Dix, Diy, and Vi, separated by a single space.
The following M lines give the launch position and velocity of the Frisbees, FPix, FPin, FVix, and FViy, separated by a single space.
The given coordinate values are real numbers, and their absolute value does not exceed 1000. The given speed is a real number, and 1 ≤ Vi ≤ 100, -25 ≤ FVix, FViy ≤ 25. It can be assumed that there is no Frisbee that cannot be acquired by any dog.
If a Frisbee is acquired by a dog at time t, no dog can acquire it before t+1e-6.
During the simulation, the absolute values of the x and y coordinates of the dogs do not exceed 1e+8.
The end of the input is indicated by N=0 and M=0.
Output
Output the number of Frisbees acquired by each dog on a single line, separated by a space. The order of the output must be the same as the order of the input.
Sample Input
2 1
12 5 3
0 17 3
0 0 2 2
2 3
2 0 2
100 100 2
0 0 -1 0
-2 -5 0 3
100 100 1 1
0 0
Output for the Sample Input
1 0
2 1

Extracted Specification

An integer N (1 ≤ N ≤ 10), representing some quantity.
An integer M (1 ≤ M ≤ 1000), representing some quantity.
N lines each containing three real numbers X, Y, and V, where -1000 ≤ X, Y ≤ 1000 and 1 ≤ V ≤ 100.
M lines each containing four real numbers P, Q, R, and S, where -1000 ≤ P, Q ≤ 1000 and -25 ≤ R, S ≤ 25. 
The input ends with a line containing N=0 and M=0.

### Example Input:
```
2 1
12 5 3
0 17 3
0 0 2 2
0 0
```

### Function Signature:
Write a function f(inputs) that takes in a list of tuples as input.
```python
def f(inputs: List[Tuple[int, int, List[Tuple[float, float, float]], List[Tuple[float, float, float, float]]]]):
    '''
    inputs: a list of tuples where each tuple contains:
        - an integer
        - an integer
        - a list of tuples, each containing three real numbers
        - a list of tuples, each containing four real numbers
    '''
```

Test Case Generator

Sure! Let's create a test case generator for the problem "Frisbee Dogs". The generator will create random scenarios within the provided constraints. Here is the Python code for the test case generator:

```python
import random

def tcgen():
    # Generate random number of dogs and frisbees
    N = random.randint(1, 10)
    M = random.randint(1, 1000)
    
    dogs = []
    for _ in range(N):
        Dix = random.uniform(-1000, 1000)
        Diy = random.uniform(-1000, 1000)
        Vi = random.uniform(1, 100)
        dogs.append((Dix, Diy, Vi))
    
    frisbees = []
    for _ in range(M):
        FPix = random.uniform(-1000, 1000)
        FPin = random.uniform(-1000, 1000)
        FVix = random.uniform(-25, 25)
        FViy = random.uniform(-25, 25)
        frisbees.append((FPix, FPin, FVix, FViy))
    
    return N, M, dogs, frisbees

def generate_test_case():
    N, M, dogs, frisbees = tcgen()
    
    print(f"{N} {M}")
    for Dix, Diy, Vi in dogs:
        print(f"{Dix:.6f} {Diy:.6f} {Vi:.6f}")
    for FPix, FPin, FVix, FViy in frisbees:
        print(f"{FPix:.6f} {FPin:.6f} {FVix:.6f} {FViy:.6f}")
    print("0 0")

# Example usage
generate_test_case()
```

### Explanation:
1. **Random Number of Dogs and Frisbees**: 
    - We generate a random number of dogs (N) between 1 and 10.
    - We generate a random number of frisbees (M) between 1 and 1000.

2. **Generating Dogs**:
    - For each dog, we generate random initial positions (Dix, Diy) between -1000 and 1000.
    - We generate a random speed (Vi) between 1 and 100.

3. **Generating Frisbees**:
    - For each frisbee, we generate random launch positions (FPix, FPin) between -1000 and 1000.
    - We generate random velocity components (FVix, FViy) between -25 and 25.

4. **Output**:
    - We print the number of dogs and frisbees first.
    - Then we print the details of each dog and each frisbee in the required format.
    - At the end, we print "0 0" to indicate the end of the input.

You can run the `generate_test_case` function to produce a random test case for the problem.

Extract Arguments

def extract_arguments(fh):
    datasets = []
    while True:
        N, M = map(int, fh.readline().strip().split())
        if N == 0 and M == 0:
            break
        dogs = []
        for _ in range(N):
            Dix, Diy, Vi = map(float, fh.readline().strip().split())
            dogs.append((Dix, Diy, Vi))
        frisbees = []
        for _ in range(M):
            FPix, FPin, FVix, FViy = map(float, fh.readline().strip().split())
            frisbees.append((FPix, FPin, FVix, FViy))
        datasets.append((N, M, dogs, frisbees))
    return datasets

# Example usage:
# with open('input.txt', 'r') as fh:
#     datasets = extract_arguments(fh)
#     for dataset in datasets:
#         N, M, dogs, frisbees = dataset
#         print("N:", N, "M:", M)
#         print("Dogs:", dogs)
#         print("Frisbees:", frisbees)