5_expspace_labyrinth.py

# The Labyrinth of Eternal Reflection

'''Deep within the ancient Labyrinth of Eternal Reflection, there resides a magical mirror that holds immense power. This mirror has the ability to reflect any sequence of symbols entered into it and generate a corresponding output sequence. However, the mirror is quite temperamental and has certain limitations:

    Limitation 1: The mirror can only handle sequences of symbols up to a certain length.
    Limitation 2: The mirror can only reflect sequences that satisfy a specific pattern.

Your task is to determine if it is possible to find a sequence of symbols that can be reflected by the mirror while satisfying these limitations. We can encode this problem as an EXP-Space problem.

Let's assume that the mirror can handle sequences of symbols up to length n. We need to find a sequence of symbols of length n that satisfies the given pattern when reflected.

To solve this EXP-Space problem, we can use an exhaustive search algorithm. We will generate all possible sequences of symbols of length n and check if any of them satisfy the reflection pattern.'''



def generate_sequences(symbols, length):
    if length == 0:
        return [[]]
    
    sequences = []
    for symbol in symbols:
        sub_sequences = generate_sequences(symbols, length - 1)
        for sub_sequence in sub_sequences:
            sequence = [symbol] + sub_sequence
            sequences.append(sequence)
    
    return sequences

def reflect_sequence(sequence):
    # Mirror reflection logic goes here
    return sequence[::-1]

def find_reflected_sequence(symbols, length, pattern):
    sequences = generate_sequences(symbols, length)
    
    for sequence in sequences:
        reflected_sequence = reflect_sequence(sequence)
        if reflected_sequence == pattern:
            return sequence
    
    return None

# Example usage
symbols = ['A', 'B', 'C']
length = 4
pattern = ['C', 'A', 'B', 'C']

reflected_sequence = find_reflected_sequence(symbols, length, pattern)
if reflected_sequence:
    print("A sequence that satisfies the reflection pattern is:", reflected_sequence)
else:
    print("No sequence satisfies the reflection pattern.")



'''In this code, we first define a function generate_sequences() that generates all possible sequences of symbols of a given length. It uses a recursive approach to generate sequences by iteratively appending symbols to the sequences of shorter length.

Next, we define a function reflect_sequence() that takes a sequence and performs the mirror reflection operation on it.

Finally, we define the main function find_reflected_sequence() that generates all possible sequences of symbols of the specified length and checks if their reflected sequence matches the given pattern. If a matching sequence is found, it is returned; otherwise, None is returned.'''