6_expspace_cryptic_vault.py

# The Cryptic Cipher Vault

'''In a hidden chamber deep beneath an ancient castle, there lies a vault containing cryptic ciphers. Each cipher consists of a sequence of symbols arranged in a particular pattern. The mysterious guardian of the vault, known as the Cipher Keeper, has set the following rules for deciphering the codes:

    Rule 1: Each cipher must be decrypted by finding a specific sequence of symbols that satisfies a given transformation pattern.
    Rule 2: The transformation pattern is complex and requires checking a large number of possibilities.

Your task is to determine if it is possible to find a sequence of symbols that satisfies the transformation pattern and decrypts the cipher. We can encode this problem as an EXP-Space problem.

Let's assume that the cipher consists of a sequence of symbols of length n. We need to find a sequence of symbols that satisfies the given transformation pattern when applied to the cipher.

To solve this EXP-Space problem, we can use a backtracking algorithm combined with pruning techniques. We will systematically generate and explore all possible sequences of symbols of length n and check if any of them satisfy the transformation pattern. Pruning techniques can be applied to eliminate certain branches of the search tree based on early failures or constraints.'''


def decrypt_cipher(cipher, pattern):
    n = len(cipher)
    symbols = set(cipher)  # Unique symbols in the cipher
    
    def backtrack(sequence):
        if len(sequence) == n:
            if apply_pattern(sequence) == pattern:
                return sequence
        
        for symbol in symbols:
            new_sequence = sequence + [symbol]
            if is_valid(new_sequence):
                result = backtrack(new_sequence)
                if result:
                    return result
        
        return None
    
    def is_valid(sequence):
        # Additional constraints on the sequence, if any
        return True
    
    def apply_pattern(sequence):
        # Transformation pattern logic goes here
        return sequence  # Placeholder logic: returning the sequence as is
    
    return backtrack([])

# Example usage
cipher = ['A', 'B', 'C', 'D']
pattern = ['C', 'A', 'D', 'B']

decrypted_sequence = decrypt_cipher(cipher, pattern)
if decrypted_sequence:
    print("A sequence that satisfies the transformation pattern is:", decrypted_sequence)
else:
    print("No sequence satisfies the transformation pattern.")


'''
In this code, we define a function decrypt_cipher() that takes a cipher and a transformation pattern as input. The main algorithm is implemented in the backtrack() function using a backtracking approach.

The backtrack() function systematically generates and explores all possible sequences of symbols by recursively appending symbols to the current sequence. At each step, it checks if the current sequence satisfies the transformation pattern by applying the apply_pattern() function. If a matching sequence is found, it is returned; otherwise, the search continues.

The is_valid() function can be used to incorporate additional constraints or pruning techniques to optimize the search process. In this example, it serves as a placeholder function that accepts all sequences as valid.


'''