Naive Solution

A straightforward approach is to iterate through the input string command and use conditional statements to check for the patterns "G", "()", and "(al)". We can build the result string by concatenating the corresponding interpretations "G", "o", and "al", respectively.

Code

def interpret_naive(command: str) -> str:
    result = ""
    i = 0
    while i < len(command):
        if command[i] == 'G':
            result += 'G'
            i += 1
        elif command[i:i+2] == '()':
            result += 'o'
            i += 2
        else:
            result += 'al'
            i += 4
    return result

Time Complexity

The time complexity is O(n), where n is the length of the command string, as we iterate through the string once.

Space Complexity

The space complexity is O(n) in the worst case, as the result string can grow up to the size of the input if the input consists only of "G" characters.

Optimal Solution

A more concise and efficient approach involves using the replace() method to directly replace the patterns in the input string with their corresponding interpretations.

Code

def interpret_optimal(command: str) -> str:
    command = command.replace("()", "o")
    command = command.replace("(al)", "al")
    return command

Time Complexity

The time complexity is O(n), where n is the length of the command string. Although replace might seem like O(n*m), where m is the length of the string being replaced, in this case, it simplifies to O(n) because we do not have overlapping patterns that we are trying to replace.

Space Complexity

The space complexity is O(n) in the worst case due to the creation of new strings during the replacement operations. However, some implementations might perform the replacement in-place, leading to O(1) space complexity.

Edge Cases

• Empty string: If the input command is an empty string, the function should return an empty string.
• Invalid characters: The problem statement specifies that the command consists only of "G", "()", and "(al)". No error handling is needed for invalid characters.
• Overlapping patterns: The patterns "()" and "(al)" do not overlap, so we don't need to worry about ambiguous interpretations.