Problem Description

You have a Goal Parser that interprets a string command containing only three possible patterns: "G", "()", and "(al)".

The parser follows these interpretation rules:

• "G" → remains as "G"
• "()" → becomes "o"
• "(al)" → becomes "al"

Given a string command that consists of these patterns in some order, you need to return the parsed result after applying all the interpretation rules. The interpreted strings are concatenated in the same order as they appear in the original command.

For example:

• If command = "G()(al)", the parser would interpret it as "G" + "o" + "al" = "Goal"
• If command = "(())", the parser would interpret it as "o" + "o" = "oo"

The solution uses string replacement to transform "()" to "o" and "(al)" to "al", while "G" remains unchanged.

Intuition

The key observation is that we have a fixed set of patterns that need to be transformed. Since there are only three possible patterns ("G", "()", and "(al)"), and each has a direct one-to-one mapping to its interpretation, we can think of this as a simple substitution problem.

Notice that:

• "G" maps to itself, so we don't need to do anything with it
• "()" always maps to "o"
• "(al)" always maps to "al"

The patterns don't overlap in a problematic way - we won't accidentally replace part of one pattern while trying to replace another. For instance, "()" and "(al)" both start with "(" but "()" is completely distinct from "(al)".

This leads us to realize we can simply use string replacement operations. We can replace all occurrences of "()" with "o" and all occurrences of "(al)" with "al". The order of these replacements doesn't matter because:

1. The patterns are non-overlapping
2. Once we replace "()" with "o", it won't interfere with replacing "(al)"
3. Once we replace "(al)" with "al", there are no more parentheses to cause confusion

This direct replacement approach is both simple and efficient, making it the natural solution for this pattern matching problem.

Solution Approach

The implementation uses a straightforward string replacement strategy. Since we identified that this is a simple substitution problem with non-overlapping patterns, we can use built-in string replacement methods.

The solution performs two sequential replacements on the input string:

1. First replacement: Replace all occurrences of "()" with "o"

   • This transforms empty parentheses into the letter 'o'
   • After this step, command.replace('()', 'o') returns a new string with all "()" substituted

2. Second replacement: Replace all occurrences of "(al)" with "al"

   • This essentially removes the parentheses around "al"
   • We apply .replace('(al)', 'al') on the result from step 1

The method chaining approach command.replace('()', 'o').replace('(al)', 'al') ensures both transformations are applied in sequence. The order of replacements is important here - we first handle "()" then "(al)" to avoid any potential interference, though in this case both orders would work correctly due to the non-overlapping nature of the patterns.

The "G" characters don't need any transformation, so they remain unchanged throughout the process.

Time Complexity: O(n) where n is the length of the command string, as string replacement operations scan through the string.

Space Complexity: O(n) for creating the new string with replacements (strings are immutable in Python, so each replace operation creates a new string).

Example Walkthrough

Let's walk through the solution with the example command = "G()()(al)".

Initial string: "G()()(al)"

Step 1: Replace all "()" with "o"

• We scan through the string and identify all occurrences of "()"
• The string has two consecutive "()" patterns after the "G"
• After replacement: "G()()(al)" → "Goo(al)"
• Notice that "G" remains unchanged and "(al)" is still intact

Step 2: Replace all "(al)" with "al"

• Now we scan the modified string "Goo(al)" for "(al)" patterns
• We find one occurrence at the end
• After replacement: "Goo(al)" → "Gooal"
• This effectively removes the parentheses around "al"

Final result: "Gooal"

Let's trace through the code execution:

command = "G()()(al)"
result = command.replace('()', 'o').replace('(al)', 'al')
#        ↓
#        "Goo(al)".replace('(al)', 'al')
#        ↓
#        "Gooal"

The beauty of this approach is that each pattern is handled independently:

• The two "()" patterns become two "o" characters
• The one "(al)" pattern becomes "al"
• The "G" stays as is
• Everything concatenates naturally in the original order: "G" + "o" + "o" + "al" = "Gooal"

Solution Implementation

Time and Space Complexity

Time Complexity: O(n) where n is the length of the input string command.

The replace() method in Python needs to scan through the entire string to find and replace occurrences of the pattern. Each call to replace() takes O(n) time. Since we have two consecutive replace() operations, the total time complexity is O(n) + O(n) = O(n). Note that the second replace() operates on the result of the first replace(), but the string length remains proportional to n (it can only get shorter, not longer).

Space Complexity: O(n) where n is the length of the input string command.

In Python, strings are immutable, so each replace() operation creates a new string. The first replace() creates an intermediate string of size at most n, and the second replace() creates the final result string also of size at most n. Since we don't keep references to the intermediate string after it's used, and considering that the output string needs to be returned anyway, the space complexity is O(n) for storing the result string.

Learn more about how to find time and space complexity quickly.

Common Pitfalls

Pitfall: Incorrect Order of Replacements

One common mistake is attempting to replace "(al)" before "()", which can lead to incorrect results when the patterns are nested or adjacent.

Problematic Code:

def interpret(self, command: str) -> str:
    # Wrong order - replacing "(al)" first
    result = command.replace('(al)', 'al')
    result = result.replace('()', 'o')
    return result

Why it fails: Consider the input "(al)()". If we replace "(al)" first, we get "al()". Then replacing "()" gives us "alo", which is correct. However, this approach is conceptually backwards and could be confusing when reasoning about the solution.

Pitfall: Attempting Complex Parsing Logic

Another mistake is overcomplicating the solution by manually iterating through the string and trying to identify patterns character by character:

Overly Complex Approach:

def interpret(self, command: str) -> str:
    result = []
    i = 0
    while i < len(command):
        if command[i] == 'G':
            result.append('G')
            i += 1
        elif command[i:i+2] == '()':
            result.append('o')
            i += 2
        elif command[i:i+4] == '(al)':
            result.append('al')
            i += 4
    return ''.join(result)

Why it's problematic: While this works, it's unnecessarily complex, harder to read, more prone to index errors, and doesn't leverage Python's built-in string methods.

Solution to Avoid Pitfalls:

Best Practice Implementation:

def interpret(self, command: str) -> str:
    # Method 1: Chain replacements in the correct order
    return command.replace('()', 'o').replace('(al)', 'al')
  
    # Alternative Method 2: Use separate steps for clarity
    # result = command.replace('()', 'o')
    # result = result.replace('(al)', 'al')
    # return result

Key Points:

1. Use built-in string methods when they perfectly fit the problem
2. Keep the solution simple and readable
3. The order replace('()', 'o') then replace('(al)', 'al') works because:
   • After replacing "()" with "o", no new "()" patterns are created
   • The "(al)" patterns remain intact after the first replacement
   • Both patterns are non-overlapping and don't interfere with each other