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Apply Operations to Make String Empty

Difficulty: Medium

Problem Description

You are given a string s. Consider performing the following operation until s becomes empty: For every alphabet character from 'a' to 'z', remove the first occurrence of that character in s (if it exists). Return the value of the string s right before applying the last operation.

Key Insights

  • Each character from 'a' to 'z' must be processed in order.
  • The operation continues until all characters are removed, leaving an empty string.
  • The result is the string just before the last operation, which can be determined by tracking the sequence of characters removed.

Space and Time Complexity

Time Complexity: O(n), where n is the length of the string s. Each character is processed a constant number of times. Space Complexity: O(1), since we use a fixed amount of space for character tracking (only 26 letters).

Solution

To solve the problem, we can iterate through the string and keep track of the characters we need to remove. A list is used to construct the string that remains before the last operation. We will use a set to keep track of characters that have been removed. The algorithm processes each character in the input string, removing the first occurrence of each character in alphabetical order until the string is empty. The last valid state of the string will be the answer.

Code Solutions

def apply_operations_to_make_string_empty(s: str) -> str:
    # Initialize a set to keep track of removed characters
    removed = set()
    result = []

    # Iterate through the string to build the result
    for char in s:
        # If the character has not been removed, add it to the result
        if char not in removed:
            result.append(char)
            removed.add(char)  # Mark this character as removed

    # Join the result list to form the final string before the last operation
    return ''.join(result)

# Example usage
print(apply_operations_to_make_string_empty("aabcbbca"))  # Output: "ba"
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