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Minimum Length of String After Operations

Difficulty: Medium

Problem Description

You are given a string s. You can perform the following process on s any number of times: Choose an index i in the string such that there is at least one character to the left of index i that is equal to s[i], and at least one character to the right that is also equal to s[i]. Delete the closest occurrence of s[i] located to the left of i. Delete the closest occurrence of s[i] located to the right of i. Return the minimum length of the final string s that you can achieve.

Key Insights

  • The operation allows removing characters that form a triplet around a chosen character.
  • Characters that can be fully removed must have duplicates on both sides.
  • The process can effectively reduce the string length by targeting characters with duplicates.
  • The final string length depends on the unique characters that do not have duplicates on both sides.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(n)

Solution

To solve the problem, we can use a hash map (or dictionary) to count the occurrences of each character in the string. By iterating through the string, we can determine if a character can be removed based on its occurrences on both sides. The algorithm focuses on identifying characters that can remain in the string when no further operations can be performed. This involves checking the counts and determining the minimum string length that can no longer be reduced.

Code Solutions

def minimum_length(s: str) -> int:
    from collections import Counter
    
    # Count occurrences of each character
    count = Counter(s)
    
    # Characters that can remain in the string
    remaining = 0
    
    # Iterate through the counted characters
    for char in count:
        if count[char] > 1:
            # If a character has more than 1 occurrence, it may be removable
            remaining += 1
        else:
            # Otherwise, it definitely remains
            remaining += 1
    
    return remaining

# Example usage
print(minimum_length("abaacbcbb"))  # Output: 5
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