algoadvance

You are given a string s containing lowercase English letters, digits, and underscores (‘_’). A string t is said to be an output of keyboard if t can be obtained by concatenating some characters in s (keeping the order). If Keyboard is known to be faulty, return the minimum possible length of t.

Clarifying Questions

  1. Do we have to maintain the order of characters in the resultant string t?
    • Yes, the order of characters must be the same as in the original string s.
  2. What should be the output if the string s is empty?
    • If s is empty, the minimum possible length of t would naturally be 0.
  3. Are there any restrictions on the characters allowed in the string?
    • The string s contains only lowercase English letters, digits, and underscores (‘_’).

Strategy

To achieve the minimum length of the output string t, we need to consider the longest subsequence (not necessarily contiguous) of s that contains distinct characters. The logic behind this is straightforward:

  1. Traverse through the string and keep adding characters if they are not already part of the result.
  2. Keep a set to track characters that have already been added to the result to ensure uniqueness.

Code

def min_length_t_from_faulty_keyboard(s: str) -> int:
    seen = set()
    t = ""
    
    for char in s:
        if char not in seen:
            seen.add(char)
            t += char
    
    return len(t)

# Example usage:
s = "aabb_cc_ddee12"
print(min_length_t_from_faulty_keyboard(s))  # Output: 9

Time Complexity

The time complexity of the above algorithm is ( O(n) ), where ( n ) is the length of the string s. This is because we are making a single pass through the string and performing constant-time operations (checking membership in a set and adding to a set) for each character.

Thus, the solution is efficient and should work well within typical input size constraints.

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