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Change Minimum Characters to Satisfy One of Three Conditions

Difficulty: Medium

Problem Description

You are given two strings a and b that consist of lowercase letters. In one operation, you can change any character in a or b to any lowercase letter. Your goal is to satisfy one of the following three conditions:

  1. Every letter in a is strictly less than every letter in b in the alphabet.
  2. Every letter in b is strictly less than every letter in a in the alphabet.
  3. Both a and b consist of only one distinct letter.

Return the minimum number of operations needed to achieve your goal.

Key Insights

  • To achieve the first two conditions, assess the smallest and largest letters in both strings.
  • For condition 3, both strings need to be transformed to a single common character.
  • The most efficient transformation involves counting how many characters need to be changed for each of the three conditions and selecting the minimum.

Space and Time Complexity

Time Complexity: O(n) where n is the length of the longer string since we may need to traverse both strings. Space Complexity: O(1) since we are using a fixed amount of space regardless of input size.

Solution

To solve this problem, we can use the following approach:

  1. Identify the minimum and maximum characters in both strings a and b.
  2. Calculate the number of changes required to satisfy each of the three conditions:
    • For condition 1 (a < b), change all characters in b that are less than or equal to the maximum character in a.
    • For condition 2 (b < a), change all characters in a that are greater than or equal to the minimum character in b.
    • For condition 3, determine how many characters in both strings need to be changed to make both strings consist of a single common character.
  3. Return the minimum number of operations from the three conditions.

Code Solutions

def min_operations(a: str, b: str) -> int:
    # Find the minimum and maximum characters in both strings
    min_a, max_a = min(a), max(a)
    min_b, max_b = min(b), max(b)
    
    # Calculate operations for condition 1 (a < b)
    operations1 = sum(1 for char in b if char <= max_a)
    
    # Calculate operations for condition 2 (b < a)
    operations2 = sum(1 for char in a if char >= min_b)
    
    # Calculate operations for condition 3 (both are one distinct letter)
    operations3 = len(a) + len(b) - max(a.count(min_a), b.count(min_a), a.count(max_a), b.count(max_a))
    
    # Return the minimum operations needed from all conditions
    return min(operations1, operations2, operations3)
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