1737 - Change Minimum Characters to Satisfy One of Three Conditions.

Medium

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:

• Every letter in a is strictly less than every letter in b in the alphabet.

• Every letter in b is strictly less than every letter in a in the alphabet.

• Both a and b consist of only one distinct letter.

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

Example 1:

Input: a = "aba", b = "caa"

Output: 2

Explanation: Consider the best way to make each condition true:

• Change b to "ccc" in 2 operations, then every letter in a is less than every letter in b.

• Change a to "bbb" and b to "aaa" in 3 operations, then every letter in b is less than every letter in a.

• Change a to "aaa" and b to "aaa" in 2 operations, then a and b consist of one distinct letter. The best way was done in 2 operations (either condition 1 or condition 3).

Example 2:

Input: a = "dabadd", b = "cda"

Output: 3

Explanation: The best way is to make condition 1 true by changing b to "eee".

Constraints:

• <code>1 <= a.length, b.length <= 10⁵</code>

• a and b consist only of lowercase letters.