2565 - Subsequence With the Minimum Score\.

Hard

You are given two strings s and t.

You are allowed to remove any number of characters from the string t.

The score of the string is 0 if no characters are removed from the string t, otherwise:

• Let left be the minimum index among all removed characters.

• Let right be the maximum index among all removed characters.

Then the score of the string is right - left + 1.

Return the minimum possible score to make ta subsequence of s.

A subsequence of a string is a new string that is formed from the original string by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. (i.e., "ace" is a subsequence of <code>"<ins>a</ins>b<ins>c</ins>d<ins>e</ins>"</code> while "aec" is not).

Example 1:

Input: s = "abacaba", t = "bzaa"

Output: 1

Explanation: In this example, we remove the character "z" at index 1 (0-indexed). The string t becomes "baa" which is a subsequence of the string "abacaba" and the score is 1 - 1 + 1 = 1. It can be proven that 1 is the minimum score that we can achieve.

Example 2:

Input: s = "cde", t = "xyz"

Output: 3

Explanation: In this example, we remove characters "x", "y" and "z" at indices 0, 1, and 2 (0-indexed). The string t becomes "" which is a subsequence of the string "cde" and the score is 2 - 0 + 1 = 3. It can be proven that 3 is the minimum score that we can achieve.

Constraints:

• <code>1 <= s.length, t.length <= 10⁵</code>

• s and t consist of only lowercase English letters.