2565. Subsequence With the Minimum Score

Problem Link

Description

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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 t a 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 "abcde" 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:

• 1 <= s.length, t.length <= 105
• s and t consist of only lowercase English letters.

Solution

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Python3

class Solution:
    def minimumScore(self, s: str, t: str) -> int:
        N, M = len(s), len(t)
        j = 0
        leftMost = []
 
        for i, x in enumerate(s):
            if x == t[j]:
                j += 1
            
            if j == M: return 0
 
            leftMost.append(j)
        
        res = M
        right = M - 1
 
        for i in range(N - 1, -1, -1):
            if leftMost[i] <= right:
                res = min(res, right - leftMost[i] + 1)
            
            if s[i] == t[right]:
                right -= 1
            
            res = min(res, right + 1)
 
        return res