Solution: Minimum Window Subsequence

Statement▼

Given two strings, s1 and s2, find and return the shortest substring of s1 in which all the characters of s2 appear in the same order, but not necessarily next to each other (i.e., s2 should be a subsequence of the substring).

If no such substring exists, return an empty string "". If there are multiple shortest substrings, return the one that appears first in s1 (i.e., with the left-most starting index).

Note: A substring is a contiguous sequence of characters within a string. A subsequence is a sequence of characters that can be derived from a string by deleting some characters without changing the order of the remaining characters. For example, “edu” is a substring and “cave” is a subsequence of “educative.”

Constraints:

$1 \leq$ s1.length $\leq 2 \times 10^{3}$
$1 \leq$ s2.length $\leq 100$
s1 and s2 consist of uppercase and lowercase English letters.

Naive approach

The naive approach would be to generate all possible substrings of str1 and then check which substrings contain str2 as a subsequence. Out of all the substrings in str1 that contain str2 as a subsequence, we’ll choose the one with the shortest length. Now, let’s look at the cost of this solution. We need two nested loops to get all possible substrings and another loop to check whether each substring contains all the required characters. This brings the time complexity to $O(n^{3})$ ...

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Solution: Minimum Window Subsequence

Statement▼

If no such substring exists, return an empty string "". If there are multiple shortest substrings, return the one that appears first in s1 (i.e., with the left-most starting index).

Note: A substring is a contiguous sequence of characters within a string. A subsequence is a sequence of characters that can be derived from a string by deleting some characters without changing the order of the remaining characters. For example, “edu” is a substring and “cave” is a subsequence of “educative.”

Constraints:

$1 \leq$ s1.length $\leq 2 \times 10^{3}$
$1 \leq$ s2.length $\leq 100$
s1 and s2 consist of uppercase and lowercase English letters.