Solution: Minimum Window Substring

Statement

Given two strings, s and t, find the minimum window substring in s, which has the following properties:

1. It is the shortest substring of s that includes all of the characters present in t.

2. It must contain at least the same frequency of each character as in t.

3. The order of the characters does not matter here.

Constraints:

• Strings s and t consist of uppercase and lowercase English characters.

• 1 $\leq$ s.length, t.length $\leq 10^3$

Solution

So far, you’ve probably brainstormed some approaches and have an idea of how to solve this problem. Let’s explore some of these approaches and figure out which one to follow based on considerations such as time complexity and any implementation constraints.

Naive approach

The naive approach would be to find all possible substrings of s and then identify the shortest substring that contains all characters of t with corresponding frequencies equal to or greater than those in t.

To find all possible substrings, we will iterate over s one character at a time. For each character, we will form all possible substrings starting from that character.

We will keep track of the frequencies of the characters in the current substring. If the frequencies of the characters of t in the substring are equal to or greater than their overall frequencies in t, save the substring given that the length of this substring is less than the one already saved. After traversing s, return the minimum window substring.

The time complexity of this approach will be $O(n^2)$, where $n$ is ...