What is the optimal time complexity of solving Minimum Window Substring?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Minimum Window Substring?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Minimum Window Substring?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Minimum Window Substring?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Minimum Window Substring

Learn how to solve the 'Minimum Window Substring' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Given two strings s and t of lengths m and n respectively, return the minimum window substring of s such that every character in t (including duplicates) is included in the window. If there is no such substring, return the empty string "".

The answer is guaranteed to be unique.

Write a function minWindow(s: str, t: str) -> str.

Constraints

•m == len(s), n == len(t)
•1 <= m, n <= 10^5
•s and t consist of uppercase and lowercase English letters

Examples

Example 1

Input

s = "ADOBECODEBANC", t = "ABC"

Output

"BANC"

Explanation

The minimum window substring "BANC" (indices 9-12) contains 'A', 'B', and 'C' from t.

Example 2

Input

s = "a", t = "a"

Output

"a"

Explanation

The entire string s is the minimum window.

Example 3

Input

s = "a", t = "aa"

Output

""

Explanation

Both 'a's from t must be included. Since s only has one 'a', return empty string.

Need a Hint?

Maintain a sliding window boundary using two pointers. Expand the right boundary, and contract the left boundary if criteria are violated.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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