What is the brute force approach and complexity for Minimum Window Substring?

For each start, grow right and check all 128 counts after every step with time complexity O(|s|² · 128) and space complexity O(128).

What is the optimal approach and complexity for Minimum Window Substring?

Track how many characters of t are still missing; covered when missing == 0 with optimal time complexity O(|s| + |t|) and space complexity O(128).

How do you identify the pattern for Minimum Window Substring?

Look for key signals in the prompt: "minimum window / shortest substring" indicates Contiguous range, minimise length → variable window, record inside the shrink loop.; "contains all characters of t" indicates The rule is about counts inside the window compared with a target → need map.; "including duplicates" indicates Counts, not a set. "AAB" needs two A's..

Minimum Window Substring

Hard·LeetCode #76 Pro OnlyInterview-Level

LeetCode

Problem Statement

You are given two strings s and t.

Find the shortest substring of s that contains every character of t, including repeats. For example, if t = "AAB", the substring needs at least two 'A' and one 'B'. Other characters may also appear in it.

Return that substring. If no such substring exists, return the empty string "".

The test data guarantees the answer is unique.

Input

Two strings s and t of uppercase and lowercase English letters.

Output

The shortest substring of s that covers all characters of t (with counts), or "" if none exists.

Example 1

Input: s = "ADOBECODEBANC", t = "ABC"

Output: "BANC"

"BANC" has an A, a B and a C. No shorter substring has all three.

Example 2

Input: s = "a", t = "a"

Output: "a"

The whole string is the answer.

Example 3

Input: s = "a", t = "aa"

Output: ""

t needs two 'a' but s has only one, so no substring works.

Constraints

• 1 ≤ s.length, t.length ≤ 10^5
• s and t contain only uppercase and lowercase English letters
• Follow-up: can you do it in O(|s| + |t|) time?

Pattern Recognition Clues

Recognising these key signals in the problem description immediately identifies the pattern:

“minimum window / shortest substring”

→ Contiguous range, minimise length → variable window, record inside the shrink loop.

“contains all characters of t”

→ The rule is about counts inside the window compared with a target → need map.

“including duplicates”

→ Counts, not a set. "AAB" needs two A's.

Approach Complexity Ladder

Brute Force — every start, grow until it covers tO(|s|² · 128)O(128)

For each start, grow right and check all 128 counts after every step

Better — sliding window with a full count checkO(128 · |s| + |t|)O(128)

Grow right; while the window covers t (checked over 128 chars), record and shrink

Optimal — sliding window with a `missing` counterO(|s| + |t|)O(128)

Track how many characters of t are still missing; covered when missing == 0

Brute Force Intuition

Try every start. Grow the end one character at a time and keep counts for the window. After each step, compare the window's counts with t's counts for all 128 characters. The first end where the window covers t gives the shortest window for that start; stop there and move to the next start.

Recognition rule for this sub-pattern:

Validity depends on the counts of things inside the window (distinct types, most frequent char, required letters). Keep a count map that updates on every add/remove.

Remember this · Sliding Window

Trigger

Contiguous subarray / substring + longest, shortest, maximum, count, or "of size K".

Think

Can I keep a valid range and move it, instead of checking every subarray from scratch?

Key question

When is my current window valid?

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