🦄 Rainbow Window: Minimum Covering Substring

Difficulty: Advanced Tags: sliding-window, hashmap, two-pointer, strings, optimization Series: CS 102: Problem Solving & Logic

Problem

In the mystical realm, rainbow windows reveal the shortest magical span containing all required runes. Find the minimum window in string s that contains all characters from string t (including their required frequencies).

Given two strings s and t, return the minimum substring of s that contains all characters from t (including duplicates). If no such substring exists, return an empty string ''.

Real-World Application

Minimum window substring appears in: - Text editors - find & highlight feature, search with wildcards - Genomics - finding DNA subsequences containing specific patterns - Data compression - identifying minimal encoding windows - Log analysis - finding log entries containing all required keywords - Search engines - ranking documents by keyword proximity - Network packet analysis - identifying frames with specific byte patterns - Cybersecurity - pattern matching in malware detection

Input

data = {
    's': str,  # Source string to search within
    't': str   # Target string with required characters
}

Output

str  # Minimum window substring, or '' if none exists

Constraints

• 1 ≤ len(t) ≤ len(s) ≤ 100,000
• ASCII letters only (uppercase and lowercase)
• Must match character frequencies (multiplicities)
• Aim for O(n) solution with sliding window

Examples

Example 1: Basic Minimum Window

Input:

{'s': 'ADOBECODEBANC', 't': 'ABC'}

Output: 'BANC'

Explanation: - Windows containing ABC: - 'ADOBEC' (length 6) - contains A, B, C ✓ - 'ODEBANC' (length 7) - contains A, B, C ✓ - 'BANC' (length 4) - contains A, B, C ✓ shortest! - Return 'BANC'

Example 2: Impossible (Not Enough Characters)

Input:

{'s': 'a', 't': 'aa'}

Output: ''

Explanation: - s has only one 'a', but t requires two 'a's - Impossible to satisfy requirement - Return empty string

Example 3: Repeated Characters

Input:

{'s': 'aaabdabcefaecbef', 't': 'abc'}

Output: 'abc'

Explanation: - Need one each of 'a', 'b', 'c' - 'abc' at position 6-8 is the shortest window - Other valid windows are longer

Example 4: Entire String

Input:

{'s': 'abc', 't': 'abc'}

Output: 'abc'

Explanation: - The entire string is the minimum (and only) valid window

Example 5: Multiple Occurrences

Input:

{'s': 'ABAACBAB', 't': 'AAB'}

Output: 'BAAC' or 'AACB' or 'ACBA'

Explanation: - Need 2 A's and 1 B - Multiple windows of length 4 exist - Any one is valid (problem asks for any minimum window)

Example 6: At the End

Input:

{'s': 'abcdefgABC', 't': 'ABC'}

Output: 'ABC'

Explanation: - Minimum window is at the very end - Length 3

What You'll Learn

• Sliding window technique with dynamic expansion/contraction
• Using hash maps to track character frequencies
• Two-pointer approach for optimization
• How to maintain a valid window invariant
• Handling character multiplicities (duplicates)

Why This Matters

This is a top-tier coding interview question (LeetCode Hard) that tests: - Advanced string manipulation - Hash map proficiency - Sliding window pattern mastery - Optimization skills (O(n) solution) - Edge case handling

Companies that ask this: Google, Facebook, Amazon, Microsoft, Uber

Starter Code

def challenge_function(data):
    """
    Find minimum window in s that contains all characters from t.

    Args:
        data: dict with keys:
            - 's' (str): source string to search within
            - 't' (str): target string with required characters

    Returns:
        str: minimum window substring, or '' if none exists
    """
    # Your implementation here
    pass