Smallest Window Containing All Features

This problem requires finding the minimum length contiguous substring of features that contains all unique characters from required (with their required frequencies). It's a classic Sliding Window + Required Characters Coverage problem.

1. Background Knowledge

Key Concepts:

• Sliding Window Technique: Maintain a window [left, right] that expands/contracts to satisfy conditions
• Character Frequency Tracking: Count occurrences of each required character in current window
• Coverage Condition: Window is valid when every character in required appears ≥ its required count
• Two-Pointer Technique: right expands window, left contracts when condition met to minimize size

Prerequisites:

• Hash maps/dictionaries for O(1) frequency updates
• Understanding of amortized analysis for sliding window

2. Algorithm Approach

Optimal Algorithm: Sliding Window with Counter Tracking

1. Count required frequencies: req_count[char] = frequency in 'required'
2. Track current window frequencies: window_count[char]
3. Maintain 'needed' = number of unique characters still required
4. Expand right pointer, update window_count
5. When needed == 0, record min_length, shrink left pointer
6. Repeat until right reaches end

Time Complexity: $O(n + m)$ where $n = |features|$, $m = |required|$ Space Complexity: $O(|\Sigma|)$ where $\Sigma$ is alphabet size (≤52 for English letters)

Why Optimal? Each character processed at most twice (right expansion + left contraction)

3. Step-by-Step Strategy

def smallest_window(features: str, required: str) -> int:
 if not required or not features:
 return 0

 # Step 1: Count required frequencies
 req_count = {}
 for char in required:
 req_count[char] = req_count.get(char, 0) + 1

 needed = len(req_count) # Unique chars needed
 window_count = {}
 left = 0
 min_len = float('inf')

 # Step 2: Slide window
 for right in range(len(features)):
 char = features[right]