migrate 392 questions to pattern format

backend/data/questions/two-sum.yaml

@@ -7,7 +7,8 @@ categories:
   - arrays
   - hash-tables
 patterns:
-  - two-pointers
+  - slug: hashing
+    is_optimal: true
 
 function_signature: "def two_sum(nums: list[int], target: int) -> list[int]:"
 
@@ -135,6 +136,34 @@ explanation:
   time_complexity: "O(n). We traverse the array once, and each hash map lookup/insert is O(1) on average."
   space_complexity: "O(n). In the worst case, we store all n elements in the hash map before finding a match (e.g., when the solution is the last two elements)."
 
+  pattern_comparison: |
+    **Hash Map vs Two Pointers: Different Problems, Different Patterns**
+
+    Two Sum is often confused with sorted-array two-pointer problems, but they require different approaches:
+
+    | Approach | Time | Space | Requires Sorted Input? | Returns |
+    |----------|------|-------|------------------------|---------|
+    | **Hash Map** | O(n) | O(n) | No | Original indices |
+    | **Two Pointers** | O(n) | O(1) | Yes | Values or sorted indices |
+    | **Brute Force** | O(n²) | O(1) | No | Indices |
+
+    **Why Hash Map is optimal for this problem:**
+    - We need **original indices**, not just values
+    - Sorting would lose index information (or require O(n) extra space to track)
+    - Hash map gives O(1) lookup while preserving indices naturally
+
+    **When Two Pointers would apply:**
+    - If the array is already sorted
+    - If we only need to find the values (not indices)
+    - In space-constrained environments where O(n) extra space is prohibitive
+
+    **The Two Sum pattern family:**
+    - **Two Sum** (unsorted): Hash map for complement lookup
+    - **Two Sum II** (sorted): Two pointers from both ends
+    - **3Sum/4Sum**: Sort + Two pointers (indices don't matter)
+
+    Remember: The right pattern depends on what the problem asks for and what guarantees you have about the input.
+
 solutions:
   - approach_name: One-Pass Hash Map
     is_optimal: true