migrate 392 questions to pattern format

backend/data/questions/contains-duplicate.yaml

@@ -7,7 +7,8 @@ categories:
   - arrays
   - hash-tables
 patterns:
-  - heap
+  - slug: hashing
+    is_optimal: true
 
 function_signature: "def contains_duplicate(nums: list[int]) -> bool:"
 
@@ -138,6 +139,38 @@ explanation:
   time_complexity: "O(n). We traverse the array once, with O(1) set operations at each step."
   space_complexity: "O(n). In the worst case (all unique elements), we store all n elements in the set."
 
+  pattern_comparison: |
+    **Hash Set vs Sorting: The Classic Space-Time Trade-off**
+
+    Two fundamentally different approaches, each optimal in different contexts:
+
+    | Approach | Time | Space | Modifies Input? | Early Exit? |
+    |----------|------|-------|-----------------|-------------|
+    | **Hash Set** | O(n) | O(n) | No | Yes |
+    | **Sorting** | O(n log n) | O(1)* | Yes | Yes |
+
+    *In-place sorting like quicksort uses O(1) extra space (ignoring recursion stack).
+
+    **When Hash Set is better:**
+    - Memory is plentiful (most modern systems)
+    - Input must not be modified
+    - You need the fastest possible runtime
+    - Data is already streaming in one element at a time
+
+    **When Sorting is better:**
+    - Memory is extremely constrained (embedded systems, very large arrays)
+    - Modifying the input is acceptable
+    - You also need the sorted array for subsequent operations
+    - The data is nearly sorted (adaptive sorts like Timsort are very fast)
+
+    **The one-liner alternative:**
+    ```python
+    return len(nums) != len(set(nums))
+    ```
+    This is clean and Pythonic, but always processes all elements (no early exit). The iterative set approach can exit immediately upon finding a duplicate, which is faster when duplicates appear early.
+
+    **Foundation pattern**: This simple problem teaches the fundamental "have I seen this before?" pattern that appears in Two Sum, cycle detection, and many other problems.
+
 solutions:
   - approach_name: Hash Set
     is_optimal: true