migrate 392 questions to pattern format

backend/data/questions/kth-largest-element-in-an-array.yaml

@@ -8,8 +8,10 @@ categories:
   - sorting
   - heap
 patterns:
-  - heap
-  - binary-search
+  - slug: heap
+    is_optimal: true
+  - slug: binary-search
+    is_optimal: false
 
 function_signature: "def find_kth_largest(nums: list[int], k: int) -> int:"
 
@@ -144,6 +146,31 @@ explanation:
   time_complexity: "O(n log k). We iterate through all `n` elements, and each heap operation (push/pop) takes `O(log k)` time since the heap size is bounded by `k`."
   space_complexity: "O(k). We maintain a heap containing at most `k` elements."
 
+  pattern_comparison: |
+    **Heap vs Quickselect: Choosing the Right Pattern**
+
+    Both approaches avoid full sorting, but they have different characteristics:
+
+    | Approach | Time (Avg) | Time (Worst) | Space | Modifies Input? |
+    |----------|------------|--------------|-------|-----------------|
+    | **Min Heap** | O(n log k) | O(n log k) | O(k) | No |
+    | **Quickselect** | O(n) | O(n²) | O(log n) | Yes |
+    | **Sorting** | O(n log n) | O(n log n) | O(1)-O(n) | Yes |
+
+    **When to choose Heap:**
+    - You need **guaranteed** performance (no worst-case quadratic time)
+    - The input array shouldn't be modified
+    - `k` is small relative to `n` (the O(log k) factor stays small)
+    - You're working with streaming data
+
+    **When to choose Quickselect:**
+    - You need the **fastest average** performance
+    - Modifying the input array is acceptable
+    - You're comfortable with randomised algorithms
+    - Space is at a premium (O(log n) recursion vs O(k) heap)
+
+    **Interview tip:** Start with Heap for its simplicity and guaranteed bounds, then mention Quickselect as an optimisation if the interviewer asks about O(n) solutions.
+
 solutions:
   - approach_name: Min-Heap
     is_optimal: true