migrate 392 questions to pattern format

backend/data/questions/reorganize-string.yaml

@@ -8,8 +8,10 @@ categories:
   - hash-tables
   - heap
 patterns:
-  - greedy
-  - heap
+  - slug: heap
+    is_optimal: true
+  - slug: greedy
+    is_optimal: false
 
 function_signature: "def reorganize_string(s: str) -> str:"
 
@@ -133,6 +135,32 @@ explanation:
   time_complexity: "O(n log k). We process each of the `n` characters, and each heap operation takes O(log k) where `k` is the number of unique characters (at most 26)."
   space_complexity: "O(k). We store at most `k` unique characters in the heap and hash map, where `k <= 26` for lowercase English letters."
 
+  pattern_comparison: |
+    **Heap Greedy vs Odd-Even Placement: Two Valid Approaches**
+
+    Both solutions achieve optimal results through different strategies:
+
+    | Approach | Time | Space | Key Insight |
+    |----------|------|-------|-------------|
+    | **Max Heap** | O(n log k) | O(k) | Always place the most frequent available character |
+    | **Odd-Even** | O(n + k log k) | O(n) | Separate characters by index parity |
+
+    **Heap Greedy (Online):**
+    - Builds the string character by character
+    - Naturally handles the "don't repeat" constraint via the hold-back pattern
+    - More intuitive: "always pick the best available option"
+
+    **Odd-Even Placement (Batch):**
+    - First fills even indices (0, 2, 4...), then odd indices (1, 3, 5...)
+    - Characters at even indices can never be adjacent to each other
+    - Exploits the constraint: if max_freq ≤ (n+1)/2, even indices can hold all instances of the most frequent character
+
+    **When to prefer each:**
+    - **Heap**: When you need to explain the greedy logic step-by-step, or for streaming inputs
+    - **Odd-Even**: When you want simpler code (no heap needed), or when explaining the mathematical feasibility condition
+
+    **Both share the same core insight**: Check `max_freq ≤ (n+1)/2` first — this determines whether a solution is even possible.
+
 solutions:
   - approach_name: Max Heap (Greedy)
     is_optimal: true