migrate 392 questions to pattern format

backend/data/patterns/patterns.yaml

@@ -177,3 +177,83 @@ patterns:
       - Flood fill
       - Rotting oranges
       - Word search in grid
+
+  - name: Topological Sort
+    slug: topological-sort
+    description: Order vertices in a directed acyclic graph (DAG) such that for every edge u→v, u comes before v.
+    when_to_use: |
+      - Course scheduling with prerequisites
+      - Build order / dependency resolution
+      - Task scheduling with dependencies
+      - Alien dictionary problems
+      - Detecting cycles in directed graphs
+
+  - name: Bit Manipulation
+    slug: bit-manipulation
+    description: Use bitwise operations (AND, OR, XOR, shifts) to solve problems efficiently.
+    when_to_use: |
+      - Finding single/missing numbers (XOR tricks)
+      - Counting set bits
+      - Power of two checks
+      - Subset generation with bitmasks
+      - Swapping without temp variable
+
+  - name: Counting / Bucket Sort
+    slug: counting-sort
+    description: Sort or process elements by using their values as indices when the range is bounded.
+    when_to_use: |
+      - Top K frequent elements (bounded frequency range)
+      - Sort Colors (Dutch National Flag)
+      - H-Index calculation
+      - Problems where values are in known small range
+      - Frequency-based grouping
+
+  - name: Cyclic Sort
+    slug: cyclic-sort
+    description: Place each element at its correct index when values are in range [1, n] or [0, n-1].
+    when_to_use: |
+      - Find missing number in [1, n]
+      - Find duplicate in [1, n]
+      - Find all missing/duplicate numbers
+      - First missing positive
+      - Set mismatch problems
+
+  - name: Divide and Conquer
+    slug: divide-and-conquer
+    description: Split problem into smaller subproblems, solve recursively, and combine results.
+    when_to_use: |
+      - Merge sort and related problems
+      - Quick select for kth element
+      - Binary search variants
+      - Matrix multiplication
+      - Closest pair of points
+
+  - name: Hashing
+    slug: hashing
+    description: Use hash tables for O(1) average lookup, insertion, and deletion.
+    when_to_use: |
+      - Two Sum and variants
+      - Detecting duplicates
+      - Frequency counting
+      - Anagram grouping
+      - LRU/LFU cache implementation
+
+  - name: Matrix Manipulation
+    slug: matrix-manipulation
+    description: Transform or process 2D matrices using rotation, transposition, or in-place modifications.
+    when_to_use: |
+      - Rotate image 90 degrees
+      - Spiral matrix traversal
+      - Set matrix zeroes
+      - Transpose matrix
+      - Game of Life state updates
+
+  - name: Synchronization
+    slug: synchronization
+    description: Coordinate multiple threads or processes using locks, semaphores, or barriers.
+    when_to_use: |
+      - Print in order problems
+      - Producer-consumer patterns
+      - Dining philosophers
+      - Building H2O molecules
+      - Concurrent data structure design