feat(content): add categories and patterns

backend/data/categories/categories.yaml

@@ -0,0 +1,60 @@
+categories:
+  - name: Arrays
+    slug: arrays
+    description: Problems involving array manipulation, traversal, and transformations.
+
+  - name: Strings
+    slug: strings
+    description: Problems focused on string manipulation, pattern matching, and text processing.
+
+  - name: Hash Tables
+    slug: hash-tables
+    description: Problems utilizing hash maps for efficient lookups and counting.
+
+  - name: Linked Lists
+    slug: linked-lists
+    description: Problems involving singly or doubly linked list operations.
+
+  - name: Trees
+    slug: trees
+    description: Problems involving binary trees, BSTs, and tree traversals.
+
+  - name: Graphs
+    slug: graphs
+    description: Problems involving graph traversal, shortest paths, and connectivity.
+
+  - name: Dynamic Programming
+    slug: dynamic-programming
+    description: Problems requiring optimal substructure and overlapping subproblems.
+
+  - name: Binary Search
+    slug: binary-search
+    description: Problems utilizing binary search for efficient searching.
+
+  - name: Sorting
+    slug: sorting
+    description: Problems involving sorting algorithms and techniques.
+
+  - name: Stack
+    slug: stack
+    description: Problems using LIFO data structure for parsing and tracking.
+
+  - name: Queue
+    slug: queue
+    description: Problems using FIFO data structure and BFS traversals.
+
+  - name: Heap
+    slug: heap
+    description: Problems using priority queues for top-k and streaming data.
+
+  - name: Two Pointers
+    slug: two-pointers
+    description: Problems solved using two pointer technique.
+
+  - name: Recursion
+    slug: recursion
+    description: Problems requiring recursive problem decomposition.
+
+  - name: Math
+    slug: math
+    description: Problems involving mathematical concepts and number theory.

backend/data/patterns/patterns.yaml

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+patterns:
+  - name: Two Pointers
+    slug: two-pointers
+    description: Use two pointers to traverse data from different positions, often moving toward or away from each other.
+    when_to_use: |
+      - Sorted arrays where you need to find pairs
+      - Linked list cycle detection
+      - Removing duplicates in-place
+      - Partitioning arrays
+      - Palindrome checking
+
+  - name: Sliding Window
+    slug: sliding-window
+    description: Maintain a window of elements that slides through the data, tracking a constraint or computing aggregates.
+    when_to_use: |
+      - Finding subarrays/substrings with specific properties
+      - Maximum/minimum sum of fixed-size windows
+      - Longest substring with at most K distinct characters
+      - Problems mentioning "contiguous" elements
+
+  - name: Fast & Slow Pointers
+    slug: fast-slow-pointers
+    description: Two pointers moving at different speeds, commonly used for cycle detection.
+    when_to_use: |
+      - Detecting cycles in linked lists or arrays
+      - Finding the middle of a linked list
+      - Finding the start of a cycle
+      - Happy number problem
+
+  - name: Binary Search
+    slug: binary-search
+    description: Efficiently search sorted data by repeatedly dividing the search space in half.
+    when_to_use: |
+      - Sorted arrays or search spaces
+      - Finding boundaries (first/last occurrence)
+      - Searching in rotated sorted arrays
+      - Finding peak elements
+      - Minimizing/maximizing with monotonic constraints
+
+  - name: BFS (Breadth-First Search)
+    slug: bfs
+    description: Level-by-level traversal using a queue, optimal for shortest paths in unweighted graphs.
+    when_to_use: |
+      - Shortest path in unweighted graphs
+      - Level-order tree traversal
+      - Finding all nodes at distance K
+      - Word ladder problems
+      - Matrix traversal
+
+  - name: DFS (Depth-First Search)
+    slug: dfs
+    description: Explore as deep as possible before backtracking, using recursion or a stack.
+    when_to_use: |
+      - Tree/graph traversal
+      - Path finding
+      - Detecting cycles
+      - Topological sorting
+      - Connected components
+      - Backtracking problems
+
+  - name: Backtracking
+    slug: backtracking
+    description: Build solutions incrementally, abandoning paths that fail to satisfy constraints.
+    when_to_use: |
+      - Generating all permutations/combinations
+      - Sudoku solver
+      - N-Queens problem
+      - Subset/partition problems
+      - Word search in grid
+
+  - name: Dynamic Programming
+    slug: dynamic-programming
+    description: Break problems into overlapping subproblems, storing results to avoid recomputation.
+    when_to_use: |
+      - Optimization problems (min/max)
+      - Counting problems
+      - Problems with optimal substructure
+      - Sequence alignment
+      - Knapsack-type problems
+
+  - name: Greedy
+    slug: greedy
+    description: Make locally optimal choices at each step, hoping for a global optimum.
+    when_to_use: |
+      - Interval scheduling
+      - Huffman coding
+      - Minimum spanning tree
+      - Activity selection
+      - When local optimum leads to global optimum
+
+  - name: Monotonic Stack
+    slug: monotonic-stack
+    description: Stack maintaining elements in sorted order, used for next greater/smaller element problems.
+    when_to_use: |
+      - Next greater/smaller element
+      - Largest rectangle in histogram
+      - Daily temperatures
+      - Stock span problem
+      - Trapping rain water
+
+  - name: Heap / Priority Queue
+    slug: heap
+    description: Data structure for efficiently finding min/max elements.
+    when_to_use: |
+      - Top K elements
+      - K-way merge
+      - Median from data stream
+      - Task scheduling
+      - Dijkstra's algorithm
+
+  - name: Union Find
+    slug: union-find
+    description: Track disjoint sets with efficient union and find operations.
+    when_to_use: |
+      - Connected components in graphs
+      - Cycle detection in undirected graphs
+      - Kruskal's minimum spanning tree
+      - Social network connections
+      - Accounts merge
+
+  - name: Trie
+    slug: trie
+    description: Tree-like data structure for efficient string prefix operations.
+    when_to_use: |
+      - Autocomplete systems
+      - Word dictionary with wildcard search
+      - Longest common prefix
+      - Word break problems
+      - Spell checker