- Dynamic Search Operations - Binary Search Trees (BST), AVL Trees, Red-Black Trees: Efficient for insertions, deletions, and searches, maintaining a sorted sequence of elements.
- Finding Nearest Lower and Higher Elements - BST, AVL Trees, Red-Black Trees: Good for operations like floor and ceiling in a sorted dataset.
- Order Statistics - Order Statistic Trees: Finds the k-th smallest or largest element in a collection.
- Priority Queue Operations - Heaps (Binary, Binomial, Fibonacci): Efficient for finding and removing the minimum or maximum element.
- Efficiently Merging K Sorted Lists - Min Heap/Max Heap: Offers a way to efficiently merge multiple sorted lists into a single sorted list.
- Graph Traversals - Graphs (using Adjacency List, Adjacency Matrix): For DFS, BFS to explore nodes and edges of graphs.
- Finding Shortest Paths in Graphs - Graphs with Weighted Edges (using Dijkstra’s, Bellman-Ford, Floyd-Warshall algorithms): Optimal for pathfinding and routing.
- Finding Minimum Spanning Tree - Graphs (using Kruskal's or Prim's algorithm): Essential in network design, like designing the least expensive network.
- Detecting Cycles in a Graph - Disjoint Set (Union-Find): Efficient for keeping track of elements divided into a number of disjoint (non-overlapping) sets.
- Network Flow Problems - Graphs (using Ford-Fulkerson, Edmonds-Karp algorithms): Crucial for solving flow problems like maximum flow.
- Text Pattern Search - Trie, Suffix Tree/Array: Efficient for quick pattern search in text, such as autocomplete features.
- Substring Search - KMP Algorithm, Rabin-Karp Algorithm: For fast searching of substring patterns within a main string.
- Database Indexing - B-Trees, B+-Trees: Used in databases for efficient data retrieval.
- Cache Implementation - Hash Tables: For fast lookups, insertions, and deletions.
- Implementing Relationships - Graphs: To model and explore relationships in social networks, recommendation systems.
- Frequency Counting of Elements - Hash Tables: For counting occurrences of elements efficiently.
- Maintaining a Sorted Stream of Data - Balanced Trees (AVL, Red-Black): To keep data sorted as it is inserted.
- Implementing Undo Feature - Stack: To track operations or changes for undo mechanisms.
- Parsing Expressions - Stack: For evaluating expressions or parsing nested structures.
- Auto-complete Feature - Trie: For efficient prefix-based search.
- Storing Dictionary Words - Trie, Hash Table: For spell checkers and autocomplete.
- Balancing Load Among Servers - Consistent Hashing: For distributed caching systems and load balancers.
- LRU Cache - Hash Table + Doubly Linked List: For implementing caches that remove the least recently used items.
- Data Compression - Huffman Trees: For encoding data efficiently.
- File System Navigation - N-ary Trees: To represent and navigate directory structures.
- Version Control History - Graphs (DAGs): To track changes over time in version control systems.
- Scheduling Jobs on a Machine - Priority Queue: For job scheduling based on priority.
- Running Median in a Stream - Heaps (Min Heap and Max Heap): To dynamically track the median of a stream of numbers.
- Implementing Middleware/Routing - Trie: For efficiently routing in web servers or middleware.
- Spatial Indexing - Quad Trees, K-D Trees, R-Trees: For geographical data and collision detection in 2D and 3D spaces.
- Finding Connected Components in a Graph - Graphs: Essential for network analysis.
- Storing Sparse Data - Hash Tables, Sparse Arrays, Sparse Matrices: Efficient for data with many default or zero values.
- Multi-dimensional Searching - K-D Trees, Quad Trees: For efficient searching in multi-dimensional data.
- Point of Intersection in Geometrical Shapes - Sweep Line Algorithms with Balanced Trees: For computational geometry problems.
- Storing and Querying Time-Based Data - Time Series Databases using Trees: For efficient storage and retrieval of time-series data.
- Dynamic Connectivity - Union-Find Data Structure: For keeping track of the connected components in a dynamic graph.
- Job Sequencing with Deadlines - Disjoint Set (Union-Find): To group jobs and manage dependencies.
- Message Broadcasting and Propagation in Networks - Graphs: For modeling network flows and broadcast operations.
- Implementing Permissions and Groups in an Operating System - Graphs, Trees: For managing hierarchical structures of users and permissions.
- Rate Limiting - Sliding Window Algorithms using Queues: To limit the rate of operations over time.
- Event Scheduling and Timers - Min Heap: To execute scheduled events in chronological order. 42 Tagging and Categorization - Hash Tables, Trie: For organizing and searching tags or categories in applications.
- Data Serialization - Trees: For representing structured data in formats like XML, JSON.
- Collision Detection in Gaming - Quad Trees, Spatial Hashing: For optimizing collision detection in 2D and 3D games.
- Building Recommendation Systems - Graphs: To model user-item relationships and preferences.
- Document Indexing for Search Engines - Inverted Index: For mapping content to document locations in search.
- Constructing Build Systems - Directed Acyclic Graphs (DAGs): For managing project dependencies in build systems.
- Blockchain and Cryptocurrency Transactions - Merkle Trees: For efficiently summarizing and verifying the integrity of blockchain data.
- Distributed Systems and Consensus - Paxos, Raft (using logs and state machines): For achieving consensus in distributed systems.
- Session Management in Web Applications - Hash Tables: For tracking user sessions efficiently.
