Data Structures and Algorithms

1. Data Structures
   1. Primitive Data Structures
      1. Integers
         1. Integer representation
            1. Binary form
            2. Hexadecimal form
            3. Octal form
         2. Signed vs. unsigned integers
         3. Operations on integers
            1. Addition, subtraction
            2. Multiplication, division
            3. Bitwise operations
      2. Floats
         1. IEEE 754 floating-point standard
         2. Precision topics
            1. Single precision
            2. Double precision
         3. Floating-point arithmetic
            1. Rounding errors
            2. Overflow and underflow
      3. Characters
         1. ASCII and Unicode standards
         2. Character manipulation
            1. Conversion between cases
            2. Character encoding/decoding
      4. Booleans
         1. Logical operations
            1. AND, OR, NOT
         2. Control structures utilizing booleans
            1. Conditional statements
            2. Loop conditions
   2. Non-Primitive Data Structures
      1. Linear Data Structures
         1. Arrays
            1. Characteristics of arrays
               1. Fixed size
               2. Element access time
            2. Operations on arrays
               1. Traversal
               2. Insertion and deletion
               3. Search and sort
            3. One-dimensional arrays
               1. Basic structure and usage
               2. Memory allocation
            4. Multi-dimensional arrays
               1. Two-dimensional arrays
               2. Applications in matrices
               3. Representing grids and tables
            5. Dynamic arrays
               1. Advantages over static arrays
               2. Implementation details
               3. Resizing strategies
         2. Linked Lists
            1. Basics of linked lists
               1. Nodes and pointers
               2. Operations like insertion and deletion
                  1. At head
                  2. At tail
                  3. At specific positions
            2. Singly linked lists
               1. Traversal and searching
               2. Use cases and limitations
            3. Doubly linked lists
               1. Bidirectional traversal
               2. Pros and cons compared to singly linked lists
            4. Circular linked lists
               1. Circular nature advantages
               2. Usage in round-robin scheduling
         3. Stacks
            1. Characteristics of stacks
               1. LIFO (Last In, First Out) nature
               2. Real-world analogies such as piles of plates
            2. Operations on stacks
               1. Push, pop, peek
               2. Stack overflow and underflow
            3. Implementation using arrays
               1. Fixed size limitations
               2. Efficiency in access
            4. Implementation using linked lists
               1. Dynamic size advantage
               2. Performance considerations
         4. Queues
            1. Characteristics of queues
               1. FIFO (First In, First Out) concept
               2. Real-world analogies like queues at ticket counters
            2. Operations on queues
               1. Enqueue, dequeue
               2. Queue front and rear access
            3. Simple queues
               1. Basic functionality
               2. Use in scheduling tasks
            4. Circular queues
               1. Overcoming limitations of simple queues
               2. Efficient space utilization
            5. Priority queues
               1. Element priority considerations
               2. Applications in task scheduling
            6. Double-ended queues (Deques)
               1. Operations at both ends
               2. Applications in complex scenarios
      2. Non-Linear Data Structures
         1. Trees
            1. Characteristics of trees
               1. Hierarchical structure
               2. Terminologies like root, leaf, node, etc.
            2. Binary trees
               1. Basic structure and traversal
               2. Types of binary trees and applications
            3. Binary search trees (BST)
               1. Properties and operations
               2. Insertion, deletion, searching
               3. Balanced vs. unbalanced BST
            4. AVL trees
               1. Self-balancing properties
               2. Rotations required to maintain balance
            5. Red-black trees
               1. Color properties and rotations
               2. Balancing mechanism advantages
            6. N-ary trees
               1. General form and uses
               2. Applications in file systems
            7. Segment trees
               1. Range query optimization
               2. Use in interval management
            8. Trie
               1. String searching efficiency
               2. Use in dictionary implementations
         2. Graphs
            1. Basics and representations
               1. Nodes and edges definition
               2. Directed vs. Undirected graphs
            2. Properties of graphs
               1. Connected, disconnected graphs
               2. Cyclic, acyclic graphs
            3. Graph representations
               1. Adjacency matrix and its properties
               2. Adjacency list and space efficiency
            4. Graph traversal techniques
               1. Depth-first search (DFS)
               2. Breadth-first search (BFS)
            5. Applications of graphs
               1. Network analysis
               2. Finding shortest paths and spanning trees