Introduction to Data Structures

Study Notes

Introduction to Data Structures

Data structures are specialized formats for organizing, processing, retrieving and storing data.
They are crucial for efficient algorithm design and implementation.
Different data structures suit various tasks based on the operations required.

Common Data Structures

Arrays: A contiguous block of memory storing elements of the same data type. Efficient for accessing elements by index, but resizing can be slow.
Linked Lists: A sequence of nodes, where each node points to the next. Can easily insert and delete elements, but accessing elements by index is less efficient than arrays.
- Singly Linked List: Each node points to the next.
- Doubly Linked List: Each node points to both the next and previous node.
Stacks: A LIFO (Last-In, First-Out) structure. Used for function calls, undo/redo operations, and expression evaluation.
Queues: A FIFO (First-In, First-Out) structure. Used for managing tasks, printing jobs, and buffering data.
Trees: Hierarchical structures with a root node and branches. Used for representing hierarchical relationships, searching, and sorting.
- Binary Trees: Each node has at most two children.
- Binary Search Trees (BSTs): Sorted binary trees where values in the left subtree are less than the node's value, and values in the right subtree are greater.
- Heaps: Specialized tree-based structures maintaining a min-heap (smallest element at the root) or max-heap (largest element at the root) property.
Graphs: Collection of nodes (vertices) connected by edges. Used to model networks, social interactions, maps, etc.
- Directed Graphs: Edges have a direction.
- Undirected Graphs: Edges have no direction.
Hash Tables: Data structures that store key-value pairs, enabling fast lookups using hash functions to determine the position of an element.

Data Structure Operations

Insertion: Adding a new element to the data structure.
Deletion: Removing an element from the data structure.
Search: Finding an element in the data structure.
Traversal: Visiting all elements in the data structure in a specific order.
Sorting: Arranging elements in a specific order.

Data Structure Complexity

Time Complexity: The amount of time an operation takes with respect to the input size.
- O(1) (Constant): Time independent of the input size, e.g., accessing an array element by index.
- O(log n) (Logarithmic): Time grows logarithmically with input size, e.g., searching in a binary search tree.
- O(n) (Linear): Time grows linearly with input size, e.g., traversing a linked list.
- O(n log n) (Linearithmic): Time is a combination of n and log n, e.g., sorting algorithms.
- O(n²) (Quadratic): Time grows quadratically with input size, e.g., nested loops.
- O(2ⁿ) (Exponential): Time grows exponentially with input size, e.g., some brute-force algorithms.
Space Complexity: The amount of memory used by the data structure with respect to the input size.

Choosing the Right Data Structure

Consider the specific operations needed.
Evaluate time and space complexity for each option.
Balance these factors for optimal performance.

Abstract Data Types (ADTs)

A conceptual description of data, without specifying how it is stored or manipulated.
Defines only the operations.
Examples include stacks, queues, lists, and trees.

Applications

Database Management Systems
Operating Systems (scheduling, memory management)
Compilers (parsing code)
Computer Graphics
Artificial Intelligence
Web Browsers

Description

Explore the foundational concepts of data structures and their importance in algorithm design. This quiz covers common types such as arrays, linked lists, stacks, and queues, highlighting their characteristics and use cases. Test your understanding of how these structures manage data efficiently.