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 algorithms.
Different data structures have varying characteristics, affecting performance in operations like searching, inserting, and deleting data.

Linear Data Structures

Arrays: Ordered collection of elements of the same data type stored in contiguous memory locations. Access is fast due to direct addressing. Insertion/deletion can be slow due to shifting elements.
- Example: Storing a list of student names alphabetically.
Linked Lists: Elements are not stored contiguously; each element points to the next. Insertion and deletion are faster than in arrays, but accessing elements requires sequential traversal.
- Types: Singly linked, doubly linked, circular linked.
- Example: Implementing a playlist where new songs can be added seamlessly.
Stacks: LIFO (Last-In, First-Out) structure. Elements are added and removed from the top. Useful for function calls and expression evaluation.
- Example: Managing a call stack in a program.
Queues: FIFO (First-In, First-Out) structure. Elements are added at the rear and removed from the front. Useful for managing tasks in a printer queue or buffering data.
- Example: Handling incoming requests in a web server.

Non-Linear Data Structures

Trees: Hierarchical structure consisting of nodes. Each node can have children. Types include binary trees, binary search trees, heaps, and AVL trees.
- Useful for representing hierarchical relationships, like an organizational chart.
- Efficient for searching and sorting in some cases.
Graphs: Collection of nodes (vertices) connected by edges. Used to model relationships between objects. Types include directed graphs and undirected graphs.
- Example: Social networks, maps, and scheduling dependencies.
Hash Tables: Data structures that use hash functions to map keys to values. Access is very fast. Performance can degrade due to collisions.
- Example: Implementing a dictionary where you look up a word to find its definition.

Abstract Data Types (ADTs)

Abstract Data Types (ADTs) are data structures defined by their behavior (operations) rather than their internal implementation.
Examples include stacks, queues, lists, and trees.
ADTs provide abstraction, hiding implementation details.
This allows programmers to use data structures without understanding the underlying implementation.

Data Structure Operations

Searching: Locating a specific element.
Insertion: Adding a new element.
Deletion: Removing an existing element.
Traversal: Visiting each element in the structure.
Sorting: Arranging elements in a specific order.

Choosing the Right Data Structure

The choice depends on the application and needed operations.
Factors include frequency of searches, insertions, deletions, and data amount.

Big O Notation

Used to analyze time and space complexity of algorithms and data structures.
Expresses growth rate of runtime or memory usage as input size increases.
Common notations include O(1), O(log n), O(n), O(n log n), and O(n^2).
Different data structures have varying time complexities for operations. For example, searching in a sorted array using binary search is O(log n), while searching in an unsorted array is O(n).

Key Considerations for Data Structures

Time Complexity: How long operations take as data size increases.
Space Complexity: How much memory the structure requires as data size increases.
Implementation: Ease of implementation.
Specific Needs: How well the structure fits the application's requirements.

Description

Explore the fundamentals of data structures, focusing on linear data structures like arrays, linked lists, and stacks. Understand their characteristics, advantages, and applications in organizing and manipulating data efficiently.