In-Depth Notes on Data Structures

Data Structures Overview

Data structures refer to the way data is organized, managed, and stored for efficient access and modification. Understanding data structures is crucial for computer science students as they provide the foundation for programming and analyzing algorithms.

1. Definition of Data Structures

• Data Structures: A data structure is a specialized format for organizing, processing, and storing data.
• Implemented using programming languages like C, C++, and Java to structure information efficiently through operations such as:
  1. create()
  2. insert()
  3. delete()
  4. display()
  5. traversal()
  6. searching()
  7. sorting()
  8. merging()
  9. splitting()

2. Classification of Data Structures

Data structures can be broadly classified into two categories:

• Primitive Data Structures: Basic data types that are directly supported by programming languages.

  • Types:
  • Integer: Whole numbers (e.g., -1, 0, 1)
  • Float: Fractional numbers (e.g., 3.14)
  • Character: Individual characters (e.g., 'A', 'B')
  • Boolean: Represents true or false

• Non-Primitive Data Structures: These are derived from primitive data structures and include:

  • Linear Data Structures:

  • Array: A collection of elements of the same type stored in contiguous memory locations.

  • Linked List: A sequence of elements where each element points to the next one, with a head pointing to the first element.

  • Stack: A collection implemented with Last-In-First-Out (LIFO) principle. Operations include push (addition) and pop (removal).

  • Queue: A collection implemented with First-In-First-Out (FIFO) principle, where elements are added at the rear and removed from the front.

  • Non-linear Data Structures:

  • Tree: A hierarchical structure with nodes, where a single node is designated as the root, and each node has children.

  • Graph: A set of nodes connected by edges, can represent various relationships.

3. Operations on Data Structures

When working with data structures, various operations can be performed, such as:

• Create: Allocate memory for a data structure.
• Insert/Delete: Add or remove data from the structure.
• Display: Show data stored in the data structure.
• Search: Find data in the structure.
• Sort/Merge: Organize data in a specific order or combine multiple lists.
• Traverse: Visit each node or element systematically.

4. Abstract Data Types (ADT)

• ADT: Defines a data type purely by its behavior from the point of view of a user, characterized by its values and operations.
• Examples of ADTs include List, Stack, Queue, and Tree.

5. Preliminaries of Algorithms

An algorithm is a step-by-step process for solving a problem. Each algorithm must adhere to certain properties:

• Input: Specified set of values.
• Output: Result from given input.
• Finiteness: Must terminate after a finite number of steps.
• Definiteness: Each step must be precisely defined.
• Effectiveness: Steps of the algorithm must be executable in a finite timeframe.

6. Time and Space Complexity

• Time Complexity measures the amount of time an algorithm takes to process relative to input size.
• Space Complexity indicates the amount of memory required by an algorithm for its execution relative to input size. Both complexities are essential for optimized algorithm design.

7. Searching Algorithms

• Linear Search: Sequentially checks each element until the target is found.
• Binary Search: Divides the search space in half each iteration; requires sorted data.
• Fibonacci Search: Utilizes Fibonacci numbers for an efficient search in sorted arrays.

8. Sorting Algorithms

Sorting involves arranging elements in order:

• Insertion Sort: Builds the final sorted array one item at a time by inserting elements in their proper position.
• Selection Sort: Selects the smallest element from the unsorted part and moves it to the beginning.
• Bubble Sort: Repeatedly swaps adjacent elements if they are in the wrong order.
• Quick Sort: Uses a pivot to partition the array and recursively sorts the partitions.
• Merge Sort: Divides the array into halves, sorts them, and merges them back together.
• Radix Sort: Sorts numbers digit by digit using counting sort as an intermediate step.

9. Linked Lists

Linked lists allow efficient insertion and deletion operations. Types include:

• Singly Linked List: Nodes point to the next node.
• Doubly Linked List: Nodes point to both their next and previous nodes.
• Circular Linked List: Last node points back to the first node.

10. Stacks and Queues

• Stacks follow LIFO; operations include push (add), pop (remove), and peek (top element).
• Queues follow FIFO; operations include enqueue (add to rear) and dequeue (remove from front).

11. Trees

Trees have various types, including:

• Binary Trees: Each node has at most two children.
• Binary Search Trees: Left child < node < right child.
• AVL Trees: Self-balancing binary search trees.
• Heaps: Complete binary trees that satisfy the heap property.

12. Graphs

Graphs represent relationships with vertices and edges. Types of graphs include:

• Directed/undirected graphs
• Weighted/unweighted graphs
• Sparse/dense graphs

13. Graph Traversals

Common traversal algorithms include:

• Breadth-First Search (BFS): Explores neighboring nodes first.
• Depth-First Search (DFS): Explores as far down a branch before backtracking.

14. Shortest Path Algorithms

Methods to compute shortest paths include Dijkstra's, Prim's, and Kruskal's algorithms for efficient graph traversal and optimization.