Lecture Notes: Data Structures and Algorithms

Introduction

• Discussion on data structures and algorithms.
• Encouragement to like, comment, and subscribe.
• Topics covered: Basic data structures, Big O notation, searching/sorting algorithms, graphs, trees.

Data Structures

Definition

• A named location for storing and organizing data.
• Example: Family tree (hierarchy of relationships).

Types of Data Structures

• Array: Collection of elements stored at contiguous memory locations.
  • Pros and cons vary by type of data structure.

Algorithms

Definition

• Steps to solve a problem.
• Example: Pizza baking algorithm - steps to bake a pizza.

Searching Algorithms

Linear Search

• Examines elements one by one.
• Example of a searching algorithm.
• Importance: Time & memory efficiency in coding interviews.

Stacks

Definition

• LIFO (Last In First Out) data structure.
• Methods: Push, pop.

Example

• Vertical tower like a stack of books.
• Example with video games using Java.

Methods

• Push: Add to top, Pop: Remove from top.
• Peek: Look at top, IsEmpty: Check if empty, Search: Find item.

Use Cases

• Undo/redo in text editors, browser history, backtracking algorithms, call stacks.

Queues

Definition

• FIFO (First In First Out) data structure.
• Example: Line of people.

Methods

• Enqueue: Add to tail, Dequeue: Remove from head.

Use Cases

• Keyboard buffer, printer queues, linked lists, priority queues.

Priority Queues

Definition

• FIFO with priority sorting.
• Higher priority elements served first.

Linked Lists

Definition

• Series of nodes, each containing data and a pointer to the next node.

Types

• Singly Linked List: One pointer per node.
• Doubly Linked List: Two pointers per node (forward and backward).

Advantages & Disadvantages

• Advantages: Dynamic, easy insertion/deletion.
• Disadvantages: Greater memory usage, no random access.

Dynamic Arrays

Definition

• Array with resizable capacity.
• Example: ArrayList in Java.

Advantages & Disadvantages

• Advantages: Random access, good cache utilization.
• Disadvantages: Wastes memory, time-consuming shifts.

Big O Notation

Definition

• Describes algorithm performance as data grows.
• Important runtimes: O(1), O(n), O(log n), O(n^2).

Searching Algorithms

Linear Search

• O(n) time complexity.
• Slow for large data sets.
• No need for sorted data.

Binary Search

• Finds position in a sorted array.
• O(log n) time complexity.
• Requirement: Data must be sorted.

Interpolation Search

• Improvement over binary search.
• Best for uniformly distributed data.

Sorting Algorithms

Bubble Sort

• Compares adjacent elements, swaps if out of order.
• O(n^2) time complexity.

Selection Sort

• Finds minimum value, swaps it to correct position.
• O(n^2) time complexity.

Insertion Sort

• Shifts elements to insert value in correct place.
• O(n^2) time complexity, but better than others for small data sets.

Merge Sort

• Divides array into halves, merges sorted halves.
• O(n log n) time complexity.

Quick Sort

• Divides array into partitions around a pivot.
• O(n log n) average case, O(n^2) worst case.

Hash Tables

Definition

• Collection of key-value pairs.
• Fast insertion, lookup, deletion.
• Collision handling by chaining.

Graphs

Definition

• Non-linear aggregation of nodes and edges.
• Types: Directed and undirected.

Representation

• Adjacency Matrix: 2D array, quick edge access.
• Adjacency List: Array of linked lists, space-efficient.

Tree Structures

Definition

• Non-linear, hierarchical data structure.
• Important types: Binary Tree, Binary Search Tree.

Traversal Techniques

• In-Order: Left, Root, Right.
• Post-Order: Left, Right, Root.
• Pre-Order: Root, Left, Right.

Conclusion

• Overview of discussed algorithms and structures.
• Emphasis on understanding efficiency and appropriate usage of each data structure and algorithm.

These notes summarize the key points from the lecture on data structures and algorithms covered by the presenter. This should serve as a useful reference for study and review.