Lecture on Data Structures and Algorithms

Jul 23, 2024

Lecture on Data Structures and Algorithms

Introduction

  • Presenter: Enthusiastic and engaging style
  • Main Content: Series on data structures and algorithms
  • Housekeeping: Like, comment, subscribe
  • Scope: Basic data structures, Big O notation, searching algorithms, sorting algorithms, graphs, trees
  • Example: A tree in data structures is like a family tree—a way to organize data hierarchically
  • Key Concept: Difference between data structures and algorithms
    • Data Structures: Named locations to store and organize data
    • Algorithms: Steps to solve a problem, e.g., a recipe for baking a pizza

Topics Covered

Basic Data Structures

  • Array: Collection of elements stored at contiguous memory locations
  • Real-Life Example: Family tree

Stack Data Structure

  • Definition: LIFO (Last In, First Out) data structure
  • Real-Life Analogy: Stack of books
  • Operations:
    • Push: Add object to the top
    • Pop: Remove object from the top
  • Example: Stack of video games
    • Push: Add Minecraft, Skyrim, Doom, Borderlands, Final Fantasy VII
    • Pop: Remove objects from the top to access the bottom object
  • Methods:
    • Push, Pop, Peek (look without removing), IsEmpty, Search
  • Exceptions: EmptyStackException when popping from an empty stack
  • Use Cases: Undo/redo features, browser history, backtracking algorithms, function calls (call stack)

Queue Data Structure

  • Definition: FIFO (First In, First Out) data structure
  • Real-Life Analogy: Line of people, first come first serve
  • Operations:
    • Enqueue (Offer): Add object to the tail
    • Dequeue (Poll): Remove object from the head
  • Example: Queue of concert tickets
    • Head: Karen
    • Tail: Harold
  • Methods:
    • Add, Remove, Element (throws exceptions)
    • Offer, Poll, Peek (returns special values)
  • Additional Methods: IsEmpty, Size, Contains
  • Use Cases: Keyboard buffers, printer queues, linked lists, breadth-first search algorithms

Priority Queue

  • Definition: FIFO data structure but with priority
  • Example: Student GPAs, higher GPAs served first
  • Java Implementation:
    • Use PriorityQueue class
    • Re-arranges elements based on priority
  • Use Cases: Scheduling tasks, managing resources

Linked Lists

  • Comparison with Arrays:
    • Arrays: Elements stored in contiguous memory locations; efficient for random access but less so for insertions/deletions
    • Linked Lists: Nodes with data and pointers to the next node; efficient for insertions/deletions
  • Types:
    • Singly Linked List: Single pointers to the next node
    • Doubly Linked List: Pointers to next and previous nodes
  • Example Implementation (Java):
    • Stack using Linked Lists
    • Queue using Linked Lists
    • Methods: Add, Remove, IndexOf, Peeking Methods (Peek First, Peek Last)
  • Advantages: Dynamic size, easier insertions/deletions
  • Disadvantages: More memory usage, no random access
  • Use Cases: Implementing stacks/queues, GPS navigation, music playlists

Dynamic Array

  • Definition: Resizable array
  • Comparison with Static Arrays: Static arrays have fixed size, dynamic arrays grow as needed
  • Java Examples: ArrayList, Vector
  • Operations and Implementation:
    • Add, Insert, Delete, Search
    • Automatic array resizing (grow/shrink methods)
  • Advantages: Random access, good data locality
  • Disadvantages: Memory waste, time-consuming element shifts
  • Use Cases: When the number of elements is not known in advance, dynamic data storage

Comparisons

  • Linked Lists vs. ArrayLists (Java):
    • Access Time: ArrayLists faster due to random access
    • Insert/Delete: Linked lists faster, especially in large data sets

Big O Notation

  • Purpose: Describes the performance of an algorithm as data increases
  • Types:
    • O(1): Constant time
    • O(n): Linear time
    • O(log n): Logarithmic time (e.g., binary search)
    • O(n log n): Quasi-linear time (e.g., merge sort, quick sort)
    • O(n^2): Quadratic time (e.g., bubble sort)
    • O(n!): Factorial time (e.g., traveling salesman problem)
  • Examples:
    • Linear Search: O(n)
    • Binary Search: O(log n)
    • Bubble Sort: O(n^2)
    • Merge Sort: O(n log n)
    • Quick Sort: O(n log n), worst-case O(n^2)

Searching Algorithms

  • Linear Search: Iterates through elements one by one, slow for large data sets
  • Binary Search: Requires sorted array, divides search interval in half each step
  • Interpolation Search: Improvement over binary search, best for uniformly distributed data, O(log log n) on average

Sorting Algorithms

  • Bubble Sort: Compares and swaps adjacent elements, O(n^2)
  • Selection Sort: Finds minimum and swaps, O(n^2)
  • Insertion Sort: Builds sorted array one item at a time, O(n^2)
  • Merge Sort: Divide and conquer, merges subarrays, O(n log n)
  • Quick Sort: Picks a pivot, sorts partitions, O(n log n) average, O(n^2) worst

Graphs and Trees

  • Graphs:
    • Definition: Collection of nodes (vertices) and edges (connections)
    • Types: Directed vs. Undirected
    • Representations: Adjacency Matrix (space: O(V^2)), Adjacency List (space: O(V + E))
    • Algorithms: BFS vs. DFS
  • Trees:
    • Binary Trees: At most two children per node
    • Binary Search Trees: Ordered binary trees, efficient search (log(N) average)
    • Tree Traversal: In-order, pre-order, post-order
    • Use Cases: File explorers, databases, DNS, HTML DOM

Recursion

  • Definition: Function that calls itself
  • Uses: Advanced sorting algorithms, tree/graph traversal
  • Pros: Easier to read/write/debug
  • Cons: Can be slower, uses more memory
  • Examples: Walking simulation, factorial calculation, exponentiation

Hash Tables

  • Definition: Collection of key-value pairs
  • Operations: Insert, Delete, Search
  • Handling Collisions: Chaining (linked lists in buckets)
  • Use Cases: Fast efficient data retrieval with large data sets

Key points to remember: Understanding the properties, implementations, benefits, and limitations of each data structure and algorithm.