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Analysis of Algorithms and Data Structures


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This training is available on our members site only. As a member, all of the training and tutorials are available to you. We will be adding more training materials here in the future. You can join now for only USD $15 total for 2 months, $25.00 for 4 months, $34.00 for 6 months, or $59.00 for 1 year. (Please note the local links to member training content do not work on this page.)

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Analysis of Algorithms

This course teaches the Analysis of the performance of Algorithms. It also discusses programming techniques and data structures used in the writing of effective algorithms. Knowledge of C programming is assumed.

Topics Covered:

  • Introduction: Analysis of Selection Sort

  • Introduction: Analysis of Merge Sort

  • Asymptotic Notation

  • Asymptotic Notation Continued

  • Heapsort

  • Heapsort Continued

  • Priority Queues (more heaps)

  • Quicksort

  • Bounds on Sorting and Linear Time Sorts

  • Stable Sorts and Radix Sort

  • Begin Dynamic Programming

  • More Dynamic Programming

  • Begin Greedy Algorithms: Huffman's Algorithm

  • Dÿkstra's Algorithm

  • Beyond Asymptotic Analysis: Memory Access Time

  • B-Trees

  • More B-Trees: Insertion and Splitting

  • Union/Find

  • Warshall's Algorithm, Floyd's Algorithm

  • Large Integer Arithmetic

  • RSA Public-Key Cryptosystem

  • Begin Algorithms and Structural Complexity Theory

  • Continue Algorithms and Structural Complexity Theory

  • End Algorithms and Structural Complexity Theory

  • Generating Permutations and Combinations

  • Exam review with sample questions and solutions



Data Structures

Teaches abstract data structures (stacks, queues, lists, trees). Dynamic memory allocation, pointers, and recursion, sorting, and searching. Some of the material here is repeated from above.

Topics Covered:

  • Introduction and Big Example

  • Complexity Analysis

  • Pointers, Dynamic Allocation, Linked Lists

  • More Linked Lists, Stacks

  • Queues

  • Recursion

  • Recursion Continued: An Extended Example

  • Trees, Binary Trees, Binary Search Trees

  • Binary Trees on Disk (A C Program)

  • B-Trees

  • Hashing

  • Sorting

  • Heapsort and Quicksort

  • Data Compression with Huffman Coding

  • Graphs

More Graphs



Data Structures
and Algorithms

This course was prepared for the Programming Languages and System Design course in the BE(Information Technology) course at the University of Western Australia. It is designed to teach you how to program efficiently. It assumes that

  • you know the basics of programming in C,
  • can write, debug and run simple programs in C, and
  • have some simple understanding of object-oriented design.


Introduction

Programming Strategies

  1. 2.1 Objects and ADTs
    • 2.1.1 An Example: Collections
  2. 2.2 Constructors and destructors
  3. 2.3 Data Structure
  4. 2.4 Methods
  5. 2.5 Pre- and post-conditions
  6. 2.6 C conventions
  7. 2.7 Error Handling
  8. 2.8 Some Programming Language Notes

Data Structures

  1. 3.1 Arrays
  2. 3.2 Lists
  3. 3.3 Stacks
    • 3.3.1 Stack Frames
  4. 3.4 Recursion
    • 3.4.1 Recursive Functions
    • 3.4.2 Example: Factorial

Searching

  1. 4.1 Sequential Searches
  2. 4.2 Binary Search
  3. 4.3 Trees

Complexity

  1. 5. Complexity (PS)

Queues

  1. 6.1 Priority Queues
  2. 6.2 Heaps

Sorting

  1. 7.1 Bubble
  2. 7.2 Heap
  3. 7.3 Quick
  4. 7.4 Bin
  5. 7.5 Radix

Searching Revisited

  1. 8.1 Red-Black trees
  2. 8.1.1 AVL trees
  3. 8.2 General n-ary trees
  4. 8.3 Hash Tables

Dynamic Algorithms

  1. 9.1 Fibonacci Numbers
  2. 9.2 Binomial Coefficients
  3. 9.3 Optimal Binary Search Trees
  4. 9.4 Matrix Chain Multiplication
  5. 9.5 Longest Common Subsequence
  6. 9.6 Optimal Triangulation

Graphs

  1. 10.1 Minimum Spanning Tree
  2. 10.2 Dijkstra's Algorithm

Huffman Encoding

FFT

Hard or Intractable Problems

  1. 13.1 Eulerian or Hamiltonian Paths
  2. 13.2 Travelling Salesman's Problem

Games

Appendices

  1. ANSI C
  2. Source code listings

Slides from lectures (PowerPoint)



More Algorithm Learning Resources:

Animated Alogorithms - A collection of animated algorithms including: Insertion Sort, QuickSort, Bin Sort, Radix Sort, Priority Queue Sorting, Hash Tables Searching, Optimal Binary Search Tree, Huffman Encoding, Dijkstra's Shortest Path, Minimum Spanning Tree ( MST ).

Algorithms CMSC 251 - A large (97 page) book on the following topics : Course Introduction, Analyzing Algorithms: the 2-D Maxima Problem, Summations and Analyzing Programs with Loops, the 2-D Maxima revisited and Asymptotics, Asymptotics, Divide and Conquer and MergeSort, Recurrences, Medians and Selection, Long Integer Multiplication, Heaps and HeapSort, HeapSort Analysis and Partitioning, QuickSort, Lower Bounds for Sorting, Linear Time Sorting, Introduction to Graphs, Graphs, Graph Representation and BFS, All Pairs Shortest Paths, Floyd Warshall Algorithm, Longest Common Subsequence, Chain Matrix Multiplication, NP Completeness: General Introduction, NP Completeness and Reductions.

More Algorithm learning materials are here.


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