Algorithms and Complexity Analysis

1. Understand fundamental concepts of computer algorithms.
2. Analyze the complexity of algorithms using asymptotic notations.
3. Apply various algorithm design techniques to solve computational problems.
4. Implement searching and sorting algorithms.
5. Understand and apply dynamic programming techniques.
6. Understand the concepts of computational complexity and NP-completeness.
7. Apply approximate algorithms to find near-optimal solutions for NP-hard problems.

13 weeks, about 29.5 hours in total. Yours will differ.

1. Week 1Module 1: Basic Algorithm Analysis

   • Unit 1: Basic Algorithm Concepts · 1.5 hours

     Read Unit 1: Basic Algorithm Concepts, focusing on the definition and characteristics of algorithms.. Understand the advantages and disadvantages of algorithms.. Differentiate between algorithms and pseudocode.. Solve self-assessment exercises to reinforce understanding of basic concepts..

2. Week 2Module 1: Basic Algorithm Analysis

   • Unit 2: Analysis and Complexity of Algorithms · 2 hours

     Study Unit 2: Analysis and Complexity of Algorithms, paying attention to time and space complexity.. Differentiate between worst-case, average-case, and best-case time complexity.. Understand typical complexities of algorithms (constant, logarithmic, linear, etc.).. Work through examples to approximate the time taken by an algorithm..

3. Week 3Module 1: Basic Algorithm Analysis

   • Unit 3: Algorithm Design Techniques · 2 hours

     Review Unit 3: Algorithm Design Techniques, focusing on divide-and-conquer, greedy techniques, and dynamic programming.. Understand asymptotic notations (Big O, Big Omega, Big Theta).. Apply asymptotic notations to analyze algorithm efficiency.. Practice problems to identify appropriate algorithm design techniques for different scenarios..

4. Week 4Module 1: Basic Algorithm Analysis

   • Unit 4: Recursion and Recursive Algorithms · 2 hours

     Study Unit 4: Recursion and Recursive Algorithms, focusing on base cases and recursive calls.. Understand different types of recursion (direct, indirect, tail, head).. Compare recursion with iteration.. Implement recursive algorithms for reversing an array and generating Fibonacci sequences..

5. Week 5Module 1: Basic Algorithm Analysis

   • Unit 5: Recurrence Relations · 2 hours

     Study Unit 5: Recurrence Relations, focusing on methods for resolving recurrence relations.. Understand the guess-and-verify, iteration, recursion tree, and master methods.. Apply recurrence relations to analyze the Tower of Hanoi problem.. Solve recurrence relations to determine algorithm complexity..

6. Week 6Module 2: Searching and Sorting Algorithms

   • Unit 1: Bubble Sort and Selection Sort Algorithm · 2 hours

     Study Unit 1: Bubble Sort and Selection Sort Algorithm, focusing on the working principles of each algorithm.. Analyze the time and space complexity of bubble sort and selection sort.. Compare the advantages and disadvantages of each algorithm.. Implement bubble sort and selection sort in a programming language of your choice..

7. Week 7Module 2: Searching and Sorting Algorithms

   • Unit 2: Insertion Sort and Linear Search Algorithms · 2 hours

     Study Unit 2: Insertion Sort and Linear Search Algorithms, focusing on the working principles of each algorithm.. Analyze the time and space complexity of insertion sort and linear search.. Compare the advantages and disadvantages of each algorithm.. Implement insertion sort and linear search in a programming language of your choice..

8. Week 8Module 2: Searching and Sorting Algorithms

   • Unit 3: Radix Sort and Stability in Sorting · 2 hours

     Study Unit 3: Radix Sort and Stability in Sorting, focusing on the working principles of radix sort.. Understand the concept of stability in sorting algorithms.. Analyze the time and space complexity of radix sort.. Compare the advantages and disadvantages of radix sort..

9. Week 9Module 2: Searching and Sorting Algorithms

   • Unit 4: Divide-and-Conquer Strategies I: Binary Search · 2 hours

     Study Unit 4: Divide-and-Conquer Strategies I: Binary Search, focusing on the divide-and-conquer paradigm.. Understand the working principle of binary search.. Analyze the time and space complexity of binary search.. Compare the advantages and disadvantages of binary search..

10. Week 10Module 2: Searching and Sorting Algorithms

    • Unit 5: Divide-and-Conquer Strategies II: Merge Sort and Quicksort Algorithms · 2 hours

      Study Unit 5: Divide-and-Conquer Strategies II: Merge Sort and Quicksort Algorithms, focusing on the working principles of merge sort and quicksort.. Analyze the time and space complexity of merge sort and quicksort.. Compare the advantages and disadvantages of each algorithm.. Implement merge sort and quicksort in a programming language of your choice..

11. Week 11Module 3: Other Algorithm Techniques

    • Unit 1: Binary Search Trees · 2 hours

      Study Unit 1: Binary Search Trees, focusing on the properties of binary search trees.. Understand different traversal methods (inorder, preorder, postorder).. Learn how to query a binary search tree (search, minimum, maximum, successor, predecessor).. Study insertion and deletion operations in binary search trees..

12. Week 12Module 3: Other Algorithm Techniques

    • Unit 2: Dynamic Programming · 2 hours

      Study Unit 2: Dynamic Programming, focusing on the principles of dynamic programming.. Understand top-down and bottom-up approaches.. Compare dynamic programming with divide-and-conquer.. Apply dynamic programming to solve optimization problems..

    • Unit 3: Computational Complexity · 2 hours

      Study Unit 3: Computational Complexity, focusing on deterministic and non-deterministic algorithms.. Understand P and NP problems.. Learn about NP-hard and NP-complete problems.. Differentiate between tractable and intractable problems..

13. Week 13Module 3: Other Algorithm Techniques

    • Unit 4: Approximate Algorithms I · 2 hours

      Study Unit 4: Approximate Algorithms I, focusing on the concept of approximation algorithms.. Understand performance ratios.. Learn about the vertex cover and traveling salesman problems.. Apply approximation algorithms to find near-optimal solutions..

    • Unit 5: Approximate Algorithms II · 2 hours

      Study Unit 5: Approximate Algorithms II, focusing on methods for finding minimum spanning trees (Kruskal's and Prim's algorithms).. Understand the steps for implementing Kruskal's and Prim's algorithms.. Apply these algorithms to find minimum spanning trees in graphs.. Compare the advantages and disadvantages of Kruskal's and Prim's algorithms..