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VTU NOTES
Subject code
21CS42
Semester
4th

## Module - 1

Introduction: What is an Algorithm? It’s Properties. Algorithm Specification-using natural language, using Pseudo code convention, Fundamentals of Algorithmic Problem solving, Analysis Framework- Time efficiency and space efficiency, Worst-case, Best-case and Average case efficiency. Performance Analysis: Estimating Space complexity and Time complexity of algorithms. Asymptotic Notations: Big-Oh notation (O), Omega notation (Ω), Theta notation ( ) with examples, Basic efficiency classes, Mathematical analysis of Non-Recursive and Recursive Algorithms with Examples. Brute force design technique: Selection sort, sequential search, string matching algorithm with complexity Analysis. Textbook 1: Chapter 1 (Sections 1.1,1.2), Chapter 2(Sections 2.1,2.2,2.3,2.4), Chapter 3(Section3.1,3.2)Textbook 2: Chapter 1(section 1.1,1.2,1.3)

## Module - 2

Divide and Conquer: General method, Recurrence equation for divide and conquer, solving it using Master’s theorem. , Divide and Conquer algorithms and complexity Analysis of Finding the maximum & minimum, Binary search, Merge sort, Quick sort. Decrease and Conquer Approach: Introduction, Insertion sort, Graph searching algorithms, Topological Sorting. It’s efficiency analysis. Textbook 2: Chapter 3(Sections 3.1,3.3,3.4,3.5,3.6) Textbook 1: Chapter 4 (Sections 4.1,4.2,4.3), Chapter 5(Section 5.1,5.2,5.3)

## Module - 3

Greedy Method: General method, Coin Change Problem, Knapsack Problem, solving Job sequencing with deadlines Problems. Minimum cost spanning trees: Prim’s Algorithm, Kruskal’s Algorithm with performance analysis. Single source shortest paths: Dijkstra’s Algorithm. Optimal Tree problem: Huffman Trees and Codes. Transform and Conquer Approach: Introduction, Heaps and Heap Sort. Textbook 2: Chapter 4(Sections 4.1,4.3,4.5) Textbook 1: Chapter 9(Section 9.1,9.2,9.3,9.4), Chapter 6( section 6.4)

## Module - 4

Dynamic Programming: General method with Examples, Multistage Graphs. Transitive Closure: Warshall’s Algorithm. All Pairs Shortest Paths: Floyd’s Algorithm, Knapsack problem, Bellman-Ford Algorithm, Travelling Sales Person problem. Space-Time Tradeoffs: Introduction, Sorting by Counting, Input Enhancement in String Matching- Harspool’s algorithm. Textbook 2: Chapter 5 (Sections 5.1,5.2,5.4,5.9) Textbook 1: Chapter 8(Sections 8.2,8.4), Chapter 7 (Sections 7.1,7.2)

## Module - 5

Backtracking: General method, solution using back tracking to N-Queens problem, Sum of subsets problem, Graph coloring, Hamiltonian cycles Problems. Branch and Bound: Assignment Problem, Travelling Sales Person problem, 0/1 Knapsack problem NP-Complete and NP-Hard problems: Basic concepts, non- deterministic algorithms, P, NP, NP- Complete, and NP-Hard classes. Textbook 1: Chapter 12 (Sections 12.1,12.2) Chapter 11(11.3) Textbook 2: Chapter 7 (Sections 7.1,7.2,7.3,7.4,7.5) Chapter 11 (Section 11.1)