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# design and analysis of algorithms

Semester :  IV

Course Code : 18CS42

CIE Marks : 40                       SEE Marks : 60

## DESIGN AND ANALYSIS OF ALGORITHMS18CS42

### Module-1

Introduction: What is an Algorithm? (T2:1.1), Algorithm Specification (T2:1.2), Analysis Framework (T1:2.1), Performance Analysis: Space complexity, Time complexity (T2:1.3). Asymptotic Notations: Big-Oh notation (O), Omega notation (Ω), Theta notation, and Little-oh notation (o), Mathematical analysis of Non-Recursive and recursive Algorithms with Examples (T1:2.2, 2.3, 2.4). Important Problem Types: Sorting, Searching, String processing, Graph Problems, Combinatorial Problems. Fundamental Data Structures: Stacks, Queues, Graphs, Trees, Sets and Dictionaries. (T1:1.3,1.4).

### Module-2

Divide and Conquer: General method, Binary search, Recurrence equation for divide and conquer, Finding the maximum and minimum (T2:3.1, 3.3, 3.4), Merge sort, Quicksort (T1:4.1, 4.2), Strassen‟s matrix multiplication (T2:3.8), Advantages and Disadvantages of divide and conquer. Decrease and Conquer Approach: Topological Sort. (T1:5.3).

### Module-3

Greedy Method: General method, Coin Change Problem, Knapsack Problem, Job sequencing with deadlines (T2:4.1, 4.3, 4.5). Minimum cost spanning trees: Prim‟s Algorithm, Kruskal‟s Algorithm (T1:9.1, 9.2). Single source shortest paths: Dijkstra’s Algorithm (T1:9.3). Optimal Tree problem: Huffman Trees and Codes (T1:9.4). Transform and Conquer Approach: Heaps and Heap Sort (T1:6.4).

### Module-4

Dynamic Programming: General method with Examples, Multistage Graphs (T2:5.1, 5.2).
Transitive Closure: Warshall‟s Algorithm, All Pairs Shortest Paths: Floyd’s Algorithm, Optimal Binary Search Trees, Knapsack problem ((T1:8.2, 8.3, 8.4), Bellman-Ford Algorithm (T2:5.4), Travelling Sales Person problem (T2:5.9), Reliability design (T2:5.8).

### Module-5

Backtracking: General method (T2:7.1), N-Queens problem (T1:12.1), Sum of subsets problem (T1:12.1), Graph colouring (T2:7.4), Hamiltonian cycles (T2:7.5). Programme and Bound: Assignment Problem, Travelling Sales Person problem (T1:12.2), 0/1 Knapsack problem (T2:8.2, T1:12.2): LC Programme and Bound solution (T2:8.2), FIFO Programme and Bound solution (T2:8.2). NP-Complete and NP-Hard problems: Basic concepts, non-10 deterministic algorithms, P, NP, NP-Complete, and NP-Hard classes (T2:11.1).