Foundations of Algorithmic Problem-Solving: A Comprehensive Approach" is a comprehensive course that aims to equip learners with essential skills to solve complex problems using algorithmic solutions. This course is designed for beginners and intermediate learners who want to enhance their problem-solving abilities in various domains. This course emphasizes teaching techniques for designing and analyzing efficient algorithms, including sorting and searching, divide-and-conquer, dynamic programming, greedy algorithms, brute force, backtracking and incremental improvement, as well as complexity analysis. The pedagogy of the "“Foundations of Algorithmic Problem-Solving: A Comprehensive Approach" course is designed to provide a dynamic and immersive learning experience, blending theoretical knowledge with hands-on practical application.
Foundations of Algorithmic Problem-Solving A Comprehensive Approach
Chhattisgarh Swami Vivekanand Technical University and IGNOU via Swayam
Overview
Syllabus
Week
Title
1
Algorithmic: Understanding their definition and Significance
Basic algorithm analysis: Bigoh, Omega, Theta
Recurrence Problems: General Recurrence equations
2
Master Method and problems
Recursive Tree Method and problems
Substitution Method and problems
3
Bubble sort algorithm and its Time Complexity calculation
Selection sort algorithm and its Time Complexity calculation
Insertion sort algorithm and its Time Complexity calculation
Radix sort and its Time Complexity calculation
4
Introduction to Divide & Conquer: Quick sort algorithm and its Time Complexity calculation
Merge sort algorithm and its Time Complexity calculation
Heapsort algorithm and its Time Complexity calculation
5
Introduction to Linear search and Binary search
Strassen’s matrix multiplication
Coin change problem using greedy approach
Data compression using Huffman Encoding Algorithm
6
Introduction to Minimum Spanning Tree (MST): Prim’sAlgorithm
Minimum Spanning Tree (MST) Problem: Kruskal’s Algorithm
Single Source Shortest Path Problem: Dijkstra’s algorithm
Single Source Shortest Path Problem: Bellman ford algorithm
7
Applications of dynamic programming: Longest Common Subsequence Problem
Matrix chain Multiplication
Knapsack Problem
8
Floyd’s Warshall algorithm
Travelling sales man problem
Hamiltonian Circuit Problem
9
N-Queens problem
Graph coloring Problem
Flow networks problem
Union by Rank and Path Compression
10
Pattern matching Problems: Knuth-Morris-Pratt algorithm
Boyer-Moore algorithm
11
Introduction to Amortized analysis
Branch and Bound: LIFO Search
Branch and Bound: FIFO Search
12
Introduction to undesirability, P, NP, NP hard and NP complete
Reducibility of P, NP and NPC
Introduction to Approximation algorithms and application
Taught by
Dr J. P. Patra & Mr. Shesh Narayan Sahu
