Explore techniques for breaking down complex problems into manageable subproblems, with applications in sorting, searching, and mathematical computations.

In this module, you will gain insights into the algorithm design technique called the greedy method, which is a technique applicable to optimization problems, and how the method makes a series of greedy choices to construct an optimal solution (or close to optimal solution) for a given problem. You will also learn about greedy algorithms like fractional knapsack, activity selection problem, and job sequencing with deadlines.

In this module, you will gain insight into dynamic programming, which is a powerful problem-solving technique used in computer science to solve optimization and decision problems. You will also be introduced to the principles, algorithms, and applications of dynamic programming and learn how to break down complex problems into smaller sub-problems, store and reuse solutions to these sub-problems, and ultimately design efficient algorithms for various real-world challenges.

In this module, you will explore the graph concepts, different types of graphs, and how we can represent a graph in a computer. You will also gain insight into how to model problems as graphs and design efficient algorithms for a wide range of graph-related challenges like minimum spanning trees, single source shortest paths, all pair shortest paths.

In this module, you will explore a wide range of graph-related problems like finding the minimum spanning trees, single source shortest paths, and all pair shortest paths.

In this module, you will learn the concept of backtracking and its applications in problem-solving. Backtracking is a systematic algorithmic approach used to find solutions to problems where you need to make a sequence of decisions and if a decision leads to an unsatisfactory outcome, you backtrack to the previous decision and try an alternative path. This module covers the fundamentals of state space and explores specific problems such as the N-queen problem (4-queen problem), graph coloring problem, sum of subsets, and Hamilton cycle. You will also learn how to apply backtracking to find solutions to these problems.

In this module, you will learn the principles and applications of randomized algorithms. Randomized algorithms use randomization as a fundamental tool to solve computational problems efficiently and often provide probabilistic guarantees of correctness. This module explores several key randomized algorithms, including randomized quicksort, min-cut algorithm, random permutation, convex hull, and Bloom filters. You will also learn how to analyze the expected performance and probabilistic guarantees of these algorithms in various problem-solving scenarios.

In this module, you will gain a foundational understanding of P, NP, NP-complete, and NP-hard problems, as well as key concepts like satisfiability problem (SAT), polynomial time reducibility, and common NP-complete problems.