Dynamic Programming, Greedy Algorithms
- Divide and Conquer Algorithms
- We will formally cover divide and conquer algorithms as a design scheme and look at some divide and conquer algorithms we have encountered in the past. We will learn some divide and conquer algorithms for Integer Multiplication (Karatsuba’s Algorithm), Matrix Multiplication (Strassen’s Algorithm), Fast Fourier Transforms (FFTs), and Finding Closest Pair of Points.
- Dynamic Programming Algorithms
- In this module, you will learn about dynamic programming as a design principle for algorithms. We will provide a step-by-step approach to formulating a problem as a dynamic program and solving these problems using memoization. We will cover dynamic programming for finding longest common subsequences, Knapsack problem and some interesting dynamic programming applications.
- Greedy Algorithms
- In this module, we will learn about greedy algorithms. We will understand the basic design principles for greedy algorithms and learn about a few algorithms for greedy scheduling and Huffman codes. We will also learn some interesting cases when being greedy provides a guaranteed approximation to the actual solution.
- Intractability and Supplement on Quantum Computing
- P vs NP, Examples such as Travelling Salesperson Problem, Vertex Cover, 3-Coloring and others; Integer Linear Programming and Translating Problems into Integer Programming.