Course Pages with Lecture notes
Duke University’s CPS130 –Introduction to Design and analysis of Algorithms is an undergraduate course. The lecture notes are good for revising basic concepts.
Jeff Erickson’s Algorithm course materials –this is a huge collection of lecture notes, homeworks and exams all in one big document (800+) pages. The tone is conversational, which helps to get a feel of the langauge of the subject. This is a graduate level course.
MIT’s Mathematics for Computer Science – 6.042J, has exhaustive notes on Discrete Mathematics.
- Algorithms by Omkar Deshpande on YouTube. Detailed explanation of concepts.
- Algorithms by Vazirani et. al
- Introduction to Algorithms aka CLRS (affl.) – the standard textbook for this course in large percentage of undergraduate and graduate classes. The book weighs a ton and looks intimidating, but is quite approachable in practice.
Probability and Randomness
Divide and conquer algorithms partition the problem into disjoint subproblems, sovle the subproblems recurisvely and then combine their solutions to solve the original problem.
Dynamic programming algorithms apply when the subproblems overlap –ie., when subproblems share subproblems. Dynamic program solves each subproblem just once and saves the answer, thereby avoiding the recomputing the answer.
DP is typically applied to optimisation problems.
Four steps of DP algorithm:
- Characterise the structure of an optimal solution.
- Recursively define the value of an optimal solution
- COmpute the value of the optimal solution, typicall bottom-up.
- Construct an optimal solution from computed info.
//Characterise the structure. Define the Value. Compute the Value. Construct.
2013-11-01: Towards a discipline of experimental algorithms by Bernard Moret.
2013-11-01: O-notation considered harmful (use Analytic Combinatorics instead)