6.046J Introduction to Algorithms (SMA 5503)

MIT OCW - 6.046J/18.410J Introduction to Algorithms (SMA 5503). This consists of 25 video lectures given by Professor Charles Leiserson and Professor Erik Demaine, introducing the analysis and design of computer algorithms. This course teaches techniques for the design and analysis of efficient algorithms, emphasizing methods useful in practice. Topics covered include: sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; amortized analysis; graph algorithms; shortest paths; network flow; computational geometry; number-theoretic algorithms; polynomial and matrix calculations; caching; and parallel computing. (from ocw.mit.edu)

Introduction


Lecture 01 - Administrivia; Introduction; Analysis of Algorithms, Insertion Sort, Mergesort
Lecture 02 - Asymptotic Notation; Recurrences; Substitution, Master Method
Lecture 03 - Divide-and-Conquer: Strassen, Fibonacci, Polynomial Multiplication
Lecture 04 - Quicksort, Randomized Algorithms
Lecture 05 - Linear-time Sorting: Lower Bounds, Counting Sort, Radix Sort
Lecture 06 - Order Statistics, Median
Lecture 07 - Hashing, Hash Functions
Lecture 08 - Universal Hashing, Perfect Hashing
Lecture 09 - Relation of BSTs to Quicksort - Analysis of Random BST
Lecture 10 - Red-black Trees, Rotations, Insertions, Deletions
Lecture 11 - Augmenting Data Structures, Dynamic Order Statistics, Interval Trees
Lecture 12 - Skip Lists
Lecture 13 - Amortized Algorithms, Table Doubling, Potential Method
Lecture 14 - Competitive Analysis: Self-organizing Lists
Lecture 15 - Dynamic Programming, Longest Common Subsequence
Lecture 16 - Greedy Algorithms, Minimum Spanning Trees
Lecture 17 - Shortest Paths I: Properties, Dijkstra's Algorithm, Breadth-first Search
Lecture 18 - Shortest Paths II: Bellman-Ford, Linear Programming, Difference Constraints
Lecture 19 - Shortest Paths III: All-pairs Shortest Paths, Matrix Multiplication, Floyd-Warshall, Johnson
Lecture 20
Lecture 21
Lecture 22 - Advanced Topics
Lecture 23 - Advanced Topics (cont.)
Lecture 24 - Advanced Topics (cont.)
Lecture 25 - Advanced Topics (cont.) - Discussion of Follow-on Classes

References
Introduction to Algorithms (SMA 5503)
Instructors: Prof. Charles Leiserson and Prof. Erik Demaine. Selected Lecture Notes. Audio Lectures. Exams and Solutions. Subtitles/Transcript. Assignments and Solutions.