In the table below, readings listed as CLRS are taken from the course textbook:
Cormen, Thomas, Charles Leiserson, Ronald Rivest, and Clifford Stein. Introduction to Algorithms. 2nd ed. Cambridge, MA: MIT Press, 2001. ISBN: 9780262032933.
LEC # | TOPICS | READINGS |
---|---|---|
Introduction and document distance | ||
L1 | Introduction and document distance | CLRS, chapters 1-3 |
L2 | More document distance, mergesort | CLRS, sections 11.1-11.2 |
Binary search trees | ||
L3 | Airplane scheduling, binary search trees | CLRS, chapter 10 and sections 12.1-12.3 |
L4 | Balanced binary search trees | CLRS, sections 13.1 and 13.2 for a different approach (red-black trees) |
Hashing | ||
L5 | Hashing I: chaining, hash functions | |
L6 | Hashing II: table doubling, Karp-Rabin | CLRS, chapter 17 and section 32.2 |
L7 | Hashing III: open addressing | CLRS, section 11.4 (and 11.3.3 and 11.5 if interested) |
Sorting | ||
L8 | Sorting I: heaps | CLRS, sections 2.1-2.3 and 6.1-6.2 |
L9 | Sorting II: heaps | CLRS, sections 6.1-6.4 |
L10 | Sorting III: lower bounds, linear-time sorting | CLRS, sections 8.1-8.4 |
L11 | Sorting IV: stable sorting, radix sort | |
Searching | ||
L12 | Searching I: graph search, representations, and applications | CLRS, sections 22.1-22.3 and B.4 |
L13 | Searching II: breadth-first search and depth-first search | CLRS, sections 22.2-22.3 |
L14 | Searching III: topological sort and NP-completeness | CLRS, sections 22.4 and 34.1-34.3 (at a high level) |
Shortest paths | ||
L15 | Shortest paths I: intro | CLRS, chapter 24 (intro) |
L16 | Shortest paths II: Bellman-Ford | |
L17 | Shortest paths III: Dijkstra | CLRS, sections 24.2-24.3 |
L18 | Shortest paths IV: Dijkstra speedups |
Wagner, Dorothea, and Thomas Willhalm. “Speed-Up Techniques for Shortest-Path Computations.” In Lecture Notes in Computer Science: Proceedings of the 24th Annual Symposium on Theoretical Aspects of Computer Science. Berlin / Heidelberg: Springer, 2007. ISBN: 9783540709176. Read up to section 3.2. |
Dynamic programming | ||
L19 | Dynamic programming I: memoization, Fibonacci, Crazy Eights, guessing | CLRS, chapter 15 |
L20 | Dynamic programming II: longest common subsequence, parent pointers | |
L21 | Dynamic programming III: text justification, parenthesization, knapsack, pseudopolynomial time, Tetris training | |
L22 | Dynamic programming IV: piano fingering, structural DP (trees), vertex cover, dominating set, and beyond |
For fun, see papers on piano fingering and polyphonic piano fingering via DP: Parncutt, Richard, et al. “An Ergonomic Model of Keyboard Fingering for Melodic Fragments.” Music Perception 14, no. 4 (1997): 341-382. Al Kasimi, Alia, Eric Nichols, and Christopher Raphael. “A Simple Algorithm for Automatic Generation of Polyphonic Piano Fingerings.” In Proceedings of the 8th International Conference on Music Information Retrieval, 2007, pp. 355-356. For fun, watch the Metamorphosis of the Cube video, which illustrates a folding DP. |
Numerics | ||
L23 | Numerics I | |
L24 | Numerics II | |
Beyond 6.006 | ||
L25 | Beyond 6.006: follow-on classes, geometric folding algorithms |