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Just looked at the "Course Description" of the "Syllabus" as at https://ocw.mit.edu/courses/6-006-introduction-to-algorithms-spring-2020/pages/syllabus/ https:

Just looked at the "Course Description" of the "Syllabus" as at https://ocw.mit.edu/courses/6-006-introduction-to-algorithms-spring-2020/pages/syllabus/ https://ocw.mit.edu/courses/6-006-introduction-to-algorithms... The course takes itself very seriously and seems to ask each student to devote a lot of time to the course. My summary reaction is that it would be a shame to devote that much time to what is basically so little material. Yes, the "Syllabus" mentions Introduction to Algorithms, Cormen, Leiserson, Rivest, and Stein, CLRS. Years ago I downloaded a PDF and didn't see much beyond what I'd gotten from Knuth, etc. I can give a fast overview here: There I see their lists of topics: dynamic arrays, heaps, balanced binary search trees, hash tables and sorting, graph searching, dynamic programming I'm a little surprised at how old these topics are: I first learned several of the topics almost entirely from Donald E. Knuth, The Art of Computer Programming, Volume 3, Sorting and Searching, 1973. (1) Dynamic Array A glance at how it works explains why I never heard of it: Can see "Dynamic array" at https://en.wikipedia.org/wiki/Dynamic_array https://en.wikipedia.org/wiki/Dynamic_array So, if have an array A and need more space, then allocate a larger array B and copy over the contents of array A to array B and continue with array B. A guess is that in nearly all cases a better solution would be a tree where the array subscripts are used as keys and the array elements, as leaves. Maybe the main reason to include dynamic arrays is to do some applied math to analyze by how much bigger array B should be than array A. (2) Heaps I like heaps. At one point in the software of my startup, I have to search through maybe 1 million numbers and end up with the, say, 20 largest. For that I programmed a heap, and it has worked out great. There are versions of the heap algorithm that are better on locality of reference and when the heap is carried mostly on slow, secondary storage. (3) Balanced Binary Search Trees AVL (Adelson-Velskii, Landis) trees are in the Knuth reference, and they are terrific. An alternative is red-black trees. One of those two is likely the key to .NET collection classes, and my startup uses two instances for a simple, light, fast key-value store instead of Redis. (4) Hash Tables Those are also in Knuth. Hashing usually leaves me in doubt due to its various possible problems. But better still sometimes is perfect hashing as I recall also in Knuth. For hashing in general, a good step forward is in Ronald Fagin, Jurg Nievergelt, Nicholas Pippenger, H. Raymond Strong, Extendible hashing-a fast access method for dynamic files, "ACM Transactions on Database Systems", ISSN 0362-5915, Volume 4, Issue 3, September 1979, Pages: 315 - 344. We used that in an AI (artificial intelligence) product we shipped. (5) Sorting Knuth covers heap sort and shows that it meets the Gleason bound for sorting by comparing pairs of keys. (6) Graph Searching Looking at their lecture notes, it appears that they mean versions of shortest paths on networks. These are all fairly simple except for minimum cost single commodity network flows where each arc has a maximum flow and also a cost per unit of flow. The problem is linear programming, and the classic simplex algorithm applies and takes on an especially simple form -- a basic solution corresponds to a spanning tree of arcs. Some good news is that if the arc capacities are all integers and if start the algorithm with an integer solution, then the simplex algorithm maintains an integer solution and will terminate with one. It is tempting to see that "good news" as a case of progress in NP-complete integer linear programming. For such content, I recommend Mokhtar S. Bazaraa and John J. Jarvis, Linear Programming and Network Flows, ISBN 0-471-06015-1, John Wiley and Sons, New York, 1977. (7) Dynamic Programming That can be a big subject but does not have to be. I got a good introduction from an expert in about 90 seconds while my cab was waiting to take me to the airport. I ended up writing my Ph.D. dissertation in dynamic programming. For an easy introduction, can have fun, like eating from the appetizer plate at Thanksgiving, say, a half hour at a bite from Stuart E. Dreyfus and Averill M. Law, The Art and Theory of Dynamic Programming, ISBN 0-12-221860-4, Academic Press, New York, 1977. One of the amazing advantages of dynamic programming is how well it handles randomness -- then have stochastic optimal control, Markov decision theory, etc. The flavor of dynamic programming in computer science can be a bit different, e.g., applied to search for some string A in some string B. Maybe another purpose of the course is to get everyone all wound up and fired up about the question of P versus NP My recommendation is to try quite hard to ignore that question.

nikhila01 4y ago
You should read about dynamic arrays more carefully. They have amortized O(1) insertion which is better than a tree, and the data is contiguous in memory which gives it better cache locality than a tree. They are one of the most popular data structures. Parts of your post also seem to me to be quite boastful and low-value: (paraphrasing) "the course takes itself very seriously", "why spend so much time teaching so little material", "these topics are mostly old; just read Knuth", and "dynamic programming is easy; I learned it in 90 seconds and then did my PhD in it".
- graycat 4y ago
  I had a revision of that post, but I had it ready only just after the end of the 2 hour window for revisions. The course pressed hard on the students to devote, what was it, 4 hours of time a week in group sessions with more hours in independent study. That's asking a lot from the students. In response I had a lesson and purpose in that post: (A) That collection of fundamental algorithms hasn't changed very fast, were much the same 40 years ago. (B) Nearly all the algorithms are quite simple and each one can be learned quickly, including the derivation of its big-O performance, and coded, running, and tested in 2 hours or so. (C) I mentioned Knuth v.3 as a reference: Tough to improve on that Knuth volume as a reference for such algorithms. (D) For hashing, network flows (graph search), and dynamic programming I gave really good references -- tough to compete with any of them. I used some of my experience to illustrate (A) -- (D). That lesson should be some quite good news for any HN readers considering studying the algorithms. > Parts of your post also seem to me to be quite boastful and low-value: No, I just used some of my experience to give examples of my points. > You should read about dynamic arrays more carefully. They have amortized O(1) insertion .... I saw all that. Get the O(1) property only with some assumptions and some math derivations, and I mentioned the math. Two obvious problems: (1) It is trivial for any of us to think of applications where the new allocations and copying would be wildly wasteful. (2) For the assumptions, we will rarely have enough information to have much confidence in our math derivation. We also can think of (3) The reallocations, when there are a lot of them, will create problems for the memory management, garbage collection. Sure, any of us can think of niche situations where (a) we do a few reallocations and (b) then go for hours, ..., months with no more reallocations and with the advantages of arrays. Dynamic arrays don't belong on a list of Best Algorithms. Again, my guess is that the interest of the course in dynamic arrays is an opportunity to do the math derivations. The people that MIT course is intended for are maybe good HN readers, so an issue for HN readers is, should they devote a lot of time to that course? We review movies, restaurants, etc., and we might also review courses. Your attack on my review was mostly an attack on me: You resented my post because I mentioned some of my background and in response attacked me. Instead, make a good contribution of your own, maybe as a review of that MIT course. I'll state the basic lesson again: The algorithms in that course are nearly all quite good but old, with some really good old references, and can be learned quickly, say, the whole course in a few weekends.

nikhila01 4y ago

You should read about dynamic arrays more carefully. They have amortized O(1) insertion which is better than a tree, and the data is contiguous in memory which gives it better cache locality than a tree. They are one of the most popular data structures. Parts of your post also seem to me to be quite boastful and low-value: (paraphrasing) "the course takes itself very seriously", "why spend so much time teaching so little material", "these topics are mostly old; just read Knuth", and "dynamic programming is easy; I learned it in 90 seconds and then did my PhD in it".

graycat 4y ago
I had a revision of that post, but I had it ready only just after the end of the 2 hour window for revisions. The course pressed hard on the students to devote, what was it, 4 hours of time a week in group sessions with more hours in independent study. That's asking a lot from the students. In response I had a lesson and purpose in that post: (A) That collection of fundamental algorithms hasn't changed very fast, were much the same 40 years ago. (B) Nearly all the algorithms are quite simple and each one can be learned quickly, including the derivation of its big-O performance, and coded, running, and tested in 2 hours or so. (C) I mentioned Knuth v.3 as a reference: Tough to improve on that Knuth volume as a reference for such algorithms. (D) For hashing, network flows (graph search), and dynamic programming I gave really good references -- tough to compete with any of them. I used some of my experience to illustrate (A) -- (D). That lesson should be some quite good news for any HN readers considering studying the algorithms. > Parts of your post also seem to me to be quite boastful and low-value: No, I just used some of my experience to give examples of my points. > You should read about dynamic arrays more carefully. They have amortized O(1) insertion .... I saw all that. Get the O(1) property only with some assumptions and some math derivations, and I mentioned the math. Two obvious problems: (1) It is trivial for any of us to think of applications where the new allocations and copying would be wildly wasteful. (2) For the assumptions, we will rarely have enough information to have much confidence in our math derivation. We also can think of (3) The reallocations, when there are a lot of them, will create problems for the memory management, garbage collection. Sure, any of us can think of niche situations where (a) we do a few reallocations and (b) then go for hours, ..., months with no more reallocations and with the advantages of arrays. Dynamic arrays don't belong on a list of Best Algorithms. Again, my guess is that the interest of the course in dynamic arrays is an opportunity to do the math derivations. The people that MIT course is intended for are maybe good HN readers, so an issue for HN readers is, should they devote a lot of time to that course? We review movies, restaurants, etc., and we might also review courses. Your attack on my review was mostly an attack on me: You resented my post because I mentioned some of my background and in response attacked me. Instead, make a good contribution of your own, maybe as a review of that MIT course. I'll state the basic lesson again: The algorithms in that course are nearly all quite good but old, with some really good old references, and can be learned quickly, say, the whole course in a few weekends.