An introduction to the analysis of algorithms
This book provides a thorough introduction to the primary techniques used in the mathematical analysis of algorithms. The authors draw from classical mathematical material, including discrete mathematics, elementary real analysis, and combinatories, as well as from classical computer science material, including algorithms and data structures. They focus on "average-case" or "probabilistic" analysis, although they also cover the basic mathematical tools required for "worst-case" or "complexity" analysis. Topics include recurrences, generating functions, asymptotics, trees, strings, maps, and an analysis of sorting, tree search, string search, and hashing algorithms.
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- In fact in these slides from a 2011/2012 talk, Sedgewick talks about exactly this, even going as far as to draw a contrast between "TCS" and "analysis of algorithms" (the "scientific method"): https://sedgewick.io/talks/#algorithms-for-the-masses = https://sedgewick.io/wp-content/uploads/2022/03/2011-12AlgsM... onwards.
(Also touched upon briefly in https://sedgewick.io/talks/#lasting-legacy-of-flajolet = https://sedgewick.io/wp-content/uploads/2022/03/2013-14Flajo...)
His point is exactly that, often researchers care only about worst-case analysis and asymptotics, which is not necessarily a useful scientific analysis of how long an algorithm is expected to take on a machine as a function of the input size (which was the original motivation for Knuth etc to develop the field).
The same authors (but ordered as Sedgewick and Flajolet!) also have a book called An Introduction to the Analysis of Algorithms; there's a course website at https://aofa.cs.princeton.edu/home/ and videos on Coursera (https://www.coursera.org/learn/analysis-of-algorithms) — it is advanced mathematics but less advanced than the Analytic Combinatorics book.
- Perhaps Knuth's "The Art of Computer Programming" and Sedgewick's (Knuth's student) "An Introduction to the Analysis of Algorithms".
Also, Ben-Ari's "Mathematical Logic for Computer Science" and Pierce's "Software Foundations".
- Depending on your level of programming ability, one algorithm a day, IMHO, is completely doable. A number of comments and suggestions say that one per day is an unrealistic goal (yes, maybe it is) but the idea of setting a goal and working through a list of algorithms is very reasonable.
If you are just learning programming, plan on taking your time with the algorithms but practice coding every day. Find a fun project to attempt that is within your level of skill.
If you are a strong programmer in one language, find a book of algorithms using that language (some of the suggestions here in these comments are excellent). I list some of the books I like at the end of this comment.
If you are an experienced programmer, one algorithm per day is roughly doable. Especially so, because you are trying to learn one algorithm per day, not produce working, production level code for each algorithm each day.
Some algorithms are really families of algorithms and can take more than a day of study, hash based look up tables come to mind. First there are the hash functions themselves. That would be day one. Next there are several alternatives for storing entries in the hash table, e.g. open addressing vs chaining, days two and three. Then there are methods for handling collisions, linear probing, secondary hashing, etc.; that's day four. Finally there are important variations, perfect hashing, cuckoo hashing, robin hood hashing, and so forth; maybe another 5 days. Some languages are less appropriate for playing around and can make working with algorithms more difficult, instead of a couple of weeks this could easily take twice as long. After learning other methods of implementing fast lookups, its time to come back to hashing and understand when its appropriate and when alternatives are better and to understand how to combine methods for more sophisticated lookup methods.
I think you will be best served by modifying your goal a bit and saying that you will work on learning about algorithms every day and cover all of the material in a typical undergraduate course on the subject. It really is a fun branch of Computer Science.
A great starting point is Sedgewick's book/course, Algorithms [1]. For more depth and theory try [2], Cormen and Leiserson's excellent Introduction to Algorithms. Alternatively the theory is also covered by another book by Sedgewick, An Introduction to the Analysis of Algorithms [3]. A classic reference that goes far beyond these other books is of course Knuth [4], suitable for serious students of Computer Science less so as a book of recipes.
After these basics, there are books useful for special circumstances. If your goal is to be broadly and deeply familiar with Algorithms you will need to cover quite a bit of additional material.
Numerical methods -- Numerical Recipes 3rd Edition: The Art of Scientific Computing by Tuekolsky and Vetterling. I love this book. [5]
Randomized algorithms -- Randomized Algorithms by Motwani and Raghavan. [6], Probability and Computing: Randomized Algorithms and Probabilistic Analysis by Michael Mitzenmacher, [7]
Hard problems (like NP) -- Approximation Algorithms by Vazirani [8]. How to Solve It: Modern Heuristics by Michalewicz and Fogel. [9]
Data structures -- Advanced Data Structures by Brass. [10]
Functional programming -- Pearls of Functional Algorithm Design by Bird [11] and Purely Functional Data Structures by Okasaki [12].
Bit twiddling -- Hacker's Delight by Warren [13].
Distributed and parallel programming -- this material gets very hard so perhaps Distributed Algorithms by Lynch [14].
Machine learning and AI related algorithms -- Bishop's Pattern Recognition and Machine Learning [15] and Norvig's Artificial Intelligence: A Modern Approach [16]
These books will cover most of what a Ph.D. in CS might be expected to understand about algorithms. It will take years of study to work though all of them. After that, you will be reading about algorithms in journal publications (ACM and IEEE memberships are useful). For example, a recent, practical, and important development in hashing methods is called cuckoo hashing, and I don't believe that it appears in any of the books I've listed.
[1] Sedgewick, Algorithms, 2015. https://www.amazon.com/Algorithms-Fourth-Deluxe-24-Part-Lect...
[2] Cormen, et al., Introduction to Algorithms, 2009. https://www.amazon.com/s/ref=nb_sb_ss_i_1_15?url=search-alia...
[3] Sedgewick, An Introduction to the Analysis of Algorithms, 2013. https://www.amazon.com/Introduction-Analysis-Algorithms-2nd/...
[4] Knuth, The Art of Computer Programming, 2011. https://www.amazon.com/Computer-Programming-Volumes-1-4A-Box...
[5] Tuekolsky and Vetterling, Numerical Recipes 3rd Edition: The Art of Scientific Computing, 2007. https://www.amazon.com/Numerical-Recipes-3rd-Scientific-Comp...
[6] https://www.amazon.com/Randomized-Algorithms-Rajeev-Motwani/...
[7]https://www.amazon.com/gp/product/0521835402/ref=pd_sim_14_2...
[8] Vazirani, https://www.amazon.com/Approximation-Algorithms-Vijay-V-Vazi...
[9] Michalewicz and Fogel, https://www.amazon.com/How-Solve-Heuristics-Zbigniew-Michale...
[10] Brass, https://www.amazon.com/Advanced-Data-Structures-Peter-Brass/...
[11] Bird, https://www.amazon.com/Pearls-Functional-Algorithm-Design-Ri...
[12] Okasaki, https://www.amazon.com/Purely-Functional-Structures-Chris-Ok...
[13] Warren, https://www.amazon.com/Hackers-Delight-2nd-Henry-Warren/dp/0...
[14] Lynch, https://www.amazon.com/Distributed-Algorithms-Kaufmann-Manag...
[15] Bishop, https://www.amazon.com/Pattern-Recognition-Learning-Informat...
[16] Norvig, https://www.amazon.com/Artificial-Intelligence-Modern-Approa...
- Read books; follow the worked out examples very closely until you completely understand them. Then try programming it on your own from your understanding and memory. You have to put in the time and effort. I suggest studying books where complete implementations are given in a language of your choice and only later studying books with pseudo-code (i.e. go from specific to general). Also the chosen language should be simple without obscuring the core logic in OO/Functional syntactic sugar and structure (C is ideal here). The following are a few chosen books from my collection (used copies of all can be had for cheap online);
1) Data Structures and Program Design in C by Kruse, Leung and Tondo.
2) Algorithms in C (Parts1-4 and Part5 two-volume set) by Robert Sedgewick.
3) Compared to What? An Introduction to the Analysis of Algorithms by Gregory Rawlins.
4) How to think about Algorithms by Jeff Edmonds.
5) Advanced Data Structures by Peter Brass.
Finally, study the ideas, concepts and techniques behind the C++ STL library to see how to design Data Structures and Algorithms in a clean and independent manner and yet can couple them as reqd. in myriad ways for actual usage.
- a book like "Code complete" or "An Introduction to the Analysis of Algorithms"
- > Actually just notice that you use "suffix trie". Note that there is trie (which is also called prefix tree) and suffix tree. There is no suffix trie.
At the risk of being snotty: someone should tell Robert Sedgwick. He uses the term in his newest book, "An Introduction to the Analysis of Algorithms, Second Edition," which just came out. Sorry if I haven't been fair to your post due to a quick reading but Kevin isn't making the term up.
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