Effective Ways to Study Algorithms: Books, Videos, and Practice Tips

Do not start with "Introduction to Algorithms" (CLRS) if you are new to the subject, because it contains many mathematical proofs. Instead, the author strongly recommends Robert Sedgewick’s Algorithms, 4th Edition , which presents Java implementations and abundant illustrations of sorting, searching, graph, and string algorithms.

The book is well‑structured: it divides algorithms into four main categories—sorting, searching, graphs, and strings—allowing readers to see how many algorithms evolve from these basics. It explains not only what each algorithm does but also why it works, discussing advantages and disadvantages.

For example, the discussion of quicksort goes beyond the basic principle and covers practical improvements such as switching to insertion sort for small arrays, three‑way partitioning, and median‑of‑three sampling. The relationship between priority queues and heap sort is also explored, noting that heap sort’s poorer performance in practice is due to cache‑miss penalties and lack of locality.

Additional suggestions include revisiting CLRS after skipping the heavy mathematical sections, reading Data Structures and Algorithm Analysis , and taking Professor Deng Junhui’s MOOC on data structures. Loop invariants are highlighted as the key to understanding algorithm correctness.

Hands‑on coding is emphasized: implement algorithms in C, Java, or Python, and repeatedly write complex structures such as Fibonacci heaps to internalize their design, even if they are rarely used in contests. Optimizations like reducing matrix dimensions in linear‑programming implementations and using sparse‑matrix techniques are also shared.

The article mentions the nuances of the Fast Fourier Transform, including precision loss in the complex domain and the alternative Number‑Theoretic Transform for high‑precision multiplication.

Solving end‑of‑chapter exercises is recommended; if more than half of the problems cannot be solved independently, readers should reread the chapter and allocate time for deeper thinking.

For visual learners, the Princeton Algorithm Coursera series (Part 1 and Part 2) is suggested, combined with note‑taking and coding each algorithm after watching. After mastering the videos, practicing with "Cracking the Coding Interview" problems organized by data structure type helps solidify knowledge.

One contributor also recommends the open‑source "Book of Elementary Algorithms and Data Structures" written by a software engineer, which provides implementations in C, C++, Haskell, Python, and Scheme/Lisp, and is hosted on GitHub (liuxinyu95/AlgoXY).

References include Chris Okasaki’s Purely Functional Data Structures , Knuth’s The Art of Computer Programming , Richard Bird’s Pearls of Functional Algorithm Design , and Bentley’s Programming Pearls . The book is released under GNU FDL with code under GPLv3.

Finally, the MIT OpenCourseWare version of the CLRS course is recommended for those who prefer a structured classroom approach and want to tackle the textbook’s exercises.