TAOCP: Volume 4B, Fascicle 5

The Art of Computer Programming, Volume 4B, Fascicle 5: Mathematical Preliminaries Redux; Introduction to Backtracking; Dancing Links

This fascicle covers three separate topics:

1.  Mathematical Preliminaries. Knuth writes that this portion of fascicle 5 "extends the ‘Mathematical Preliminaries’ of Section 1.2 in Volume 1 to things that I didn't know about in the 1960s. Most of this new material deals with probabilities and expectations of random events; there's also an introduction to the theory of martingales."
2.  Backtracking: this section is the counterpart to section 7.2.1 which covered the generation of basic combinatorial patterns. This section covers non-basic patterns, ones where the developer needs to make tentative choices and then may need to backtrack when those choices need revision.
3.  Dancing Links: this section is related to 2 above. It develops an important data structure technique that is suitable for backtrack programming described above.

• https://www-cs-faculty.stanford.edu/~knuth/taocp.html
• https://www.amazon.com/gp/product/0134671791/
• https://devwebcl.blogspot.com/2018/06/dominosa.html