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The Art of Computer Programming, Volume 4A: Combinatorial Algorithms, Part 1

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The TITLE of Volume 4 is Combinatorial Algorithms, and when I proposed it I was strongly inclined to add a subtitle: The Kind of Programming I Like Best. Mv editors have decided to tone down such exuberance, but the fact remains that programs with a combinatorial flavor have always been my favorites.

On the other hand I've often been surprised to find that, in many people's minds, the word "combinatorial" is linked with computational difficulty. Indeed, Samuel Johnson, in his famous dictionary of the English language (1755), said that the corresponding noun "is now generally used in an ill sense." Colleagues tell me tales of woe, in which they report that "the combinatorics of the situation defeated us." Why is it that, for me, combinatorics arouses feelings of pure pleasure, yet for many others it evokes pure panic?

It's true that combinatorial problems are often associated with humongously large numbers. Johnson's dictionary entry also included a quote from Ephraim Chambers, who had stated that the total number of words of length 24 or less,  in a 24-letter alphabet, is 1,391,724,288,887,252,999,425,128,493,402,200. Thecorresponding number for a 10-letter alphabet is 11.111,111.110; and it's only 3905 when the number of letters is 5. Thus a "combinatorial explosion" certainly does occur as the size of the problem grows from 5 to 10 to 24 and beyond.

 

The book is Volume 4A, because Volume 4 has itself become a multivolume undertaking. Combinatorial searching is a rich and important topic, and Knuth has too much to say about it that is new, interesting, and useful to fit into a single volume, or two, or maybe even three. This book alone includes approximately 1500 exercises, with answers for self-study, plus hundreds of useful facts that cannot be found in any other publication. Volume 4A surely belongs beside the first three volumes of this classic work in every serious programmer’s library.

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