This fascicle inaugurates the eagerly awaited publication
of Knuth's The Art of Computer Programming, Volume 4: Combinatorial Algorithms. Part of what will be a long chapter on combinatorial searching, the fascicle begins his treatment
of how to generate all possibilities. Specifically, it discusses
the generation of all n-tuples, then extends those ideas to
all permutations. Such algorithms provide a natural motivation by means of which many of the key ideas of combinatorial mathematics can be introduced and explored. In this and other fascicles of Volume 4, Knuth illuminates important theories by discussing related games and puzzles. Even
serious programming can be fun.
Chapter 7 – Combinatorial Searching
7.2 Generating All Possibilities
7.2.1 Generating Basic Combinatorial Patterns
7.2.1.1 Generating all n-typles
7.2.1.2 Generating all permutations
Answers to Exercises