The Art of Computer Programming 4 Generating all n-Tuples, Permutations, Combinations
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English Pages [203] Year 2004
1 Tuples
Preface
Generating basic combinatorial Patterns
Algorithm M - mixed-Radix
Gray Binary Code
Algorithm G - Gray Binary
Faster
Algorithm L - loopless Gray Binary
Other Binary Gray Codes
Theorem D & Corollary B
Binary Gray Paths
Nonbinary Gray Codes
Algorithm H - loopless reflected Mixed-Radix Gray
Subforests
Algorithm K - loopless reflected Subforest
Shift Register Sequences
Algorithm S - generic Shift Register
Algorithm A - almost-linear Bit-Shift
Algorithm R - recirsive de Bruijn Cycle
Algorithm D - doubly recursive de Bruijn C
Definition P
Theorem P
Definition Q & Theorem Q
Algorithm F - prime & preprime String
Exercise
Answers
Index
2 Permutations
Preface
Algorithm L - lexicographic Permutation
Adjacent Interchanges
Algorithm P - plain Changes
Algorithm T - plain Change Transitions
Alphametics
General Framework
Lemma S
Using the General Framework
Algorithm G - general Permutation
Bypassing unwanted Blocks
Algorithm X - lexicographic Permutations with restricted Prefixes
Dual Methods
Algorithm H - dual Permutation
Algorithm C - cyclic Shifts
Algorithm E - Ehrlich Swaps
Using fewer Generators
Theorem R
Faster
Topological Sorting
Algorithm V - all topological Sorts
Think twice
Exercises
Answers
Index
3 Combinations
Preface
Generating all Combinations
Lexicographic Generation
Algorithm L - lexicographic Combinations
Algorithm T - lexicographic Combinations
Theorem L
Binomial Trees
Algorithm F - filling a Rucksack
Gray Codes for Combinations
Algorithm R - Revolving-Door Combinations
Near-perfect Schemes
Theorem N
Algorithm C - Chase Sequence
Analysis of Chase Sequence
Near-perfect Multiset Permutations
Perfect Schemes
Theorem P
Combinations of Multiset
Shadows
Theorem K
Theorem M
Theorem W
Lemma S
Corollary C
Exercises
Answers
Index
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- Donald E. Knuth
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