A simplified loop-free algorithm for generating permutations

Nachum Dershowitz

doi:10.1007/BF01932689

A simplified loop-free algorithm for generating permutations

Nachum Dershowitz^*

^*Corresponding author for this work

Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

A simple loop-free algorithm for generation of all permutations of a set of elements is presented and its validity is proved. It is a simplification of Ehrlich's loop-free version of Johnson and Trotter's algorithm. Each permutation is generated by exchanging two adjacent elements of the preceding permutation. A very simple data structure obviates the need for looping during the generation of each successive permutation.

Original language	English
Pages (from-to)	158-164
Number of pages	7
Journal	BIT
Volume	15
Issue number	2
DOIs	https://doi.org/10.1007/BF01932689
State	Published - Jun 1975
Externally published	Yes

Keywords

loop-free algorithms
ordering
permutation generation
permutations
permutations and combinations

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10.1007/BF01932689

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abstract = "A simple loop-free algorithm for generation of all permutations of a set of elements is presented and its validity is proved. It is a simplification of Ehrlich's loop-free version of Johnson and Trotter's algorithm. Each permutation is generated by exchanging two adjacent elements of the preceding permutation. A very simple data structure obviates the need for looping during the generation of each successive permutation.",

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AB - A simple loop-free algorithm for generation of all permutations of a set of elements is presented and its validity is proved. It is a simplification of Ehrlich's loop-free version of Johnson and Trotter's algorithm. Each permutation is generated by exchanging two adjacent elements of the preceding permutation. A very simple data structure obviates the need for looping during the generation of each successive permutation.

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KW - ordering

KW - permutation generation

KW - permutations

KW - permutations and combinations

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A simplified loop-free algorithm for generating permutations

Abstract

Keywords

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