Design and Analysis of a Tree-Backtracking Algorithm for Multiset and Pure Permutations
A tree-backtracking-based technique, permutation tree generation with Anterior-items-in-an-array for Remaining Distinct Elements (ARDE), is introduced for multiset and pure permutations. We analyze the algorithm at the assembly level and obtain its time formula for pure permutations. We mathematically prove that our time formula is 11.5% faster than the corresponding formula of the previous fastest algorithm for pure permutations for any length N > 3. We also offer related source codes and executable files on our web site for others to use.
Keywordstree-backtracking tree generation multiset permutation
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- 1.Chen, R.J., Reschke, K.S., Tong, M.: Code of evaluation and comparison for multiset permutations (2010), http://software.xmu.edu.cn/View/ArticleShow.aspx?aid=3108
- 2.Knuth, D.E.: MMIX: A RISC Computer for the New Millennium. In: The Art of Computer Programming. Fascicle, vol. 1. Addison-Wesley, Co., Inc., Reading (2005)Google Scholar
- 4.Sedgewick, R.: Permutation generation methods. Dagstuhl Workshop on Data Structures, Wadern, Germany (2002), http://www.cs.princeton.edu/~rs/talks/perms.pdf (accessed March 22, 2009)