Abstract
We design an algorithm that generates multiset permutati- ons in O(1) time from permutation to permutations, using only data structures of arrays. The previous O(1) time algorithm used pointers, causing O(n) time to access an element in a permutation, where n is the size of permutations. The central idea in our algorithm is tree traversal. We associate permutations with the leaves of a tree. By traversing this tree, going up and down and making changes when necessary, we spend O(1) time from permutation to permutation. Permutations are generated in a one-dimensional array.
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Takaoka, T. (1999). An O(1) Time Algorithm for Generating Multiset Permutations. In: Algorithms and Computation. ISAAC 1999. Lecture Notes in Computer Science, vol 1741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46632-0_25
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DOI: https://doi.org/10.1007/3-540-46632-0_25
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