Abstract
A priority queue transforms an input sequence σ into an output sequence τ which is a re-ordering of the sequence σ. The setR of all such related pairs is studied in the case that σ is a binary sequence. It is proved thatR is a partial order and that ¦R¦=c n+1, the (n+1)th Catalan number. An efficient (O(n 2)) algorithm is given for computing the number of outputs achievable from a given input.
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References
D. E. Knuth, (1973)Fundamental Algorithms, Addison-Wesley, Reading, Mass.
T. H. Cormen, C. H. Leiserson, and R. L. Rivest (1992)Introduction to Algorithms, McGraw-Hill, Cambridge, Mass.
M. D. Atkinson and Robert Beals, Priority queues and permutations, in preparation.
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Communicated by N. Zaguia
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Atkinson, M.D. Transforming binary sequences using priority queues. Order 10, 31–36 (1993). https://doi.org/10.1007/BF01108706
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DOI: https://doi.org/10.1007/BF01108706