Abstract
A sequence of priority queue operations can transform a permutation π of n elements to some, but not necessarily all, permutations σ. A recent result of Atkinson and Thiyagarajah (1993) states that the number of distinct transformation pairs (π, σ) is ( n + 1) n −1 . By Cayley's theorem this is also the number of labelled trees with n + 1 nodes. We present a direct correspondence between labelled trees and transformation pairs and a linear time algorithm for constructing the tree corresponding to a pair of permutations along with related results.
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