An almost sure result for path lengths in binary search trees
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This paper studies path lengths in random binary search trees under the random permutation model. It is known that the total path length, when properly normalized, converges almost surely to a nondegenerate random variableZ. The limit distribution is commonly referred to as the ‘quicksort distribution’. For the class 𝒜mof finite binary trees with at mostmnodes we partition the external nodes of the binary search tree according to the largest tree that each external node belongs to. Thus, the external path length is divided into parts, each part associated with a tree in 𝒜m. We show that the vector of these path lengths, after normalization, converges almost surely to a constant vector timesZ.
2003 ◽
Vol 35
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pp. 363-376
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2000 ◽
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pp. 485-513
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2010 ◽
Vol 19
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pp. 561-578
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2003 ◽
Vol 14
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pp. 465-490
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2016 ◽
Vol 26
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pp. 1650015
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1990 ◽
Vol 01
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pp. 449-463
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2006 ◽
Vol 21
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pp. 133-141
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2010 ◽
Vol 19
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pp. 391-424
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