Zip Trees

We introduce the zip tree , 1 a form of randomized binary search that integrates previous ideas into one practical, performant, and pleasant-to-implement package. A is in which each node has numeric rank (max)-heap-ordered with respect to ranks, ties broken favor smaller keys. Zip trees are essentially treaps [8], except ranks drawn from geometric distribution instead uniform distribution, we allow ties. These changes enable us use fewer random bits per node. perform insertions deletions by unmerging merging paths ( unzipping zipping ) rather than doing rotations, avoids some pointer improves efficiency. The methods take inspiration top-down approaches insertion deletion Stephenson [10], Martínez Roura [5], Sprugnoli [9]. From theoretical standpoint, this work provides two main results. First, require only O (log log n (with high probability) represent largest an -node tree; data structures for rank. Second, naturally isomorphic skip lists [7], simplify Dean Jones’ mapping between