treaper's trangout
The treap was first described by Cecilia R. Aragon andRaimund Seidel in 1989;[1][2]its name is a portmanteau of tree and heap. It is a Cartesian tree[3] in which each key is given a (randomly chosen) numeric priority. As with any binary search tree, the inorder traversal order of the nodes is the same as the sorted order of the keys. The structure of the tree is determined by the requirement that it be heap-ordered: that is, the priority number for any non-leaf node must be greater than or equal to the priority of its children. Thus, as with Cartesian trees more generally, the root node is the maximum-priority node, and its left and right subtrees are formed in the same manner from the subsequences of the sorted order to the left and right of that node.
An equivalent way of describing the treap is that it could be formed by inserting the nodes highest-priority-first into a binary search tree without doing any rebalancing. Therefore, if the priorities are independent random numbers (from a distribution over a large enough space of possible priorities to ensure that two nodes are very unlikely to have the same priority) then the shape of a treap has the same probability distribution as the shape of arandom binary search tree, a search tree formed by inserting the nodes without rebalancing in a randomly chosen insertion order. Because random binary search trees are known to have logarithmic height with high probability, the same is true for treaps.
Aragon and Seidel also suggest assigning higher priorities to frequently accessed nodes, for instance by a process that, on each access, chooses a random number and replaces the priority of the node with that number if it is higher than the previous priority. This modification would cause the tree to lose its random shape; instead, frequently accessed nodes would be more likely to be near the root of the tree, causing searches for them to be faster.
Blelloch and Reid-Miller[4] describe an application of treaps to a problem of maintaining sets of items and performing set union, set intersection, and set difference operations, using a treap to represent each set. Naor and Nissim[5] describe another application, for maintaining authorization certificates in public-key cryptosystems.
Howdy, Stranger!
It looks like you're new here. If you want to get involved, click one of these buttons!