Treap (A Randomized Binary Search Tree) Last Updated : 15 Dec, 2022 Comments Improve Suggest changes Like Article Like Report Like Red-Black and AVL Trees, Treap is a Balanced Binary Search Tree, but not guaranteed to have height as O(Log n). The idea is to use Randomization and Binary Heap property to maintain balance with high probability. The expected time complexity of search, insert and delete is O(Log n). Every node of Treap maintains two values. 1) Key Follows standard BST ordering (left is smaller and right is greater) 2) Priority Randomly assigned value that follows Max-Heap property. Basic Operation on Treap: Like other self-balancing Binary Search Trees, Treap uses rotations to maintain Max-Heap property during insertion and deletion. T1, T2 and T3 are subtrees of the tree rooted with y (on left side) or x (on right side) y x / \ Right Rotation / \ x T3 – – – – – – – > T1 y / \ < - - - - - - - / \ T1 T2 Left Rotation T2 T3 Keys in both of the above trees follow the following order keys(T1) < key(x) < keys(T2) < key(y) < keys(T3) So BST property is not violated anywhere. search(x) Perform standard BST Search to find x. Insert(x): 1) Create new node with key equals to x and value equals to a random value. 2) Perform standard BST insert. 3) Use rotations to make sure that inserted node's priority follows max heap property. Delete(x): 1) If node to be deleted is a leaf, delete it. 2) Else replace node's priority with minus infinite ( -INF ), and do appropriate rotations to bring the node down to a leaf. Refer Implementation of Treap Search, Insert and Delete for more details. References: https://en.wikipedia.org/wiki/Treap https://courses.cs.washington.edu/courses/cse326/00wi/handouts/lecture19/sld017.htm Comment More infoAdvertise with us Next Article Treap (A Randomized Binary Search Tree) kartik Follow Improve Article Tags : Advanced Data Structure DSA Self-Balancing-BST Practice Tags : Advanced Data Structure Similar Reads Advanced Data Structures Advanced Data Structures refer to complex and specialized arrangements of data that enable efficient storage, retrieval, and manipulation of information in computer science and programming. These structures go beyond basic data types like arrays and lists, offering sophisticated ways to organize and 2 min read Generic Linked List in C A generic linked list is a type of linked list that allows the storage of different types of data in a single linked list structure, providing more versatility and reusability in various applications. 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