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In this tree, the lowest common ancestor of the nodes x and y is marked in dark green. Other common ancestors are shown in light green. In graph theory and computer science, the lowest common ancestor (LCA) (also called least common ancestor) of two nodes v and w in a tree or directed acyclic graph (DAG) T is the lowest (i.e. deepest) node that has both v and w as descendants, where we define ...
In computer science, Tarjan's off-line lowest common ancestors algorithm is an algorithm for computing lowest common ancestors for pairs of nodes in a tree, based on the union-find data structure. The lowest common ancestor of two nodes d and e in a rooted tree T is the node g that is an ancestor of both d and e and that has the greatest depth ...
Binary search Visualization of the binary search algorithm where 7 is the target value Class Search algorithm Data structure Array Worst-case performance O (log n) Best-case performance O (1) Average performance O (log n) Worst-case space complexity O (1) Optimal Yes In computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search ...
Fig. 1: A binary search tree of size 9 and depth 3, with 8 at the root. In computer science, a binary search tree (BST), also called an ordered or sorted binary tree, is a rooted binary tree data structure with the key of each internal node being greater than all the keys in the respective node's left subtree and less than the ones in its right subtree.
To perform a finger search on a binary tree, the ideal way is to start from the finger, and search upwards to the root, until we reach the least common ancestor, [4] [5] also called the turning node, [3] of x and y, and then go downwards to find the element we're looking for. Determining if a node is the ancestor of another is non-trivial.
The cost of a search is modeled by assuming that the search tree algorithm has a single pointer into a binary search tree, which at the start of each search points to the root of the tree. The algorithm may then perform any sequence of the following operations: Move the pointer to its left child. Move the pointer to its right child.
The longest common substrings of a set of strings can be found by building a generalized suffix tree for the strings, and then finding the deepest internal nodes which have leaf nodes from all the strings in the subtree below it. The figure on the right is the suffix tree for the strings "ABAB", "BABA" and "ABBA", padded with unique string ...
In the theory of optimal binary search trees, the interleave lower bound is a lower bound on the number of operations required by a Binary Search Tree (BST) to execute a given sequence of accesses. Several variants of this lower bound have been proven.