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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 ...
Due to this decomposability, some data structures answer -majority queries on one-dimensional arrays by finding the Lowest common ancestor (LCA) of the endpoints of the query range in a Range tree and validating two sets of candidates (of size (/)) from each endpoint to the lowest common ancestor in constant time resulting in (/) query time.
Range minimum query reduced to the lowest common ancestor problem.. Given an array A[1 … n] of n objects taken from a totally ordered set, such as integers, the range minimum query RMQ A (l,r) =arg min A[k] (with 1 ≤ l ≤ k ≤ r ≤ n) returns the position of the minimal element in the specified sub-array A[l …
Tarjan's off-line lowest common ancestors algorithm Tarjan's algorithm for finding bridges in an undirected graph [ 1 ] Tarjan's algorithm for finding simple circuits in a directed graph [ 2 ]
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 ...
Else, find what would have been the lowest common ancestor of the point and the cell in an uncompressed quadtree. Call this ancestor cell u {\displaystyle u} . Find the existing cell in the compressed tree that comes before u {\displaystyle u} in the Z -order and return it.
English: A directed acyclic graph with the common ancestors of two nodes in green, and their lowest common ancestors in dark green. Date 5 August 2014, 11:04:41