Lowest Common Ancestor(LCA)

Before embarking into the technicalities of the different algorithms for LCA, let us first agree on the terminology that we will be using throughout this article. Let there be a rooted tree T(E,V). A node x ∈ T is called an ancestor of a node y ∈ T if the path from the root of T to y goes through x. Also, a node v ∈ T is called to be a common ancestor of x and y if it is an ancestor of both x and y. Hence, the Nearest/Lowest Common Ancestor, NCA or LCA, of two nodes x, y is the common ancestor of x and y whose distance to x (and to y) smaller than the distance to x of any common ancestor of x and y. From now on, we denote the NCA of two nodes x and y from the tree T as nca(x, y). As we have already pointed out, efficiently computing NCAs has been studied extensively for the last 3 decades in both online and offline settings.