lowest common ancestor - OpenGenus IQ: Computing Expertise & Legacy

Using Farach Colton and Bender Algorithm to solve LCA【O(V) query】

The basic idea of Farach Colton and Bender Algorithm is to traverse all the nodes using the Depth First Search graph traversal and keep a record of all the visited nodes and there corresponding heights. This allows to answer LCA queries in O(V) time complexity

Algorithms

Binary Lifting with k-th ancestor and lowest common ancestor (LCA)

Binary Lifting is a technique used to find the k-th ancestor of any node in a tree in O(log N). This also leads to a faster algorithm in finding the lowest common ancestor (LCA) between two nodes in a tree. The technique requires preprocessing the tree in O(N log N) using dynamic programming.