What is LCA algorithm?
In ontologies, the lowest common ancestor is also known as the least common ancestor. In a tree data structure where each node points to its parent, the lowest common ancestor can be easily determined by finding the first intersection of the paths from v and w to the root.
Can we reduce Rmq problem to LCA in linear time?
From RMQ to LCA. We have shown that the LCA problem can be reduced to RMQ in linear time.
What is ancestor in graph theory?
Ancestor. In a rooted tree, a vertex on the path from the root to the vertex. Vertex v is an ancestor of vertex w if and only if w is a descendant of v.
What is range in DBMS?
A range query is a common database operation that retrieves all records where some value is between an upper and lower boundary.
What is ancestor and descendant in graph?
A node that is connected to all lower-level nodes is called an “ancestor”. The connected lower-level nodes are “descendants” of the ancestor node.
What is the difference between BST and heap?
The Heap differs from a Binary Search Tree. The BST is an ordered data structure, however, the Heap is not. In computer memory, the heap is usually represented as an array of numbers. The heap can be either Min-Heap or Max-Heap.
What is the Tarjan algorithm?
The algorithm is named after Robert Tarjan, who discovered it in 1979 and also made many other contributions to the Disjoint Set Union data structure, which will be heavily used in this algorithm. The algorithm answers all queries with one DFS traversal of the tree.
What happens during the LCA walk in Tarjan?
During the LCA walk, our queries gets processed and outputted (in a random order). After the LCA walk of the whole tree, all the nodes gets coloured BLACK. Tarjan Offline LCA Algorithm steps from CLRS, Section-21-3, Pg 584, 2nd /3rd edition.
Can the LCA also be one of the two nodes?
The node v is also an ancestor of v, so the LCA can also be one of the two nodes. In this article we will solve the problem off-line, i.e. we assume that all queries are known in advance, and we therefore answer the queries in any order we like.