Algorithm to find lowest common ancestor in directed acyclic graph?

Question

Imagine a directed acyclic graph as follows, where:

• \"A\" is the root (there is always exactly one root)
• each node knows its parent(s)
• the no

Answer 1

I am proposing O(|V| + |E|) time complexity solution, and i think this approach is correct otherwise please correct me.

Given directed acyclic graph, we need to find LCA of two vertices v and w.

Step1: Find shortest distance of all vertices from root vertex using bfs http://en.wikipedia.org/wiki/Breadth-first_search with time complexity O(|V| + |E|) and also find the parent of each vertices.

Step2: Find the common ancestors of both the vertices by using parent until we reach root vertex Time complexity- 2|v|

Step3: LCA will be that common ancestor which have maximum shortest distance.

So, this is O(|V| + |E|) time complexity algorithm.

Please, correct me if i am wrong or any other suggestions are welcome.