Question: Given a rooted tree (T, o) with n vertices and a set of k pairs of vertices {(u1, v1), (u2, v2), . . . ,

Given a rooted tree (T, o) with n vertices and a set of k pairs of vertices {(u1, v1), (u2, v2), . . . , (uk, vk)}, design an algorithm to find the lowest common ancestor of ui and vi for all i = 1, . . . , k. Analyse the running time of your algorithm. Faster and correct algorithms worth more points.

You should try to find an algorithm to solve the problem for an undirected rooted tree but if you solve the directed version you will get partial credit.

Hint: Consider the labels prev() and post(). Consider the set S of all vertices DFS discovered but havent finish exploring (i.e. those vertices with a prev() but no post()). Note that the set S changes as we run DFS. Now, for any pair with prev(ui)

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