Maurice Tutor

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    Argosy University/ Phoniex University/
    Nov-2005 - Oct-2011

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    Phoniex University
    Oct-2001 - Nov-2016

Category > Computer Science Posted 17 Sep 2017 My Price 7.00

least common ancestor

Tarjan"s off-line least-common-ancestors algorithm

The least common ancestor of two nodes u and v in a rooted tree T is the node w that is an ancestor of both u and v and that has the greatest depth in T. In the off-line least-commonancestors problem, we are given a rooted tree T and an arbitrary set P = {{u, v}} of unordered pairs of nodes in T, and we wish to determine the least common ancestor of each pair in P.

To solve the off-line least-common-ancestors problem, the following procedure performs a tree walk of T with the initial call LCA(root[T]). Each node is assumed to be colored WHITE prior to the walk.

a. Argue that line 10 is executed exactly once for each pair {u, v} ? P.

b. Argue that at the time of the call LCA(u), the number of sets in the disjoint-set data structure is equal to the depth of u in T.

c. Prove that LCA correctly prints the least common ancestor of u and v for each pair {u, v} ? P.

d. Analyze the running time of LCA, assuming that we use the implementation of the disjoint-set data structure in Section 21.3.

Answers

Maurice Tutor
(5)
Status NEW Posted 17 Sep 2017 08:09 AM My Price 7.00

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