Introduction to Algorithms
Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 18, Problem 2P

(a)

Program Plan Intro

Show how to maintain for every node of x of a 2-3-4 tree, the height of the subtree rooted at x as an attribute ofx .height.

(b)

Program Plan Intro

Describe join operation in two 2-3-4 tree as T and T’ and a key k , the join operation should run in O(1 + (h  h)) time.

(c)

Program Plan Intro

Explain the relationship between the heights of Ti1 and Ti . Describe how p breaks S” into sets of trees and keys.

(d)

Program Plan Intro

Implement the split operation on Tusingthe join operation to assemble the keys in S’ into a single 2-3-4 tree T’ and the keys in S” . The running time of the split operation should be O ( lg n ).

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