Unformatted text preview: 19.41 . Professor Pinocchio claims that the height of an nnode Fibonacci heap is 0(1g‘
Show that the professor is mistaken by exhibiting, for any positive integer n sequence of Fibonacciheap operations that creates a Fibonacci heap consistin
just one tree that is a linear chain of n nodes. 193 More F ibon'acciheap operations
We wish to augment a Fibonacci heap H to support two new operations without
changing the amortized running time of any other Fibonacciheap operations. a. The operation FIBHEAPCHANGB—KEY (H, x, k) changes the key of node x
to the value k. Give an efﬁcient implementation of FIB~HEAP—CHANGE—KEY, and analyze the amortized running time of your implementation for the cases
in which k is greater than, less than, or equal to x. key. 20.28 Suppose that we designed a proto —vEB structure in which each cluster array had
only u 1/4 elements. What would the running times of each operation be? 20.34 . . .
What happens if you call VEBTREE—INSERT with an element that 18 already in,
the VEB tree? What happens if you call VEBTREE—DELETE with an element that
is not in the VEB tree? Explain why the procedures exhibit the behavror that they do. Show how to modify VEB trees and their operations so that we can check in
constant time whether an element is present. 21 .3 3 Give a sequence of m MAKESET, UNION, and FIND—SET operations, 11 of whiCh are MAKE~SET operations, that takes 52(m lg n) time when we use union by rank
only. ...
View
Full Document
 Summer '09

Click to edit the document details