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hw4-problems - 19.4-1 Professor Pinocchio claims that the...

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Unformatted text preview: 19.4-1 . Professor Pinocchio claims that the height of an n-node Fibonacci heap is 0(1g‘ Show that the professor is mistaken by exhibiting, for any positive integer n sequence of Fibonacci-heap operations that creates a Fibonacci heap consistin just one tree that is a linear chain of n nodes. 19-3 More F ibon'acci-heap operations We wish to augment a Fibonacci heap H to support two new operations without changing the amortized running time of any other Fibonacci-heap operations. a. The operation FIB-HEAP-CHANGB—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. 20.2-8 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? 20.3-4 . . . What happens if you call VEB-TREE—INSERT with an element that 18 already in, the VEB tree? What happens if you call VEB-TREE—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 MAKE-SET, 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. ...
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