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 19, Problem 2P
(a)
Program Plan Intro
To shows the properties of the binomial tree.
(b)
Program Plan Intro
To explain the relationship between the binomial trees contain H and the binary representation of n .
(c)
Program Plan Intro
To explains the different operations of the binomial heap with running time.
(d)
Program Plan Intro
To explain the maximum degree of Fibonacci heap and alsodefined the DECREASE-KEY operation.
(e)
Program Plan Intro
To explain the running time of insertion and union operation on the McGee heaps.
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A binomial tree, Bn is defined recursively as follows.
B0 is the tree with a single vertex.Create Bn+1, where n is a nonnegative integer, by making two copies of Bn; the first copy becomes the root tree of Bn+1, and the second copy becomes the leftmost child of the root in the first copy.Here are examples for n = 0 to 3:
A. Create a table that has the number of nodes in each depth, d, of B0 to B4, where d ≥ 1 (you should NOT have to draw B5!).
B. What do you think the answers for problem d, above, for B5?
When iterating over a hierarchical data structure, such as a tree,Group of answer choices
1. Iterating must be done recursively and it must start at the root, visiting each node once.
2. Iterating must start at the children, and must be done with recursion.
3. Iterating starts at the root but can continue depth first or breadth first, and must be done recursively.
4. Iterating must start at the root and it must traverse nodes exactly once.
In this task, a binomial heap should be implemented. A binomial heap is implemented byan array with its elements being binomial trees: on the first place there is the binomial treeB0 with one element, on the second place there is the binomial tree B1 with two elements,on the third place there is the binomial tree B2 with four elements,. . . Each binomial treeis implemented recursively using the class BinomialNode. In this class there is nothing toimplement. Methods in this class are needed for the implementation of the methods in theclass BinomialHeap. More precisely, in the class BinomialHeap you should implement thefollowing methods:(i) insert, which takes an integer (a key) and inserts it in the binomial heap. Themethod returns true, if the key is successfully inserted and false otherwise. In thecase, if the array should be resized, use the method resizeArray (see below).(ii) getMin, which returns the minimal key in binomial heap. The implementation willbe also efficient if you…
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