Question: a. Prove that for binary heaps, buildHeap does at most 2N2 comparisons between elements. b. Show that a heap of eight elements can be constructed

a. Prove that for binary heaps, buildHeap does at most 2N−2 comparisons between elements.

b. Show that a heap of eight elements can be constructed in eight comparisons between heap elements.

c. Give an algorithm to build a binary heap in 13/8 N + O(logN) element comparisons.

Step by Step Solution

★★★★★

3.48 Rating (178 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a We show that H N which is the sum of the heights of nodes in a complete binary tree of N nodes is N b N where b N is the number of ones in the binar... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

1486-C-S-A(406).docx

120 KBs Word File

Students Have Also Explored These Related Algorithms Questions!

A scaling algorithm solves a problem by initially considering only the highest-order bit of each relevant input value (such as an edge weight). It then refines the initial solution by looking at the...

Suppose that binary heaps are represented using explicit links. Give a simple algorithm to find the tree node that is at implicit position i.

We can perform buildHeap in linear time for leftist heaps by considering each element as a one-node leftist heap, placing all these heaps on a queue, and performing the following step: Until only one...

Prove that for binary heaps, buildHeap () does at most 2N - 2 comparisons between elements. Show that a heap of 8 elements can be constructed in eight comparisons

make a project on topic priority queue using binary heap help with the research paper giving above to implementation code in python data structure do it in one day S.L. Graham, R.L. Rivest Editors...

1. Show that a binary heap of 8 elements can be constructed in eight comparisons. Explain your method. 2. Show the following regarding the maximum item in a binary min-heap. (a) It must be a leaf...

QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...

1. (30 pts) Recall from Boolean algebra that there are2216 different binary Boolean functions including AND, OR, NOT and XOR. Show that XOR and XOR are the only two binary Boolean functions among all...

Problem | Binary exponentiation Recall the exponentiation algorithm given in class for evaluating a n (mod m) (a Z, m,n N): 1. Compute the binary representation of n: n = b 0 2 k + b 1 2 k-1 + ... +...

For monotone functions f, f0: P Q between posets (P, vP ) and (Q, vQ), let f v f(i) Prove that the binary relation v is a partial order. [3 marks] (ii) For monotone functions between posets p : P 0...

What value of C would make f(x) continuous at x = -2? Decimal approximations are not allowed for this problem. Compute the exact value for C and express your answer algebraically. . f(x) = x + 4x +...

Bob owns a rental property that he bought several years ago for $250,000 He has taken depreciation on the house of $35,000 since buying it He sells it in 2019 for $290,000 His selling expenses are...

Assuming an interest rate of 5 . 5 percent, what is the value of the following cash flows four years from today? YearCash Flow 1 $ 3 , 0 2 5 2 4 , 0 6 0 3 5 , 9 1 0 4 8 , 0 0 5

11. Suppose, at a party for economics majors, you win a choice among three mystery boxes. You dont know what each contains, but you know that each box has a pair of gifts. You know that one box has a...

Use a recursion tree to give an asymptotically tight solution to the recurrence T(n) = T(n) + T((1 - )n) + cn, where is a constant in the range 0 0 is also a constant.

Suppose that you want to output 0 with probability 1/2 and 1 with probability 1/2. At your disposal is a procedure BIASED-RANDOM, that outputs either 0 or 1. It outputs 1 with some probability p and...

In HIRE-ASSISTANT, assuming that the candidates are presented in a random order, what is the probability that you will hire exactly one time? What is the probability that you will hire exactly n...

A bond with a face value of $1,000 matures in 9 years and has a 7% semiannual coupon. The bond currently is traded at $900. Which of the following statements is CORRECT? Select one: a. The nominal...

When is hypothesis testing carried out about a median? Explain and present an example.

A researcher wants to determine whether adolescents spend more time in a day around friends than adults do. He gathers a sample of n = 10 adolescents (aged 12-17) and a sample of n = 6 adults (aged...