+1-415-315-9853

info@mywordsolution.com

## Engineering

 Civil Engineering Chemical Engineering Electrical & Electronics Mechanical Engineering Computer Engineering Engineering Mathematics MATLAB Other Engineering Digital Electronics Biochemical & Biotechnology

1. On the east coast of the U.S. there are many toll roads such as the Pennsylvania Turnpike and the Garden State Expressway. When you enter the toll road you get handed a ticket with your entrance location marked on it. Then when you exit the toll road you pay an amount based on where you entered and exited. To be precise, each segment (from exit i to exit i+1) has a cost Ci,i+1 and the cost of entering at exit j and exiting at exit k (for j < k) is equal to k-1i=j Ci,i+1. If the road has n exits then it has n-1 segments which can be represented in a one dimensional array, C[1,....,n-1], where C[i] holds the cost to travel from exit i to exit i + 1. Clearly, if you have the array C you can determine the cost of traveling from exit j to exit k by computing k-1i=j Ci,i+1 which will take O(k-j) time.

Show how to build a data structure that will allow you to determine the cost of traveling from exit j to exit k on the toll road in O(1) time. A fair answer creates a data structure that has O(n2) elements. A better answer creates a data structure that has O(n) elements.

Be sure to justify the correctness of your solution and analyze the running time required to build your data structure.

2. A binary tree is full if all of its nodes have either zero or two children. Let Bn denote the number of full binary trees with n nodes.
(a) Draw all full binary trees with 3, 5, and 7 nodes and determine the exact values of B3,B5,B7.

(b) Why did I leave out trees with an even number of nodes?

(c) For odd n devise a recurrence relation for Bn and bound its value in terms of n.

3. A one pass auction is an auction in which each bid must be immediately and irrevocably accepted or refused. Specifically, a one pass auction works as follows:

• A seller announces the availability of an item

• n buyers agree to bid on the item and are presented to the seller in random order.

• When buyer i appears he must make a bid bi > 0 without any knowledge of the bids thus far.

• The seller must decide immediately whether to accept or reject buyer i's bid. If the seller accepts then all future buyers are turned away. If the seller rejects then buyer i leaves and his bid is withdrawn.

Obviously the seller would like to maximize her profit but since she doesn't know what future bids will be and she can't accept a bid she has already rejected she will never be able to formulate an algorithm that ensures that she accepts the highest bid. She must turn to a probabilistic algorithm. Consider the following two phase algorithm that a seller may follow:

1) Reject the first n/10 bids but keep track of the largest bid seen. Call that bid B*.

2) In the remaining bids accept the first bid that surpasses B* (if none surpass B* then accept the very last bid).

Investigate this algorithm and try to answer the following problems:

(a) Using the given algorithm what is the probability that the seller accepts the highest bid?

(b) Can you come up with a better probabilistic algorithm for a one pass auction? Justify why it is better.

(c) In general, how do you determine whether one algorithm is better than another for this type of auction?

Computer Engineering, Engineering

• Category:- Computer Engineering
• Reference No.:- M91926

Have any Question?

## Related Questions in Computer Engineering

### Composing and using regular expressionsregular expressions

Composing and Using Regular Expressions Regular expressions became popular with the introduction of the UNIX operating system in 1960s and its text processing tools such as  grep  and  ed . Write a two to three (2-3) pag ...

### For this problem interpret the n-point dft as an n-periodic

For this problem, interpret the N-point DFT as an N-periodic function of k. Answer yes or no if the following frequencydomain signals are valid DFTs. For each valid DFT, determine the size N of the DFT and whether the ti ...

### The algorithm we have developed may not reproduce the

The algorithm we have developed may not reproduce the original text if the output was used as input. This would happen because if there was a space at the end of an input line it would be turned into two spaces in the re ...

### Case study - directors requirementsyour office has outgrown

Case Study - Director's Requirements Your office has outgrown its old desktop machines and is in the market for new PCs, but would like some guidance on what to purchase. The Director wants to ensure that the office obta ...

### 1 what is the definition of single loss expectancy what is

1. What is the definition of single loss expectancy? What is annual loss expectancy? 2. What is residual risk?

### Describe google and amazons new information technology

Describe Google and Amazon's new information technology infrastructure. What is the relationship between this new infrastructure and the global, Web-based platform? Explain why IT is a business pressure as well as an ena ...

### 1 compare the authorization model used by the network

1. Compare the authorization model used by the network operating systems (NOS) to that used by the old stand-alone operating systems. 2. List and discuss the most common access privileges in a computing system. 3. Discus ...

### Technical paper programming for the health care industryits

Technical Paper: Programming for the Health Care Industry It's common knowledge that using computers in the health care industry can improve the quality and effectiveness of care while reducing costs. However, the adopti ...

### 1 in a very small as using ospf is it more efficient to use

1. In a very small AS using OSPF, is it more efficient to use only one single area (backbone) or several areas? 2. Why do you think we need only one RIP update message, but several OSPF update messages? 3. OSPF messages ...

### 1 can a host have more than one multicast address explain2

1. Can a host have more than one multicast address? Explain. 2. A multicast router is connected to four networks. The interest of each network is shown below. What is the group list that should be advertised by the route ...

• 4,153,160 Questions Asked
• 13,132 Experts
• 2,558,936 Questions Answered

## Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

### Section onea in an atwood machine suppose two objects of

SECTION ONE (a) In an Atwood Machine, suppose two objects of unequal mass are hung vertically over a frictionless

### Part 1you work in hr for a company that operates a factory

Part 1: You work in HR for a company that operates a factory manufacturing fiberglass. There are several hundred empl

### Details on advanced accounting paperthis paper is intended

DETAILS ON ADVANCED ACCOUNTING PAPER This paper is intended for students to apply the theoretical knowledge around ac

### Create a provider database and related reports and queries

Create a provider database and related reports and queries to capture contact information for potential PC component pro

### Describe what you learned about the impact of economic

Describe what you learned about the impact of economic, social, and demographic trends affecting the US labor environmen