The Night Owls Society is arranging a conference. To minimize costs, they want to schedule as many sessions as possible in the main ballroom. Since night owls go to bed late and wake up late, they want sessions to begin as late as possible and don't care how late they run. Each session has a fixed start time and a fixed end time, though sessions may overlap. For example, the sessions may be as follows. (In a realistic version of this problem, there may be many more sessions.) Session Name Basket weaving Floral arrangements Cake decoration Start time End time 10:30 AM 11:45 AM 10:45 AM 12:30 PM 12:15 AM 2:00 PM Cookie baking 12:45 PM Pasta making Table decoration 3:00 PM 4:30 PM 5:45 PM 2:15 PM 3:30 PM a. Define what it means for this problem to have optimal substructure. b. Show that this problem does have optimal substructure. c. What algorithmic strategy can one use to solve a problem with optimal substructure? (Do not write out the algorithm.) d. What does it mean for a problem to have the greedy choice property?

Suppose you always eat a particular brand of cookies out of the standard-sized package it comes in from the store, which has 4 rows of cookies in equal amounts. You notice that when you eat 3 at a time, there's always one cookie left over. you decide when you purchase the next package, you'll eat 5 at a time but still, there's always one cookie left over. Since it really isn't helpful to always have a leftover cookie you decide to eat 7 at a time and there are no cookies leftover, but you do notice that in your last grab of 7 cookies, you're one cookie short

Let's revisit our first problem, where we want to set up a series of chess matches so we can rank six players in our class. As we did before, we will assume that everyone keeps their chess rating a private secret; however, when two players have a chess match, the person with the higher rating wins 100% of the time. But this time, we are only interested in identifying the BEST of these six players and the WORST of these six players. (We don't care about the relative ordering or ranking of the middle four players.) Your goal is to devise a comparison-based algorithm that is guaranteed to identify the player with the highest rating and the player with the lowest rating. Because you are very strong at Algorithm Design, you know how to do this in the most efficient way. Here are five statements. A. There exists an algorithm to solve this problem using 6 matches, but there does not exist an algorithm using only 5 matches. B. There exists an algorithm to solve this problem using 7 matches,…

As we've previously seen, equations describing situations often contain uncertain parameters, that is, parameters that aren't necessarily a single value but instead are associated with a probability distribution function. When more than one of the variables is unknown, the outcome is difficult to visualize. A common way to overcome this difficulty is to simulate the scenario many times and count the number of times different ranges of outcomes occur. One such popular simulation is called a Monte Carlo Simulation. In this problem-solving exercise you will develop a program that will perform a Monte Carlo simulation on a simple profit function. Consider the following total profit function: PT=nPv Where Pr is the total profit, n is the number of vehicles sold and P, is the profit per vehicle. PART A Compute 5 iterations of a Monte Carlo simulation given the following information: n follows a uniform distribution with minimum of 1 and maximum 10 P, follows a normal distribution with a mean…

All businesses want to keep their customers happy. To do that, many companies assign a certain amount of time to each customer to optimize the business. The alternative would be to hire more employees, which would lead to higher costs.  This problem requires you to simulate how authorities optimize the number of cashiers at the entrance of a toll bridge to make sure drivers are satisfied. Make the following assumptions: There is one cashier per line. The line works as a queue with no cars cutting the line or leaving it. One car arrives at the entrance every 10 seconds.  It takes 90 seconds (1.5 minutes) to process the payment, starting from the moment a cashier is available. Assume there is no pause between cars.  Your Tasks:  Design class CarInLine, with the following specifications: The class has two instance variables: arrivalTime and DepartureTime, stored as integers. Define a constructor that accepts an integer as an argument representing the arrival time, in which you set…

All businesses want to keep their customers happy. To do that, many companies assign a certain amount of time to each customer to optimize the business. The alternative would be to hire more employees, which would lead to higher costs.  This problem requires you to simulate how authorities optimize the number of cashiers at the entrance of a toll bridge to make sure drivers are satisfied. Make the following assumptions: There is one cashier per line. The line works as a queue with no cars cutting the line or leaving it. One car arrives at the entrance every 10 seconds.  It takes 90 seconds (1.5 minutes) to process the payment, starting from the moment a cashier is available. Assume there is no pause between cars.  Written in java, Your Tasks:  Design class CarInLine, with the following specifications: The class has two instance variables: arrivalTime and DepartureTime, stored as integers. Define a constructor that accepts an integer as an argument representing the arrival time, in…