A project to build a new railroad along a county road needs to decide on the locations of the train stations to be constructed. Along the county road there are multiple towns, with their location known (assume the road to be a straight line, with mile marker 0 at the state line, with town locations marked along the way). Design an algorithm that decides at which locations to build train stations along the route with the constraints that: 1) each town must be within a distance D from a train station and 2) a minimum number of train stations are built. Example: Consider a scenario where D = 1 and towns are located at coordinates 0, 2, 3, 4, and 5. An optimal solution would be to place train stations at locations 1 and 4, which would cover all the towns. Note: to prove that your greedy strategy yields the optimal solution, you have to prove that

A project to build a new railroad along a county road needs to decide on the locations of the train stations to be constructed. Along the county road there are multiple towns, with their location known (assume the road to be a straight line, with mile marker 0 at the state line, with town locations marked along the way). Design an algorithm that decides at which locations to build train stations along the route with the constraints that: 1) each town must be within a distance D from a train station and 2) a minimum number of train stations are built. Example: Consider a scenario where D = 1 and towns are located at coordinates 0, 2, 3, 4, and 5. An optimal solution would be to place train stations at locations 1 and 4, which would cover all the towns. Note: to prove that your greedy strategy yields the optimal solution, you have to prove that

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter19: Probabilistic Dynamic Programming

Section19.4: Further Examples Of Probabilistic Dynamic Programming Formulations

Problem 7P

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Scenario:One of the renowned supermarket in Dhaka City, “Shwapno” is celebrating their firstanniversary of opening. They have become very popular among people in a short amount oftime. As a method of celebration they have designed three interesting and exciting offer for theircustomers for that day only!! The offers are described as follows:Offer 1: This offer says, if the name of any customer starts with “S” OR ends with “o”, theywill receive a gift which contains 1 kg miniket rice and 1 litre soyabean oil. This offer isdedicated from their name, Shwapno.Offer 2: This offer says, if one customer have taken products and his/her total product weightis less than 1.50 kg, then Shwapno will give all the products to the customer for free. If the totalweight is 1.50 kg or more, the customer will have to pay the full amount.Offer 3: This offer says, if a customer is aged less than 15, then he/she will receive chocolates.If aged 15 or more, then no gifts for the customer.Implementation:Create…
The distance d between a point p(x, y), where x and y are the coordinates of p, and the center of a circle (a, b), where a and b are the coordinates of the center, is given by the formula: (a, b). r d = (x – a)² + (y – b)² r The point p(x, y) is considered inside the circle if d r. (x, y)' (x', y') Write a Java class called CirclePointthat: a. Reads from the user 2 integer values x and y represent the coordinates of the point p, b. Reads from the user 2 integer values a and b represent the coordinates of the center of the circle, c. Reads from the user a real value r represents the radius of the circle, d. Calculates and prints the distance d (rounded to 2 decimal places) between the point p and the center of the circle, and e. Checks and prints whether the point is inside, on or outside the circle. NOTE: if the radius value is negative, an error message should be shown. Sample Run 1: ==================== Enter the coordinates of the point: 5 7 Enter the coordinates of the center of…
Admission to college is just beginning and Chef has also just finished his high school. There are N colleges, listed from 11 to N, and listed from 11 to N. Each college has only one seat left. To apply for a college, each student must submit the same examination, the result of which determines their future, that is, the best student (the highest scorer) gets the first choice of college. Each student has a list of favourite colleges. They will want to get to the top ranked college on their list. If they can't get into it, they'll want to get into a second-ranked college in the middle of their list, and so on. If one vacant college seat is filled, that year's admission closes at that college. Then, people who have applied for that college should look for a lower college in their preferred list as long as it still has vacancies. Looking at the information about MM students, about their exam scores (given as standards) and the college IDs they apply for, find out which college the Chef…
Problem You have a fence post located at the point (x,y) where a goat is tethered by a rope. You also have a house, which is a rectangle with diagonally opposite corners at the points bottom-left: (x1,y1) and top-right: (x2,y2). You want to pick a length of rope that guarantees the goat cannot reach the house. Determine the minimum distance from the fence post to the house, so that you can make sure to use a shorter rope. Recall that the distance formula is: (x2−x1)2+(y2−y1)2 The input consists of a single line containing six space-separated integer values: x, y, x1, y1, x2, and y2. You are guaranteed that x1<x2 and y1<y2, and that (x,y) is strictly outside the axis-aligned rectangle with corners at (x1,y1) and (x2,y2). Return the minimum distance from the goat’s post to the house as a floating-point value from main(). Learning Objectives Be able to create a program with a lesser template. Be able to calculate the min/max of integers. Be able to write a mathematical…
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A midterm exam has two parts. Part 1 consists of ten multiple choice questions. Each question hasfour choices, labeled (a), (b), (c), and (d), and one may pick any combination of responses on each ofthese questions. For example, one could choose just (a) alone on one question, or both (b) and (c),or all four possibilities, or none of them. In Part 2, one may choose either to answer eight true/falsequestions, or to select the proper definition of each of seven terms from a list of ten possible definitions.Every question must be answered on whichever portion (true/false or definition) of Part 2 is chosen,but one is not allowed to complete both the true/false and the definition portions. How many waysare there to complete the exam?
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From the following list of bus rapid transit system (one way):Name RouteVacation A->B->C->DWork 1 E->B->F->G->HWork 2 B->N->EWork 3 H->D->N The problem:➢ Task: Design an algorithm to read the bus rapid transit system routes list and print the numberof tickets we need to purchase if we want to visit all places minimal twice. The complexity ofthe algorithm must be O(V+E). V is the number of places. E-> is the number of transits.➢ PS: Use Tarjan’s or Kosaraju’s strongly connected component algorithm.
A local charity has set up a carnival for small children in a park with existing walkways and they need to create a map and advertising campaign. (a) Draw a simple graph that models the walkways and attractions of the carnival given the following information: • the entrance is an attraction because of the funny clowns that perform • from the clowns you can go to the slide, food truck, or carousel • the food truck is also connected to the petting zoo, ice cream cart, and ring toss • you can get to the petting zoo from the slide as well • from the carousel you can go to the face painting station or the ice cream cart, but there is also a direct path between the ice cream cart and face painting station too • the ice cream cart and ring toss both lead to the fishing game (b) To advertise the event, (i) Can the charity claim each attraction can be visited exactly once? (e.g. does the graph have a Hamilton circuit? or a Hamilton path?) If so, give one example, as proof. (ii) For members of…
A Rajesh teaches a cooking class. The course is attended by NN students, numbered 11 to NN. The cook must participate in the presence before each class, i.e. call out the names of the students one by one and indicate which students are present. Each student has a first and last name. To save time, Rajesh only wants to call up students' first names. However, if there are multiple students with the same first name, the Rajesh must call out the full names (first and last names) of all those students. For any student who does not share a first name with any other student, the cook can still only call that student's first name. Help the Rajesh decide for each student whether to call that student's full name or just their first name. Note: Please Answer in java language only. Input 1 1 hasan jaddouh Output hasan
Create a scenario that involves solving the real-life problem using a piecewise function and give a brief explanation.
An avid hiker keeps meticulous records of their hikes. During the last hike that took exactly steps, for every step it was noted if it was an uphill, , or a downhill, step. Hikes always start and end at sea level, and each step up or down represents a unit change in altitude. We define the following terms: A mountain is a sequence of consecutive steps above sea level, starting with a step up from sea level and ending with a step down to sea level. A valley is a sequence of consecutive steps below sea level, starting with a step down from sea level and ending with a step up to sea level. Given the sequence of up and down steps during a hike, find and print the number of valleys walked through. Example The hiker first enters a valley units deep. Then they climb out and up onto a mountain units high. Finally, the hiker returns to sea level and ends the hike. Function Description Complete the countingValleys function in the editor below. countingValleys has the following…