Say in a scheduling scenario you are given a number of jobs, each with a start time and a finish time. Two jobs conflict if they overlap in time, i.e., one of them starts between the start and finish times of the other. Your goal is to select a maximum-size subset of jobs that have no conflicts. Example: Three jobs consuming the intervals [0, 3], [2, 5], and [4, 7]. The optimal solution in this case would consist of the first and third ones. Design and describe a greedy algorithm that computes an optimal solution to this problem. Informally argue why the solution is likely to be optimal and demonstrate on an example. You may assume that there are no ties.
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- A school is creating class schedules for its students. The students submit their requested courses and then a program will be designed to find the optimal schedule for all students. The school has determined that finding the absolute best schedule cannot be solved in a reasonable time. Instead they have decided to use a simpler algorithm that produces a good but non-optimal schedule in a more reasonable amount of time. Which principle does this decision best demonstrate?8. A school is creating class schedules for its students. The students submit their requested courses and then a program will be designed to find the optimal schedule for all students. The school has determined that finding the absolute best schedule cannot be solved in a reasonablo time. Instead they have decided to use a simpler algorithm that produces a good but non-optimal schedule in a more reasonable amount of time. Which principle does this decision best demonstrate? O A Unreasonable algorithms may sometimes also be undecidable O B. Heuristics can be used to solve some problems for which no reasonable algorithm exsts O C. efficiency Two algorithms that solve the same problem must also have the same O B. Approximate solutions are often identical to optimal solutionsClasses are scheduled at a school. Once students have submitted their course requests, a computer algorithm can determine the optimal schedule for everyone. The school has concluded that it will take too long to determine the best schedule. Instead, they resort to a less sophisticated method that produces a serviceable if not ideal timetable. Which guiding concept is represented here?
- The Weighted Interval Scheduling Problem is defined as n requests labelled 1,...,n, with each request i specifying a start time s, a finish time f; and a weight v. For each request i, s;Use the greedy algorithm below to solve the activity problem. Suppose the s={a1,a2,...,an} is a set of n activities that wish to use the resource. Each activity a; has a start time s; and a finish time fi, where Activities a; and a; are called compatible if the one starts after the other is finished. It is about to select the maximum-size subset of mutually compatible activities. Solve this problem of activity-selection problem. Is this optimal solution? What is the optimal solution? How can you improve it? i S₁ fi 1 0 4 2 1 3 3 3 4 4 5 11 5 5 9 6 10 11 The greedy algorithm 1 n = s.length 2 min = f[1] 3 k = 1 4 5 6 7 for i = 2 to n if f[i]A prominent masseuse is pondering which appointment invitations to accept after receiving a string of them. She requires a 15-minute pause between visits and hence cannot take any subsequent inquiries. Find the optimal (highest total booked minutes) set the masseuse can honour given a sequence of back-to-back appointment requests (all multiples of 15 minutes, none overlap, and none may be changed). Return the time in minutes.Input EXAMPLE: 30, 15, 60, 75, 45, 15, 15, 45180 minutes output (30, 60, 45, 45).Hi please answer the following follow up questions as well, posted them as another question. Question 4 For the 9-tile soring problem, assume that you start from this initial state 7 2 4 5 6 8 3 1 The Goal State is: 1 2 3 4 5 6 7 8 The cost of moving any tile is 1. Let the heuristic function h(n) = number of misplaced tiles. For the shown configuration, there are four options for the next move: Move 5 to the right Move 6 to the left Move 2 down Move 3 up Each of these moves has a value f(n) = h(n) + g(n). If we choose to Move 5 to the right, then g(n) = 1. That is, it took us one step to reach this state from the initial state. h(n) = number of misplaced tiles. The misplaced tiles are {7,4,8,3,1}. So the number of misplaced tiles = h(n) = 5. If we choose to Move 6 to the left, g(n) is still = 1, but h(n) will change because the number of misplaced tiles is different. A* works by computing f(n) = h(n) + g(n) for each of these possible moves. Then it…Consider the following Job Scheduling problem. We have one machine and a setof n jobs {1, 2, . . . , n} to run on this machine, one at a time. Each job has a start time sifinish time fi and profit pi where 0 ≤ si < fi < ∞ and pi > 0. Two jobs i and j are compatible if the intervals [si, fi)and [sj , fj ) do not overlap. The goal is to find a set A of mutually compatible jobs with the maximumtotal profit, i.e.,P j∈A pj is maximized.Consider the following two greedy choices. For each one, determine whether it is a “safe” greedy choicefor this Job Scheduling problem. If your answer is yes, prove the “Greedy-choice property”. If your answeris no, please give a counterexample and show that the greedy choice will not lead to an optimal solution. a.Greedy choice 1: Always select a job with the earliest finish time that is compatible with allpreviously selected activities.b.Greedy choice 2: Always select a job with the highest profit per time unit (i.e., pi/(fi − si))that is…I have spent hours on internet to find an example of iterative lengthening search algorithm but found nothing. I need it ASAP. Can anyone help me? Please. It is its definition: Iterative lengthening search is an iterative analogue of uniform-cost search. The basic idea is to use increasing limits on path cost. If a node is generated whose path cost exceeds the current limit, it is immediately discarded. For each new iteration, the limit is set to the lowest path cost of any node discarded in the previous iteration. I dont understand many things in this definition. 1-What is the first limit before we start? 2-Do we delete the discarded node from the graph or what? 3-What is the generated node? Is it expanded or is it just found as neigbor? 4-What is "lowest path cost of any node discarded"?? Path from where to where?? From start to that node or what? 5-What does path cost mean in this problem? Is it from source to the new node or between current node and next chosen node? I am literally…In the Activity Selection Problem, there are many ways to design a Greedy Algorithm. In the textbook, you saw how this Greedy Algorithm guaranteed an optimal solution: choose the activity with the earliest finish time, eliminate all activities that conflict with that choice, and then repeat these steps on the activities that are remaining. Here are five other ways we can design the choice function of our Greedy Algorithm. A. Choose the activity with the latest finish time B. Choose the activity with the earliest starting time C. Choose the activity with the latest starting time D. Choose the activity with the shortest duration E. Choose the activity with the longest duration One of these five Greedy Algorithms guarantees an optimal solution, while the other four do not. Determine which of these Greedy Algorithms is optimal. Answer one of A, B, C, D, or E.No plagarism please! Correct and detailed answer will be Upvoted else downvoted. Thank you! Q. Which of the following is CORRECT for the weighted interval scheduling problem? 1. The original problem is one of the subproblems. 2. To ensure that a problem can be solved using dynamic programming, there should be a natural ordering on subproblems from “smallest” to “largest”. In the weighted interval scheduling problem, OPT(j) is a smaller problem than OPT(p(j)) 3. The recursive implementation of the algorithm for computing the optimal value without using memoization has o(n) complexity 4. Weighted interval scheduling problem has exponential computing complexity.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 Cookie baking Pasta making Start time End time 10:30 AM 11:45 AM 10:45 AM 12:30 PM 12:15 AM 2:00 PM 12:45 PM 3:00 PM 2:15 PM 4:30 PM Table decoration 3:30 PM 5:45 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…SEE MORE QUESTIONSRecommended textbooks for youDatabase System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill EducationStarting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSONDigital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSONC How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. Deitel, Harvey DeitelPublisher:PEARSONDatabase Systems: Design, Implementation, & Manag…Computer ScienceISBN:9781337627900Author:Carlos Coronel, Steven MorrisPublisher:Cengage LearningProgrammable Logic ControllersComputer ScienceISBN:9780073373843Author:Frank D. 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