Exercise 10 (This is the rod cutting problem from Section 15.1 in the textbook.) Design a dynamicprogramming algorithm for the following problem. A rod has length n and a segment of length i costs p[i]dollars. The costs p[i] are known for all i = 1,..., n. The problem is to determine what is the maximumrevenue a company can obtain by cutting the rod and selling the segments obtained after the cutting.For the dynamic programming solution, we define the subproblems r[i] =max revenue by cutting a rod oflength i.(a) How much is r[0]?(b) Give a recurrence formula that calculates r[i] as a function of r[j], for j

QUESTION a) r[0] is the maximum revenue by cutting a rod of length 0. This is 0 since there is no…

Answered: Exercise 10 (This is the rod cutting…

Computer Networking: A Top-Down Approach (7th Edition)

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Chapter1: Computer Networks And The Internet

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Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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Boolean Satisfaction Problem Boolean Satisfiability Problem (SAT) (https://en.wikipedia.org/wiki/Boolean_satisfiability_problem) is one of the most important problems in Computer Science. SAT is a problem that has NP-Complete complexity, where the only way to solve the problem is to try all the possibilities and check which one is correct. [LO 1, LO 2, LO 3 & LO 4,] Briefly describe how you used Backtracking to solve the Boolean Satisfiability Problem. Note that your solution must have exponential complexity. [LO 1, LO 2, LO 3 & LO 4,] Briefly explain how you use Strongly Connected Component (SCC) to solve the special case of the Boolean Satisfiability Problem, namely 2-SAT (https://en.wikipedia. org/wiki/2-SAT) . This solution has linear complexity. Solve the Subparts A&B thank u NOTE LO1: Explain fundamental concept of analysis arithms. LO2: Apply algorithm techniques and methods. LO3: Solve a problem using specific algorithm. LO4: Compare several algorithm design…
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3. Design a dynamic programming algorithm for the Longest Alternating Subsequence problemdescribed below:Input: A sequence of n integersOutput: The longest subsequence where the numbers alternate between being larger and smaller thantheir predecessorThe algorithm must take O(n) time. You must also write and explain the recurrence.Example 1:Input: [3, 5, 4, 1, 3, 6, 5, 7, 3, 4]Output: [3, 5, 4, 6, 5, 7, 3, 4]Example 2:Input: [4, 7, 2, 5, 8, 3, 8, 0, 4, 7, 8]Output: [4, 7, 2, 5, 3, 8, 0, 4] Write in Pseudocode, please
Write a fraction calculator program that adds, subtracts, multiplies, and di-vides fractions. Your program should check for the division by 0, have and use the following functions:(a) subtract - finds the reduced difference of a pair of given fractions, by makingthe second fraction negative then using the add function.(b) multiply - finds the reduced product of a pair of given fractions.(c) divide - finds the reduced quotient of a pair of given fractions by inverting the second fraction then using the multiply function
Recall the rod cutting problem we discussed in class and in the book. While it might be possible for a theoretical person to cut the rod of length n, up to n times to achieve the maximum possible sale value, enterprising children do not possess the stamina to cut the rod so many times. They instead get tired or bored after only k cuts. Design a dynamic programming algorithm to maximize the value of selling cut rods if at most we can cut the rod k times. Please use elements in the table P to calculate the value of a continuous rod, e.g. an uncut rod of length i has value pi. Further you should analyze: 1. The time complexity of a baseline solution that does not use dynamic programming or memoization that exhaustively explores all potential solutions 2. The time complexity of your dynamic programming solution 3. Describe how you could change your algorithm to so to reconstruct the actual cuts in order achieve the highest value for the rod pieces.
A university assigns student IDs of the form 1, 2, 3, ... such that if n students are currently enrolled, then the next student to enroll will receive and ID of n + 1. Consider the following algorithm that accomplishes this. // Global variable storing number of students currently enrolled current_student_count = 0 // Function that reads the above global variable, calculates new ID, and increments the global count assign_new_id(): count = current_student_count new_id = count + 1 current_student_count = count + 1 return new_id (a) If two different threads run the above code in parallel to enroll two different students, it is possible for the two students to receive the same ID, and for the current_student_count to have a wrong value. Explain how this is possible. (b) Modify the code above so that the problem in (a) does not happen.
Knapsack 0/1 problem: Given N items where each item has some weight and profit associated with it and also given a bag with capacity W, [i.e., the bag can hold at most W weight in it]. The task is to put the items into the bag such that the sum of profits associated with them is the maximum possible. Given the problem is solved using a dynamic programming approach and the matrix derived is given below, answer the below set of questions by analyzing the DP matrix. weights = [2, 3, 4, 5], profits = [1, 2, 5, 6], Capacity W = 8 Capacity 2 3 Profits weights|0 1 2 5 16 14 |-> 5 10 0 O 10 1 2 3 4 0 O 0 1 1 0 1 0 1 O 10 1 2 2 2 5 2 O 15 50 1 356 6 O 1 3 6 18 00378 7 10 10 1 3 7 7 1 18
Rod cutting problem: A cutting factory buys long steel rods and then and cuts them into shorter rods, which it then sells. Each cut is free. The selling price is based on the length of the cut. The factory want to determine the best cuts in order to maximize its revenue. Below, the price that the factory can make for each length of rod is given. Determine the maximum revenue, rn, obtainable by cutting up the rod and selling the pieces using bottom-up dynamic-programming approach. Length, I 1 2 3 4 5 6 7 Price, pi 2 4 5 6 9 10 12 r5 = ?
Write a complete C or C++ program to implement a digital music archive program. The program should be able to allow the following operations through the menu structure. Use FILE to write the outputs, the song directory: Menu: 1- Add a new song to directory 2- Delete a song from the directory 3- List all songs in the directory 4- Search a song: A – Search according to song name B – Search according to singer’s name 5- Update song information 6- Sort according to song name 7- Sort according to singer’s name 8- Quit struct date { int day, month, year; }; struct car { int ID; char songname[100], singersname[30], category[10]; struct date albumdate; }song_directory[100];

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