Suppose that you are given a set T of projects where each project t € T' is associ-ated with• a positive integer e, denoting the amount of effort (e.g., the amount of timeor energy) required to complete the project t, and• a positive integer pi denoting the profit gained by completing the project t.Given a positive integer c denoting the maximum amount of effort that you canspend on these projects, the goal is to find the largest amount of profit that you canmake by completing a subset of these projects such that the total amount of effortspent to complete the projects is at most c.State the decision version of this optimization problem: Input?Output?Prove that the decision version is in NP.

Subset:- The subset is a part of Set. The Set is a collection of elements that is enclosed in the…

Answered: Suppose that you are given a set T of…

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

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

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

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This mini project has two parts. Given coordinates of five points: A(x1, y1), B(x2, y2), C(x3, y3) and D(x4, y4), P(x, y) in a plane: A B P D Part I: Find if the four points: A, B, C, D form a square or not. In order to identify this, both conditions (a) and (b) must be met: a) All four sides formed by points are the same. b) The angle between any two sides is 90 degree. A register r0 must be set to 1 if the four points form a square and 0 otherwise. Part II: If four points A, B, C, D form a square, check if the fifth point P lies within the square or not. In order to identify this, assume A1, A2, A3, and A4 are the areas of PAB, PBD, PCD, and PAC and A is the area of the square. If P lies inside the square, then A1 + A2 + A3 + A4 must be equal to A. The area of the triangle can be calculated from the following formula: Triangle Area %3D[x1(у2 - у3) + x2(у3 - у1) + х3(у1-у2)]/2 Your program should store the areas of square at 0x40000000 and all 4 triangles: PAB, PBD, PCD, and PAC in 4…
A performance venue hosts many concerts a year. Performers perform several times a year for the concerts. Each concert has one or more performers and has a name and a specified seating arrangement. A concert is held in one (and only one) of several concert halls, each of which has a room number and the number of seats. Each concert generates revenues from the sales of tickets. Assume that the price of the ticket is the same for the same concert, but different prices for different concerts.Identify several attributes and a key field for each entity. Represent this situation of concerts and performers with an E-R diagram
I need to write a program for a Lion Hunt. The program should calculate the number of hours it will take a group of hunters to find the lion in the worst case scenario. We asumme that The lion has b b Hiding spots where 2 ≤ b ≤ 10 , 000 2 ≤ b ≤ 10 , 000 . We assume that there are s s Hunters where 1 ≤ s ≤ 1 , 000 1 ≤ s ≤ 1 , 000 . We assume that there are g g number of hunters, who need to be in a group to travel safely where 1 ≤ g ≤ s 1 ≤ g ≤ s . We assume that it takes a group 1 hour to search any of The lions hiding spots The input consists of a single line containing three integers ?, ? and ?, where 2≤?≤1000 is the number of hiding spots in the jungle. 1≤ e. Sample input/output is shown in attached photo
A group of m people is considering sharing the cost of buying some items for their summer camp. There are a total of n possible items to purchase. Each person writes a list of the items they are interested in purchasing on a paper. For example, person one may write “boat, trampoline, hot tub,” whereas person two may write “ hot tub, kayak, paddleboard”. There is no limit to how many items a person registers on their sheet. The goal is to determine if at least k items can be purchased. The following rules apply 1. The cost of any purchased item must be split equally among all those who listed that item on their sheet. No person can refuse to contribute to an item chosen for purchase, which is listed on their sheet. 2. Since each person has a limited budget, they may only contribute to at most one item on their list. The problem of determining if at least k items can be purchased is called SummerCamp. Show that this problem is NP-complete.

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