A group of firends Anna (A), Bjorn (B), Candice (C), David (D) and Ellen (E) want to enter a basketball contest that caters for teams of different sizes. A team with n players is called an n-team. A player can be in several different teams, including teams of the same size. There is a restriction however: players in a 2-team cannot polay together in any larger team. For example, if friends A,B,C,D form the teams AB, BCD, ACD, then they cannot also form the teams BD or ABC, among others. The five friends want to enter 8 teams including at least one 2-

A group of firends Anna (A), Bjorn (B), Candice (C), David (D) and Ellen (E) want to enter a basketball contest that caters for teams of different sizes. A team with n players is called an n-team. A player can be in several different teams, including teams of the same size. There is a restriction however: players in a 2-team cannot polay together in any larger team. For example, if friends A,B,C,D form the teams AB, BCD, ACD, then they cannot also form the teams BD or ABC, among others. The five friends want to enter 8 teams including at least one 2-

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter10: Classes And Data Abstraction

Section: Chapter Questions

Problem 19PE

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If the first number in a sequence is a positive integer, x Let ao= x, an is defined as follows if an is even, then an+1 = an/2 if an is odd, then an+1 =3 *an+ 1 Then there exists an integer k, such that ak =1 For example, if: 75, then k = 14 and the numbers in the sequence are: 75, 226, 113, 340, 170, 85, 256, 128, 64, 32, 16, 8, 4, 2, 1. The largest number in the sequence is 340 and it is a position 4 in the sequence (assuming 75 is at position 1) Design and implement a complete C++ program that will • read a series of integers (greater than 0) from a file and for each integer display (to the screen) − the integer − the number of steps it takes to reach 1 − the largest value in the sequence and its position
Answer the following: This problem exercises the basic concepts of game playing, using tic-tac-toe (noughts and crosses) as an example. We define Xn as the number of rows, columns, or diagonals with exactly n X’s and no O’s. Similarly, On is the number of rows, columns, or diagonals with just n O’s. The utility function assigns +1 to any position with X3=1 and −1 to any position with O3=1. All other terminal positions have utility 0. For nonterminal positions, we use a linear evaluation function defined as Eval(s)=3X2(s)+X1(s)−(3O2(s)+O1(s)). a. Show the whole game tree starting from an empty board down to depth 2 (i.e., one X and one O on the board), taking symmetry into account. b. Mark on your tree the evaluations of all the positions at depth 2. c .Using the minimax algorithm, mark on your tree the backed-up values for the positions at depths 1 and 0, and use those values to choose the best starting move. Provide original solutions including original diagram for part a!
Answer the following: This problem exercises the basic concepts of game playing, using tic-tac-toe (noughts and crosses) as an example. We define Xn as the number of rows, columns, or diagonals with exactly n X’s and no O’s. Similarly, On is the number of rows, columns, or diagonals with just n O’s. The utility function assigns +1 to any position with X3=1 and −1 to any position with O3=1. All other terminal positions have utility 0. For nonterminal positions, we use a linear evaluation function defined as Eval(s)=3X2(s)+X1(s)−(3O2(s)+O1(s)). a. Show the whole game tree starting from an empty board down to depth 2 (i.e., one X and one O on the board), taking symmetry into account. b. Mark on your tree the evaluations of all the positions at depth 2. c .Using the minimax algorithm, mark on your tree the backed-up values for the positions at depths 1 and 0, and use those values to choose the best starting move. Provide original solution!
Three prisoners have been sentenced to long terms in prison, but due to over crowed conditions, one prisoner must be released. The warden devises a scheme to determine which prisoner is to be released. He tells the prisoners that he will blindfold them and then paint a red dot or blue dot on each forehead. After he paints the dots, he will remove the blindfolds, and a prisoner should raise his hand if he sees at least one red dot on the other two prisoners. The first prisoner to identify the color of the dot on his own forehead will be release. Of course, the prisoners agree to this. (What do they have to lose?) The warden blindfolds the prisoners, as promised, and then paints a red dot on the foreheads of all three prisoners. He removes the blindfolds and, since each prisoner sees a red dot (in fact two red dots), each prisoner raises his hand. Some time passes when one of the prisoners exclaims, "I know what color my dot is! It's red!" This prisoner is then released. Your problem…
4. Let N(x) be the statement “x has visited North Dakota,” where the domain consists of the students in your school. Express each of these quantifications in English. a) ∃x N(x) b) ∀x N(x) c) ˺∃x N(x) d) ∃x ˺N(x) e) ˺∀x N(x) f ) ∀x ˺N(x)
You and your friends decided to hold a “Secret Santa” gift exchange, where each person buys a gift for someone else. To see how this whole thing works, let’s consider the following example. Suppose there are 7 people A, B, C, D, E, F, and G. We denote x → y to mean “x gives a gift to y.” If the gift exchange starts with person A, then they give a gift to E. Then E gives a gift to B. And it is entirely possible that B gives a gift to A; in such a case we have completed a “cycle.” In case a cycle occurs, the gift exchange resumes with another person that hasn’t given their gift yet. If the gift exchange resumes with person D, then they give a gift to G. Then G gives a gift to F. Then F gives a gift to C. Then finally C gives a gift to D, which completes another cycle. Since all of the people have given their gifts, the giftexchange is done, otherwise the gift exchange resumes again with another person. All in all, there are two cycles that occurred during the gift exchange: A → E → B → A…
In order to beat AlphaZero, Grandmaster Hikaru is improving her chess calculation skills.Today, Hikaru took a big chessboard with N rows (numbered 1 through N) and N columns (numbered 1 through N). Let's denote the square in row r and column c of the chessboard by (r,c). Hikaru wants to place some rooks on the chessboard in such a way that the following conditions are satisfied:• Each square of the board contains at most one rook.• There are no four rooks forming a rectangle. Formally, there should not be any four valid integers r1, c1, r2, c2 (≠r2,c1≠c2) such that there are rooks on squares (r1,c1), (r1,c2 (r2,c1)and (r2,c2).• The number of rooks is at least 8N.Help Hikaru find a possible distribution of rooks. If there are multiple solutions, you may find any one. It is guaranteed that under the given constraints, a solution always exists.InputThe first line of the input contains a single integer T denoting the number of test cases. The first and only line of each test case contains…
Please answer the following question in depth with full detail. Consider the 8-puzzle that we discussed in class. Suppose we define a new heuristic function h3 which is the average of h1 and h2, and another heuristic function h4 which is the sum of h1 and h2. That is, for every state s ∈ S: h3(s) =h1(s) + h2(s) 2 h4(s) =h1(s) + h2(s) where h1 and h2 are defined as “the number of misplaced tiles”, and “the sum of the distances of the tiles from their goal positions”, respectively. Are h3 and h4 admissible? If admissible, compare their dominance with respect to h1 and h2, if not, provide a counterexample, i.e. a puzzle configuration where dominance does not hold.
A library must build shelving to shelve 200 4-inch high books, 150 8-inch high books, 300 10-inch high books and 180 12-inch high books. Each book is 0.5 inch thick. The library has several ways to store the books. For example, an 8-inch high shelf may be built to store all books of height less than or equal to 8 inches, and a 12-inch high shelf may be built for the 12-inch books. Alternatively, a 12-inch high shelf might be built to store all books. The library believes it costs $2,300 to build a shelf and that a cost of $5 per square inch is incurred for book storage. (Assume that the area required to store a book is given by height of storage area times book’s thickness.) Formulate and solve a shortest-path problem that could be used to help the library determine how to shelve the books at minimum cost. (Hint: Have nodes 0, 4, 8, 10 and 12, with cij being the total cost of shelving all books of height >i and ≤ j on a single shelf.)
Suppose that a manufacturing company builds n different types of robots, sayrobots 1, 2, . . . , n. These robots are made from a common set of m types of materials, saymaterials 1, 2, . . . , m. The company has only a limited supply of materials for each year,the amount of materials 1, 2, . . . , m are limited by the numbers b1, b2, . . . , bm, respectively.Building robot i requires an aij amount from material j. For example, building robot 1requires a11 from material 1, a12 from material 2, etc. Suppose the profit made by sellingrobot i is pi. Write an integer linear program for maximizing the annual profit for thecompany
We examine a problem in which we are handed a collection of coins and are tasked with forming a sum of money n out of the coins. The currency numbers are coins = c1, c2,..., ck, and each coin can be used as many times as we want. What is the bare amount of money required?If the coins are the euro coins (in euros) 1,2,5,10,20,50,100,200 and n = 520, we need at least four coins. The best option is to choose coins with sums of 200+200+100+20.
To cut an 'n' centimeter-long gold bar into 2 pieces costs $n. When a gold bar is cut into many pieces, the order in which the cuts occur can affect the total amount of costs. For example, to cut a 20 centimeter gold bar at length marks 2, 8, and 10 (numbering the length marks in ascending order from the left-hand end, starting from 1). If the cuts to occur in left-to-right order, then the first cut costs $20, the second cut costs $18 (cutting the remaining 18 centimeter bar at originally length mark 8), and the third cut costs $12, totaling $50. If the cuts to occur in right-to-left order, however, then the first cut costs $20 time, the second cut costs $10, and the third cut costs $8, totaling $38. In yet another order, the first cut is at 8 (costing $20), then the 2nd cut is at 2 (costing $8), and finally the third cut is at 10 (costing $12), for a total cost of $40. Given an 'n' centimeter-long gold bar G and an array C[1..m] containing the cutting points in ascending order): a.…