Explanation of Solution
a.
Solution A: There exists a variable corresponding to every “n2” positions on the board.
Solution B: There is a variable corresponding to every knight.
Explanation of Solution
b.
Solution A: Each of the variables can be taken one of two values. The values can be taken are, “occupied” and “vacant”.
Solution B: Domain of each variable is the set of squares.
Explanation of Solution
c.
Solution A: Each and every pair of square separated by knight’s move constrained, such that both cannot be occupied. The entire set of squares is constrained, such that the number of occupied squares should be “k”.
Solution B: Each and every pair of knights is constrained, such that no two knights can be on the same square or on squares separated by a knight’s move. The solution B may be preferable because there is no global constraint, although the solution A has the smaller state space when “k” is large.
Explanation of Solution
d.
The solutions must be describing a complete-state formulation. This is because the use of local search
Solution C: Ensure that no attack at any time. Actions are to remove any knight, add a knight in any unattacked square, or move a knight to any unattacked square.
Solution D: allow attacks but try to get rid of them. Actions are to remove any knight, add a knight in any square, or move a knight to any square.
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Chapter 6 Solutions
Artificial Intelligence: A Modern Approach
- 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…arrow_forwardProblem 1. You are playing a version of the roulette game, where the pockets are from 0 to 10and even numbers are red and odd numbers are black (0 is green). You spin 3 times and add up the values you see. What is the probability th at you get a total of 17 given on the first spin you spin a 2? What about a 3? Solve by simulation and analytically.arrow_forwardOn a chess board of r rows and c columns there is a lone white rook surrounded by a group of opponent's black knights. Each knight attacks 8 squares as in a typical chess game, which are shown in the figure - the knight on the red square attacks the 8 squares with a red dot. The rook can move horizontally and vertically by any number of squares. The rook can safely pass through an empty square that is attacked by a knight, but it must move to a square that is not attacked by any knight. The rook cannot jump over a knight while moving. If the rook moves to a square that contains a knight, it may capture it and remove it from the board. The black knights. never move. Can the rook eventually safely move to the designated target square? The figure illustrates how the white rook can move to the blue target square at the top-right corner in the first sample case. The rook captures one black knight at the bottom-right of the board on its way. Rok nd kight lcoes by Chunen Input The first line…arrow_forward
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- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole