Consider the following state for the 8-queens problem with heuristic h = number of pairs of queens that are attacking each other. What is the value of 'h' for the state obtained by moving the queen in the left-most column (circled) to the location marked X?
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- The rook is a chess piece that may move any number of spaces either horizontally or vertically. Consider the “rooks problem” where we try to place 8 rooks on an 8x8 chess board in such a way that no pair attacks each other. a. How many different solutions are there to this?b. Suppose we place the rooks on the board one by one, and we care about the order in which we put them on the board. We still cannot place them in ways that attack each other. How many different full sequences of placing the rooks (ending in one of the solutions from a) are there?Correct answer will be upvoted else downvoted. Today we will play a red and white shading game (no, this isn't the Russian Civil War; these are only the shades of the Canadian banner). You are given a n×m matrix of "R", "W", and "." characters. "R" is red, "W" is white and "." is clear. The neighbors of a cell are those that share an edge with it (those that main offer a corner don't count). Your responsibility is to shading the clear cells red or white so every red cell just has white neighbors (and no red ones) and each white cell just has red neighbors (and no white ones). You are not permitted to recolour currently hued cells. Input The primary line contains t (1≤t≤100), the number of experiments. In each experiment, the principal line will contain n (1≤n≤50) and m (1≤m≤50), the tallness and width of the network separately. The following n lines will contain the matrix. Each character of the matrix is either 'R', 'W', or '.'. Output For each experiment,…业 In the 8 queens problem, you are to place 8 queens on the chessboard in such a way that no two queens attack each other. That is, there are no two queens on the same row, column, or diagonal. The picture above shows a near solution--the top left and bottom right queens attack each other. We want to solve this problem using the techniques of symbolic Al. First, we need states. What would the best choice be for states? Each queen and its position x Michigan, Illinois, Indiana, etc. How many queens we have placed so far A board with the positions of all the queens that have been placed so far 00 What would the start state be? A single queen's position Crouched, with fingers on the starting line Placing the first queen x An empty board What would the goal state be? CA board with 8 queens placed Ball in the back of the net The positions of all 8 queens A board with 8 queens placed, none attacking each otherv What would the best choice for "edges" or "moves" be? Tiktok Moving a queen from…
- On 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…Given a deck of 52 playing cards, we place all cards in random order face up next to each other. Then we put a chip on each card that has at least one neighbour with the same face value (e.g., on that has another queen next to it), we put a chip. Finally, we collect all chips that were each queen placed on the cards. For example, for the sequence of cards A♡, 54, A4, 10O, 10♡, 104, 94, 30, 3♡, Q4, 34 we receive 5 chips: One chip gets placed on each of the cards 100, 10♡, 104, 30, 3♡. (a) Let p5 be the probability that we receive a chip for the 5th card (i.e., the face value of the 5th card matches the face value of one of its two neighbours). Determine p5 (rounded to 2 decimal places). (b) Determine the expected number of chips we receive in total (rounded to 2 decimal places). (c) For the purpose of this question, you can assume that the expectation of part (b) is 6 or smaller. Assume that each chip is worth v dollars. Further, assume that as a result of this game we receive at least…This problem is taken from the delightful book "Problems for Mathematicians, Young and Old" by Paul R. Halmos. Suppose that 931 tennis players want to play an elimination tournament. That means: they pair up, at random, for each round; if the number of players before the round begins is odd, one of them, chosen at random, sits out that round. The winners of each round, and the odd one who sat it out (if there was an odd one), play in the next round, till, finally, there is only one winner, the champion. What is the total number of matches to be played altogether, in all the rounds of the tournament? Your answer: Hint: This is much simpler than you think. When you see the answer you will say "of course".
- Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. Artem is building another robot. He has a network a comprising of n lines and m sections. The cell situated on the I-th line from the top and the j-th segment from the left has a worth ai,j written in it. In the event that two nearby cells contain a similar worth, the robot will break. A lattice is called acceptable if no two adjoining cells contain a similar worth, where two cells are called nearby on the off chance that they share a side. Artem needs to increase the qualities in certain cells by one to make a decent. All the more officially, find a decent network b that fulfills the accompanying condition — For all substantial (i,j), either bi,j=ai,j or bi,j=ai,j+1. For the imperatives of this issue, it tends to be shown that such a framework b consistently exists. In case there are a few such tables, you can output any of them. Kindly note that you don't need to limit…Imagine there are N teams competing in a tournament, and that each team plays each of the other teams once. If a tournament were to take place, it should be demonstrated (using an example) that every team would lose to at least one other team in the tournament.Correct answer will be upvoted else Multiple Downvoted. Computer science. Polycarp got the accompanying issue: given a framework piece of size 2×n, a few cells of it are obstructed. You want to check in case it is feasible to tile all free cells utilizing the 2×1 and 1×2 tiles (dominoes). For instance, if n=5 and the strip appears as though this (dark cells are obstructed) Polycarp handily tackled this errand and accepted his New Year's gift. Would you be able to settle it? Input The main line contains an integer t (1≤t≤104) — the number of experiments. Then, at that point, t experiments follow. Each experiment is gone before by a vacant line. The main line of each experiment contains two integers n and m (1≤n≤109, 1≤m≤2⋅105) — the length of the strip and the number of impeded cells on it. Every one of the following m lines contains two integers ri,ci (1≤ri≤2,1≤ci≤n) — numbers of lines and sections of hindered cells. It is ensured that all impeded cells are…
- 10 Is A-(BU C) = (A-B) (A-C)? Prove it or disprove it.Dingyu is playing a game defined on an n X n board. Each cell (i, j) of the board (1 2, he may only go to (2, n).) The reward he earns for a move from cell C to cell D is |value of cell C – value of cell D|. The game ends when he reaches (n, n). The total reward - is the sum of the rewards for each move he makes. For example, if n = 1 2 and A = 3 the answer is 4 since he can visit (1, 1) → (1, 2) → (2, 2), and no other solution will get a higher reward. A. Write a recurrence relation to express the maximum possible reward Dingyu can achieve in traveling from cell (1, 1) to cell (n, n). Be sure to include any necessary base cases. B. State the asymptotic (big-O) running time, as a function of n, of a bottom-up dynamic programming algorithm based on your answer from the previous part. Briefly justify your answer. (You do not need to write down the algorithm itself.)Suppose a biking environment consists of n ≥ 3 landmarks,which are linked by bike route in a cyclical manner. That is, thereis a bike route between landmark 1 and 2, between landmark 2 and 3,and so on until we link landmark n back to landmark 1. In the centerof these is a mountain which has a bike route to every single landmark.Besides these, there are no other bike routes in the biking environment.You can think of the landmarks and the single mountain as nodes, andthe bike routes as edges, which altogether form a graph G. A path is asequence of bike routes.What is the number of paths of length 2 in the graph in termsof n?What is the number of cycles of length 3 in the graph in termsof n?What is the number of cycles in the graph in terms of n?