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The puzzle called the Towers of Hanoi consists of three pegs, one of which contains several rings stacked in order of descending diameter from bottom to top. The problem is to move the stack of rings to another peg. You are allowed to move only one ring at a time, and at no time is a ring to be placed on top of a smaller one. Observe that if the puzzle involved only one ring, it would be extremely easy. Moreover, when faced with the problem of moving several rings, if you could move all but the largest ring to another peg, the largest ring could then be placed on the third peg, and then the problem would be to move the remaining rings on top of it. Using this observation, develop a recursive
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- 1. The entrance room (or the starting of the maze) is considered as level 1. Now, answer these following questions: (a). Write an algorithm to figure out how many maximum levels the maze can go up to. (b). Figure out the complexity of your algorithm. To create a maze some rooms of a building is connected. Starting room is called Entrance room. From the entrance room other rooms are there connected from it. However, some rooms of that maze- building have connected room from it, and some rooms do not have any connected room. Each of the room can have at most or up to two rooms connected from it. The starting room is the entrance room of the maze or building. Fore example: It can be any one like the followings: Exemple -: Room1 Roono Room Entrance Room Raom Room2 Room? Roo Roomo Here, maxinum level =7 Example -2; Entrace Room D- Room5 Room 2 Room 4 Maxximum level=3arrow_forwardNote: Answer the question using Java language only. Shaker is the first child who got scholarship into the village. He went to London to study where he finds it very interesting to calculate number of ways of going to point (c, d) from point (a, b) in co-ordinate plane. We can take horizontal and vertical steps only and cannot visit at a point twice. In a step, you can move one unit only. We have to reach to the point (c, d) from the point (a, b) using abs(a-c) + abs(b-d) steps only. Shaker has two sets of points. Set A contains points having X co- ordinate 0 and Y co-ordinates varying from 1 to N (both inclusive). Set B contains points having X co-ordinate K and Y co-ordinates varying from 1 to N (both inclusive). Both sets contain N number of integral points. He wants to calculate the sum of number of ways to going to each point of set B from each point of set A. Input 1 22 Output 8arrow_forwardPython Please. An interesting puzzler for chess buffs is the Knight’s Tour problem, originally proposed by the mathematician Euler. Can the knight piece move around an empty chessboard and touch each of the 64 squares once and only once? We study this intriguing problem in depth here. The knight makes only L-shaped moves (two spaces in one direction and one space in a perpendicular direction). Thus, as shown in the figure below, from a square near the middle of an empty chessboard, the knight (labeled K) can make eight different moves (numbered 0 through 7). A: Draw an eight-by-eight chessboard on a sheet of paper, and attempt a Knight’s Tour by hand. Put a 1 in the starting square, a 2 in the second square, a 3 in the third, and so on. Before starting the tour, estimate how far you think you’ll get, remembering that a full tour consists of 64 moves. How far did you get? Was this close to your estimate? B: Now let’s develop a script that will move the knight around a chessboard…arrow_forward
- A tile of a monkey puzzle has four monkey halves that can be labelled as north(N), east (E), south (S), and west (W) half. In addition to the shape of the borderrectangle, these halves determine which edges can be placed next one other. There isalso another way to define how the tiles can be placed: Each tile corner (i.e. compassdirections NE, SE, SW, and NW) has a monkey quarter. If we abstract this quarter, forexample, with a letter, only the tiles with the same letter in their touching corners canbe adjacent. illustrates one valid solution for this quarter monkey puzzle.Are the two monkey puzzle representations equivalent in the sense that if we have apile of ‘half monkey’ tiles H, it is possible to define a pile of ‘quarter monkey’ tilesQ that gives exactly the same set of solutions for the puzzle (and vice versa)?arrow_forwardIn computer science and mathematics, the Josephus Problem (or Josephus permutation) is a theoretical problem. Following is the problem statement: There are n people standing in a circle waiting to be executed. The counting out begins at some point (rear) in the circle and proceeds around the circle in a fixed direction. In each step, a certain number (k) of people are skipped and the next person is executed. The elimination proceeds around the circle (which is becoming smaller and smaller as the executed people are removed), until only the last person remains, who is given freedom. Given the total number of persons n and a number k which indicates that k-1 persons are skipped and kth person is killed in circle. The task is to choose the place in the initial circle so that you are the last one remaining and so survive. For example, if n = 5 and k = 2, then the safe position is 3. Firstly, the person at position 2 is killed, then person at position 4 is killed, then person at position 1…arrow_forwardComputer science. Correct answer will be upvoted else downvoted. Think about a n by n chessboard. Its columns are numbered from 1 to n from the top to the base. Its sections are numbered from 1 to n from the passed on to one side. A cell on a convergence of x-th line and y-th section is indicated (x,y). The fundamental corner to corner of the chessboard is cells (x,x) for all 1≤x≤n. A stage of {1,2,3,… ,n} is composed on the fundamental slanting of the chessboard. There is actually one number composed on every one of the cells. The issue is to segment the cells under and on the principle askew (there are by and large 1+2+… +n such cells) into n associated areas fulfilling the accompanying imperatives: Each district ought to be associated. That implies that we can move from any cell of a locale to some other cell of a similar area visiting just cells of a similar district and moving from a cell to a neighboring cell. The x-th area ought to contain cell on the fundamental…arrow_forward
- Can you help me with this code because I am struggling. The Lights Out puzzle consists of an m x n grid of lights, each of which has two states: on and off. The goal of the puzzle is to turn all the lights off, with the caveat that whenever a light is toggled, its neighbors above, below, to the left, and to the right will be toggled as well. If a light along the edge of the board is toggled, then fewer than four other lights will be affected, as the missing neighbors will beignored. In this section, you will investigate the behavior of Lights Out puzzles of various sizes by implementing a LightsOutPuzzle class. Once you have completed the problems in this section, you can test your code in an interactive setting using the provided GUI. See the end of the section for more details. Task: A natural representation for this puzzle is a two-dimensional list of Boolean values, where True corresponds to the on state and False corresponds to the off state. In the LightsOutPuzzle class, write an…arrow_forwardIn programming, we use the mask concept to indicate information that can be shown to the user and information that must be “masked”, that is, hidden. In an implementation of a hangman game, we use a mask to indicate which secret word positions the player has already guessed right (whose the contents must therefore be shown to the player), and which positions must remain hidden. Each time that the player hits a letter of the hidden word, the mask is updated so that it has little dashes in the places of letters that the player has not hit yet and show it, in their proper place, the letters that he already hit it. For example, if the word is "cards", the current mask is: - a - - s and the player guesses the letter "d", the mask should be updated to: - a - ds.Write a function called update_mask that takes as input a string containing the word secret (in the example above, this word would be “cards”), a list whose elements are the characters of the current mask (in the example above…arrow_forwardCan you help me trying to do this code because I am struggling big time with this. question that i need help with: the Eight Puzzle consists of a 3 x 3 board of sliding tiles with a single empty space. For each configuration, the only possible moves are to swap the empty tile with one of its neighboring tiles. The goal state for the puzzle consists of tiles 1-3 in the top row, tiles 4-6 in the middle row, and tiles 7 and 8 in the bottom row, with the empty space in the lower-right corner.you will develop two solvers for a generalized version of the Eight Puzzle, in which the board can have any number of rows and columns. A natural representation for this puzzle is a two-dimensional list of integer values between 0 and r · c -1 (inclusive), where r and c are the number of rows and columns in the board, respectively. In this problem, we will adhere to the convention that the 0-tile represents the empty space.tasks:In the TilePuzzle class, write an initialization method __init__(self,…arrow_forward
- An n × n square consists of black and white cells arranged in a certain way. The problem is to determine the number of white areas and the number of white cells in each area. For example, a regular 8 × 8 chessboard has 32 one-cell white areas; the square in Figure 5.22a consists of 10 areas, 2 of them of 10 cells, and 8 of 2 cells; the square in Figure 5.22b has 5 white areas of 1, 3, 21, 10, and 2 cells. Write a program that, for a given n × n square, outputs the number of white areas and their sizes. Use an (n + 2) × (n + 2) array with properly marked cells. Two ad- ditional rows and columns constitute a frame of black cells surrounding the entered square to simplify your implementation. For instance, the square in Figure 5.22b is stored as the square in Figure 5.22c. (a–b) Two n 3 n squares of black and white cells and (c) an (n + 2) 3 (n + 2) array implementing square (b). bbbbbbbbbb bwbbwwbwwb bbbbbwbwwb bwwwbbwwwb bwbwbwwbbb bwbwwwbwbb bwbbbbwwwb bwbwbbwwwb bwbwbbwwwb…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_forwardConsider a maze represented by a matrix of m rows and n columns with obstacles (see the figure below). A cell with a value = -1 is an obstacle that cannot be overcome. The goal is to start from cell [0, 0] and reach the last cell [m-1, n-1]. This may be possible by taking several paths. Count the number of these paths. The movement is allowed from cells (i+ 1, j) and (i, j+ 1) only. -1 -1 Provide two solutions, one iterative and one recursive to the above problem.arrow_forward
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