The user can type the length of the cube in the edit box, the program will generate a new cube in the specified size.Wiki Blog Search Turing Chat Room Members When the cube is turned along the certain axis and certain layer, the array of the blocks in that layer is rotated and the position of each block is also rotated by the applying rotational matrix to the position of each vertex.īy the way, this program is capable of presenting rubik's cubes in any sizes. Each block contains the positions of vertices and the color of each face. In this program, a NxNxN array is constructed to contain all pieces of blocks. Also, note the fact that the edge blocks and the vertex blocks may have different orientations. Note that the blocks in the cube may have 1 colors (center blocks) or 2 colors (edge blocks) or 3 colors (vertex blocks). To implement a rubik's cube, the first point is to have a good data structure to represent it. Besides, the user can zoom-in/out the screen by scrolling the wheel on the mouse. The rotate button in the screen allows the user to make a three-dimensional rotation to the cube and take a look at the faces behind. When ever the user finish scrambling the cube, the user can simply click on the solve button, and the program will solve the cube by the breadth-first-search (BFS) method. It also provides a functionality to scramble the cube randomly by the computer.
It visualizes the rubik's cube in three-dimension and allows the user to turn it like a real cube. This program is just like a real rubik's cube simulator. By comparing two players' game point, the program will announce which player is the winner. Once the game is finished, the program will compute the total area of each player and then subtract it to the stones that have been killed to obtain a game point. If the players want to give up or think that it's time to finish the game, they can press the 'Give up' or 'Finish' button to do so. Besides, players are allowed to pause their turn at any time by pressing their own 'Pause' button. A counter counting the number of stones which have been killed is also provided. This program also provides a timer which counts the total time elapses during the players' turn. During the player moving the mouse, a position indicator (little grey square on the board) follows the mouse simultaneously, indicating the actual position the stones will drop if the player clicks on at the moment. Once a player drops the stone, the turn indicator (large grey square at the top right of the figure) switches to another player, indicating it's now his turn to drop. The Go game allows players to drop their stones by control the mouse and click on the right position. This solver can solve the hardest sudoku within 5 sec by a personal computer, and the result is shown on the right side. If these methods cannot solve the puzzle directly, the recursive back tracking method is applied to search all possible solutions. For human solving techniques, the solver is able to use candidate, naked single, hidden single, pointing intersection, claiming intersection, naked pair, hidden pair, and X-Wing methods. There are several solving methods applied to the solver. The snapshot on the right side shows the hardest sudoku devised by Arto Inkala, a Finnish mathematician.
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In addition, the solutions will also display in the list box, which allows the user to learn how to solve the puzzle easily. And then, with a single click on 'Solve!' button, the answer will be shown. The users can make use of 'tab' key and arrow keys to switch the input cell in order to speed up the process. This allows user input the known numbers to the solver easily. The sudoku solver uses 81 edit boxes to represent each cell in the puzzle. The results on the right-hand side show the behaviour when the white ball hit the balls arranged in a triangle with different velocity and different direction. To simulate the holes on the board, fix/evaporate command is used to delete the balls in certain region conveniently. There is no friction between the side wall and the balls, thus, the balls will perform a perfect reflection when hitting the side wall. In addition, gravity in the z-direction is considered to make the balls fully contact with the board. Besides, friction between the board and balls is also taken into account, which is achieved by the tangential force between a granular wall (the board) and each ball, and this consideration makes the balls gradually slow down. The consideration of this model including normal force, tangential force, damping normal force, and damping tangential force during every contact between each pair of balls.
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This program takes advantage of Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) to simulate the behaviour of billiards.