if a cube is not found, enter a cube into the space and continue to the next space. if a sphere is found or the space is empty, go to step 3.Ĥ)If the space is still empty or the algorithm previously entered a sphere, check each row along the four axes for a cube. if a sphere is not found, enter a sphere into the space and continue to the next space. If no initial value is present, proceed to step 3.ģ)If the space is empty, check each row along the four axes for a sphere.
If it does and the solver is backtracking, proceed to a previous space without erasing the symbol initially entered. If it does and the solver is proceeding, skip over the space and proceed to the next space in the sequence. a value entered by the user to test the algorithm). My brute force solving algorithm takes the following steps:Ģ) Check if the space has an initial value (i.e. Pressing the "=" key solves a single space. It was inspird by a "brute-force" algorithm that is sometimes used to solve Sudoku puzzles. My brute force solving algorithm solves the puzzle one space at a time. The algorithm will consider these spaces to be initial values, and will try to find a solution that incorporates these given spaces. By selecting a space with the cursor and pressing the 1, 2, and 3 keys, the user can place spheres, cubes, and tetrahedrons in the puzzle gird. This cursor can be moved to other spaces using the "a", "d", "e", "s", "i", "k", "j", and "l" keys.
Pressing the "c" key will disable most of the keyboard inputs used to control camera motion (the camera can still be controlled using the mouse and mouse buttons) and cause a white cursor to appear in the grids. My program contains an option for users to set up a puzzle for the solving algorithm to solve. In this picture the near-upper-left corners of each grid are considered to be in the same row. My project creates a variation of this puzzle, except the grid is four-dimensional and it is played using a three-dimensional computer interface.Įach row along the four axes must contain a sphere, a cube, and a tetrahedron. Also, the coming of Sudoku has made solving Latin Squares a very popular recreational activity, as all solved Sudoku are 9x9 Latin Squares. Research in Latin Squares has led to advances in combinatorics and experimental design.
For example, if the square has five spaces per side, each row and column must contain the numbers one through five. The program compiles using MVC98 after running vcvars32.bat and using the run command, assuming run.bat and win.mf are in the same folder as the source file.Ī Latin square is basically a square grid in which each of the spaces on the grid is entered a number between one and the maximum number of spaces in that row or column. The project was written in C and uses OpenGL. The goal of my project was to create a brute-force algorithm for generating a four-dimensional Latin Square and create a computer interface that demonstrates it. Last edited 3dec10 by 2: Generating a Four-Dimensional Latin Square Abstract
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