![]() ![]() draw_networkx_edges ( G, pos = pos, edgelist = column_edges, width = 2, edge_color = "tab:green" ) plt. draw_networkx_edges ( G, pos = pos, edgelist = row_edges, width = 2, edge_color = "tab:blue" ) nx. Each 3×3 block can only contain numbers from 1 to 9. What are the basic rules of Sudoku Sudoku grid consists of 9x9 spaces. Its rules are quite simple, so even beginners can handle the simple levels. draw_networkx_edges ( G, pos = pos, edgelist = box_edges, edge_color = "tab:gray" ) nx. 1 2 What is Sudoku and what are the rules of this game Sudoku is a popular logic puzzle with numbers. draw ( G, pos = pos, labels = mapping, with_labels = True, node_color = "orange" ) nx. circular_layout ( G ) if layout = "grid" : pos = dict ( zip ( list ( G. ![]() In addition, we manage an auxiliary NxN matrix of BitSet objects. At the beginning, only clue cells are set with their values, while all other cells are set to zero. figure ( figsize = ( 12, 12 )) if layout = "circular" : pos = nx. Backtracking We represent a Sudoku puzzle by an NxN matrix holding all values that have already been set on the grid. Wikipedia entry on Sudoku, available at http : //wikipedia. sudoku_graph ( n ) board = generate_random_sudoku ( n ) mapping = dict ( zip ( G. strategies, used to solve the vast majority of Sudoku puzzles, to the formulation of. nodes ()), 2 ) ) return row_edges, box_edges, column_edges def plot_edge_colored_sudoku ( n = 3, layout = "grid" ): row_edges, box_edges, column_edges = separate_edges ( n ) G = nx. The objective of Sudoku is to fill a 9x9 grid made of squares (shown above circled in blue) so that each row, each column, and each full 9x9 square use the numbers 1-9. combinations ( boxes, 2 )) column_edges += list ( itertools. combinations (, 2 ) ) box_edges += list ( itertools. append ( box ) for i in range ( n * n ): row_edges += list ( itertools. Sudoku is a puzzle game played on a 9x9 board, where the objective is to fill in each square with the numbers 1 through 9. sudoku_graph ( n ) box_edges = row_edges = column_edges = boxes = for i in range ( n ): for j in range ( n ): box = boxes. The puzzle setter provides a partially completed grid, which for a well-posed puzzle has a single solution. Import itertools def separate_edges ( n ): G = nx. In classic Sudoku, the objective is to fill a 9 × 9 grid with digits so that each column, each row, and each of the nine 3 × 3 subgrids that compose the grid (also called 'boxes', 'blocks', or 'regions') contain all of the digits from 1 to 9. The aim of the puzzle is to enter a numerical digit from 1 to N in each cell of N × N grid made up of sub-grids (. Killer sudoku combines the classic puzzle with the addition game Kakuro to limit where you place numbers even more. Informally the Sudoku graph is an undirected graph- its vertices represent the cells and edges represent pairs of cells that belong to the same row, column, or block of the puzzle. Sudoku is a logic-based placement puzzle. ![]() Here pre-coloring extension simply means translating the pre-existing cues into a graph with 81 nodes, coloring the nodes that are already given as clues, and then trying to color the rest of the vertices within the contraints.Ĭayley graph is simply a way of encoding information about group in a graph, as in we can define the sudoku puzzle completely in terms of a Graph, without missing any logical information or mathematical properties Problem Formulation # The problem of solving a Sudoku puzzle can be represented as precoloring extension on this graph. I will try to find a better example.In the mathematics of Sudoku, the Sudoku graph is an undirected graph whose vertices represent the cells of a (blank) Sudoku puzzle and whose edges represent pairs of cells that belong to the same row, column, or block of the puzzle. That is why one must first scan before analyzing. *note: Candidate elimination is note the fastest nor easiest method for for finding the green cells answer. Candidate elimination can also be used with three number in three cells. This means 3 is in the top cell(marked green) and 9 is in the 'middle' cell. We can see that 3 can not be in the 'middle' open cell. It is a type of constraint satisfaction problem, where the solver is given a finite number of objects (the numerals 1-9) and. 1 A normal magic square has consecutive numbers from 1 to (where n equals the order). There is two other blank cells in this column and the missing numbers is 9 and 3. The two cells which 7 and 8 can be in is in the same column, thus it cannot be elsewhere in the column. Yet, classic 9x9 Sudoku impose the additional. I have concluded(with the help of cross hatching) that 7 and 8 can only be in two places in the lower left region(i filled both in). Sudoku puzzles are actually a special case of Latin Squares any solution to a Sudoku puzzle is a Latin Square. the method for candidate elimination I'm showing now is the matched pair method.This method happens when a pair of numbers are the only possible answer to two cells. It's slow progress and i don't like to erase that much. I will not be showing the what if to you because i don't like it. Analysis consists of two methods namely candidate elimination and the what if. ![]()
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