A Pencil and Paper Algorithm for Solving Sudoku Puzzles英文电子书.pdf

A Pencil-and-Paper Algorithm for Solving Sudoku Puzzles J. F. Crook he puzzle Sudoku has become the pas- down into nine 3 × 3 subboards that do not over- sion of many people the world over in lap. We call these subboards boxes and number the past few years. The interesting fact them from 1 to 9 in typewriter order beginning Tabout Sudoku is that it is a trivial puzzle in the upper left-hand corner of the board, as to solve. The reason it is trivial to solve displayed in Figure 1. is that an algorithm exists for Sudoku solutions. The notation for referring to a particular cell The algorithm is a tree-based search algorithm on the board is to give the row number followed based on backtracking in a tree until a solution is by the column number. For example, the notation found. c (6, 7)—where c denotes cell—denotes the cell at If all a person needs to do is sit down at their the intersection of row 6 and column 7. personal computer, punch in the numbers given in The theory we develop in the next section uses the puzzle, and then watch a computer program the widely known concept of matching numbers compute the solution, we can reasonably ask why across cells. Various authors, as suits their whim, a person would bother to struggle to solve Sudoku name matching numbers differently. For example, puzzles. The reason is that people enjoy strug- Sheld