If a cell is discovered where none of the 9 digits is allowed, then the algorithm leaves that cell blank and moves back to the previous cell. When checking for violations, if it is discovered that the “1” is not allowed, the value is changed to “2”. If there are no violations (checking row, column and box constraints) then the algorithm advances to the next cell and places a “1” in that cell. Initially, the program would solve the puzzle by placing the digit “1” in the first empty cell and checking if it is allowed to be there. Our problem, goal, and constraints in a step-by-step algorithm.Ī brute force algorithm visits the empty cells in sequential order, filling in digits sequentially, or backtracking when no digit can be filled without violating any rule. We will now create a Sudoku solver using backtracking by Backtracking is all about choices and consequences. As soon as it determines that a candidate cannot possibly lead to a valid solution, it abandons the candidate. ‘īacktracking is an algorithm for finding all (or some) of the solutions to a problem that incrementally builds candidates to the solution(s). You may assume that the given Sudoku puzzle will have a unique solution.Įmpty cells are indicated by the character ‘. The given board contains only digits 1–9 and the character Must occur exactly once in each of the 3x3 sub-boxes of the grid. The grids are partially filled (with hints) to ensure a solution can be reached.Īnd you need to fill the empty cells without violating any rules.Ī sudoku solution must satisfy all of the following rules: The most common Sudoku puzzles use a 9x9 grid. The numbers must be placed so that each column, each row, and each of the sub-grids (if any) contains all of the numbers from 1 to ‘n’. Sudoku is a number-placement puzzle where the objective is to fill a square grid of size ’n’ with numbers between 1 to ’n’.
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