Sudoku Solver

This sudokkusolver could apply on easy, medium, hard level.

• In the game of Sudoku, you are given a partially-filled 9 x 9 grid, grouped into a 3 x 3 grid of 3 x 3 blocks.

• The objective is to fill each square with a digit from 1 to 9, subject to the requirement that each row, column, and block must contain each digit exactly once.

• I will implement the AC-3 constraint satisfaction algorithm for Sudoku, along with two extensions that will combine to form a complete and efficient solver.

   Function infer_ac3(self) that runs the AC-3 algorithm on the current board to narrow down each cell's set of values as much as possible. Although this will not be powerful enough to solve all Sudoku problems, it will produce a solution for easy-difficulty puzzles.
   
   Function infer_improved(self) that runs this improved version of AC-3, using infer_ac3(self) as a subroutine (perhaps multiple times). Deductions will be made about a specific cell by examining the possible values for other cells in the same row, column, or block. Using this technique, it should be able to solve all of the medium-difficulty puzzles.
   
   Function infer_with_guessing(self) that calls infer_improved(self) as a subroutine, picks an arbitrary value for a cell with multiple possibilities if one remains, and repeats. You should implement a backtracking search which reverts erroneous decisions if they result in unsolvable puzzles. For efficiency, the improved inference algorithm should be called once after each guess is made. This method should be able to solve all of the hard-difficulty puzzles.
  

** HAVE FUN **