The working of the code works on Backtracking using Recursion. The main aim being able to fill in the empty spaces in the puzzle denoted by 0’s with values from 1-9 that fulfill the requirements to solve a sudoku. If no such value exists for a particular empty space the code backtracks to the previous position of 0 in the puzzle, resets its value back to 0 and tries other values until a result is reached. Once the last 0 is replaced by a value, the solution for that particular puzzle has been reached.
solved_sudoku []: is a list that stores the solved sudoku
wrong_puzzle []: stores a 9*9 list whose values are -1
This function takes the sudoku puzzle as a parameter and returns the position of a ‘0’ if found. The position is returned as row, col. If there is not any 0’s to be found in the puzzle it will return False.
This function checks if a value that is going to be entered into the puzzle along with its respective position row, col is valid in its 3*3 box and returns True if it is valid that is the same number does not exist in its square and returns False if it’s a duplicate number.
Each 3*3 box in the sudoku puzzle can be given a certain address:
(row index position//3 , column index position//3)
Example:
Parameters entered:
r = 5 (index position in the row) c = 8 (index position in the column)
3*3 Address of value 6:
(r//3 , c//3) = (5//3 , 8//3) => (1,2)
In the sudoku puzzle this would be box number 6, as shown in the below table
| (0,0) | (0,1) | (0,2) |
Box:1 Box:2 Box:3
| (1,0) | (1,1) | (1,2) |
Box:4 Box:5 Box:6
| (2,0) | (2,1) | (2,2) |
Box:7 Box:8 Box:9
From this we can get the range of the row and column of the 3*3 box. After which we run the value through that range and check for a duplicate in the box.
This function checks if a value that is going to be entered into the puzzle along with its respective position row, col is valid for its respective column and row. It returns True is both conditions for the row and the column are valid and False if either or both conditions is not valid.
It uses 2 different for-loops to loop through the different elements of its respective row and column.
This function is responsible for the main working of the code.
It first checks if there are any 0’s in the puzzle using the check_0() function, if there are any 0’s it returns the position and assigns it to row and col respectively, else returns True if there are no 0’s left in the puzzle.
If there are 0’s left it runs a for loop from 1 to 9 to place values into the position. It then checks if the for-loop value, ‘v’ can be inserted into the board. To check its validity, it calls the col_row_chk() and box_chk() function and if they both return true then the value is assigned to the board.
It then calls the same function check(board) and checks if the puzzle is complete. If it is then it returns True
If after going through all the values from 1-9 and no value is valid for that position the code backtracks to the previous position where a ‘0’ was seen and resets its value to 0:
If there is no solution to the sudoku then it returns False.
This function checks if the entered puzzle is valid or not. It checks this by entering all the values of the puzzle through the col_row_chk() and box_chk() function. If both the functions return True for all the values of the puzzle and ignores all the instances of 0’s in the code, then the puzzle is valid and returns True else it returns False.
This function received the sudoku puzzle and prints the result of the puzzle. It first checks if the entered puzzle is valid by passing it through the complete_check() function. It then passes the puzzle through the check() function. If a solution is found it returns the solution through the as a numpy array called solved_sudoku else, it returns wrong_puzzle. And if the entered board is not valid it returns wrong_puzzle