Added more optimized sudoku solver algorithm

Author: SandeepaDilshanAlagiyawanna

backtracking/sucoku-solver-optimized.py

@@ -0,0 +1,109 @@
+def is_valid(board, row, col, num):
+    """ Checks if the given number is valid for the given cell in the Sudoku board """
+    for i in range(9):
+        if (
+                # checking is there any same number in row
+                board[row][i] == num or
+                # checking is there any same number in column
+                board[i][col] == num or
+                # checking is there any same number in cell(3*3)
+                board[(row // 3) * 3 + i // 3][(col // 3) * 3 + i % 3] == num
+        ):
+            # if so return false
+            return False
+    return True
+
+
+"""Taking the Board and checking the availability"""
+
+
+def solve_sudoku(board):
+    # use of recursive function solve.
+    def solve(row, col):
+
+        # if row number is 9, return true as there is no any other row (last Row Solved)
+        if row == 9:
+            return True
+
+        # if column number is 9, then we should change the row and check again
+        if col == 9:
+            # resetting row number to next and column number to 0
+            return solve(row + 1, 0)
+
+        # if the number of the board[row][col] is not the 0, then it is solved, then we  should move o next.
+        if board[row][col] != 0:
+            # moving to next column
+            return solve(row, col + 1)
+
+        # setting a number between 1-9
+        for num in range(1, 10):
+
+            # checking the availability of that number
+            if is_valid(board, row, col, num):
+
+                # if the number is ok,then setting the number
+                board[row][col] = num
+
+                # moving to next column
+                if solve(row, col + 1):
+                    return True
+
+                # if none above are not fitting, lets hold the value of cell as zero, and then we can call it again
+                board[row][col] = 0
+
+        # returning none as algorithm cannot find any solution
+        return False
+
+    # starting with (0,0) cell
+    if solve(0, 0):
+
+        # return the solution
+        return board
+    else:
+
+        # no solution
+        return None
+
+
+""" printing the board """
+
+
+def print_board(board):
+    if board:
+
+        # printing the board row by row
+        for row in board:
+
+            # joining the int as strings by including space in between
+            print(" ".join(map(str, row)))
+    else:
+
+        print("No solution found.")
+
+
+def main():
+
+    board = [
+        [0, 0, 3, 0, 0, 0, 0, 0, 0],
+        [0, 4, 0, 2, 0, 0, 6, 3, 0],
+        [0, 8, 2, 1, 0, 0, 0, 0, 9],
+        [0, 0, 0, 4, 0, 6, 0, 0, 0],
+        [5, 0, 0, 0, 9, 0, 1, 0, 0],
+        [3, 0, 0, 0, 0, 0, 0, 0, 0],
+        [0, 0, 0, 0, 0, 0, 7, 8, 0],
+        [0, 0, 0, 9, 0, 0, 0, 6, 0],
+        [0, 0, 1, 7, 2, 0, 4, 0, 0]
+    ]
+
+    # taking the solution board
+    solution = solve_sudoku(board)
+
+    if solution:
+        print("The solved Sudoku puzzle:")
+        print_board(solution)
+    else:
+        print("No solution found.")
+
+
+if __name__ == "__main__":
+    main()