Sudoku validation is a crucial task in game development and puzzle-solving applications, ensuring that a given Sudoku board adheres to specific rules. In Ruby, writing a function to validate a 9×9 Sudoku board is essential for verifying its correctness. In this article, we’ll delve into how to implement a function in Ruby to determine the validity of a Sudoku board, considering rules such as no repetition in rows, columns, and sub-grids, with comprehensive examples and outputs provided for clarity.

### Understanding Sudoku Validation Rules

Validating a Sudoku board involves ensuring that each row, each column, and each 3×3 sub-grid contains all digits from 1 to 9 without repetition.

### Example: Validating Sudoku in Ruby

Let’s define a Ruby function called `valid_sudoku?`

to determine the validity of a 9×9 Sudoku board.

```
def valid_sudoku?(board)
rows = Array.new(9) { Hash.new(0) }
cols = Array.new(9) { Hash.new(0) }
boxes = Array.new(9) { Hash.new(0) }
board.each_with_index do |row, i|
row.each_with_index do |val, j|
next if val == '.'
box_index = (i / 3) * 3 + j / 3
return false if rows[i][val] > 0 ||
cols[j][val] > 0 ||
boxes[box_index][val] > 0
rows[i][val] += 1
cols[j][val] += 1
boxes[box_index][val] += 1
end
end
true
end
# Test the function with examples
sudoku_board1 = [
["5","3",".",".","7",".",".",".","."],
["6",".",".","1","9","5",".",".","."],
[".","9","8",".",".",".",".","6","."],
["8",".",".",".","6",".",".",".","3"],
["4",".",".","8",".","3",".",".","1"],
["7",".",".",".","2",".",".",".","6"],
[".","6",".",".",".",".","2","8","."],
[".",".",".","4","1","9",".",".","5"],
[".",".",".",".","8",".",".","7","9"]
]
sudoku_board2 = [
["8","3",".",".","7",".",".",".","."],
["6",".",".","1","9","5",".",".","."],
[".","9","8",".",".",".",".","6","."],
["8",".",".",".","6",".",".",".","3"],
["4",".",".","8",".","3",".",".","1"],
["7",".",".",".","2",".",".",".","6"],
[".","6",".",".",".",".","2","8","."],
[".",".",".","4","1","9",".",".","5"],
[".",".",".",".","8",".",".","7","9"]
]
puts valid_sudoku?(sudoku_board1) # Output: true
puts valid_sudoku?(sudoku_board2) # Output: false
```

### Output:

```
true
false
```