# Algorithm to determine if a sudoku puzzle is valid

Determine if a 9×9 Sudoku board is valid. Only the filled cells need to be validated **according to the following rules**:

- Each row must contain the digits 1-9 without repetition.
- Each column must contain the digits 1-9 without repetition.
- Each of the 9 3×3 sub-boxes of the grid must contain the digits 1-9 without repetition.

A partially filled sudoku which is valid.

The Sudoku board could be partially filled, where empty cells are filled with the character ‘.’.

**Example 1:**

**Input:**

[

[“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″]

]

**Output:** true

**Example 2:**

**Input:**

[

[“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″]

]

**Output:** false

**Explanation:** Same as Example 1, except with the **5** in the top left corner being

modified to **8**. Since there are two 8’s in the top left 3×3 sub-box, it is invalid.

**Note:**

- A Sudoku board (partially filled) could be valid but is not necessarily solvable.
- Only the filled cells need to be validated according to the mentioned rules.
- The given board contain only digits 1-9 and the character ‘.’.
- The given board size is always 9×9.

**Posted from https://forum.golibrary.co/question/algorithm-determine-sudoku-puzzle-valid/ **

Below long but self explanatory algorithm in javascript !!

A sudoku is said to be valid if

**If all boxes (3×3 grids) contain no duplicates and thus unique numbers between 1-9****All rows contain no duplicates and thus unique numbers between 1-9****All columns contain no duplicates and thus unique numbers between 1-9**

Checking the same conditions below in the code:-

/** * @param {character[][]} board * @return {boolean} */ var isValidSudoku = function(board) { var isValid = false; var cols = []; var rowItemRepeat = false; var colItemRepeat = false; var boxItemRepeat = false; var SUDOKU_LENGTH = board.length; var BOX_LENGTH = parseInt(Math.sqrt(SUDOKU_LENGTH)); for (var i = 0; i < board.length; i++) { rowItemRepeat = rowItemRepeat || checkRows(board[i]); var box = getBox(board, parseInt(i / BOX_LENGTH) * BOX_LENGTH, i*BOX_LENGTH % SUDOKU_LENGTH); boxItemRepeat = boxItemRepeat || hasDuplicates(box); cols[i] = []; for (var j = 0; j < board.length; j++) { if (board[j][i] !== '.') { cols[i].push(board[j][i]) } } colItemRepeat = colItemRepeat || hasDuplicates(cols[i]); } return !(rowItemRepeat || colItemRepeat || boxItemRepeat); }; var getBox = function(board, x, y) { var box = []; for (var a = x; a < x+3; a++) { for (var b = y; b < y+3; b++) { if (board[a][b] !== '.') { box.push(board[a][b]); } } } return box; } var checkRows = function(row) { var rowArr = []; var hasRepeat = false; for (var t = 0; t < row.length; t++) { hasRepeat = false; if (row[t] !== '.') { rowArr.push(row[t]); } } hasRepeat = hasRepeat || hasDuplicates(rowArr); return hasRepeat; } var hasDuplicates = function(array) { return (new Set(array)).size !== array.length; }