# Algorithm to determine if a sudoku puzzle is valid

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

1. Each row must contain the digits 1-9 without repetition.
2. Each column must contain the digits 1-9 without repetition.
3. 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/

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Here is another cryptic but short solution in javascript

var isValidSudoku = function(board) {
for (let i = 0; i < 9; i++) {
let row = new Set(), col = new Set(), sqr = new Set();
for (let j = 0; j < 9; j++) {
let rowc = board[i][j];
let colc = board[j][i];
let sqrc = board[Math.floor(i / 3) * 3 + Math.floor(j / 3)][(i % 3) * 3 + j % 3];
if (row.has(rowc) || col.has(colc) || sqr.has(sqrc)) return false;
};