Valid Sudoku
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# LeetCode #36: Valid Sudoku (C/C++).

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source: https://leetcode.com/problems/valid-sudoku/
C/C++ Solution to LeetCode problem 36. Valid Sudoku.

## Problem

Determine if a 9 x 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 nine 3 x 3 sub-boxes of the grid must contain the digits 1-9 without repetition.

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.

## Examples

### Example 1:

Input: board = [[“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: board = [[“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 3x3 sub-box, it is invalid.

## Constraints

• board.length == 9
• board[i].length == 9
• board[i][j] is a digit 1-9 or '.'.

## Solution

• For every “cell” with a number, we explore the whole row and column to see if the number is located in any other place. If so, return false.
• For every “cell” with a number, we explore the the 3x3 neighbourhood to which the number belongs.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 class Solution { public: bool isValidSudoku(vector<vector<char>>& board) { for (int row=0; row<9; row++) { for (int col=0; col<9; col++) { if (board[row][col] == '.') continue; for (int i=0; i<9; i++) { if (i != row && board[i][col] == board[row][col]) return false; if (i != col && board[row][i] == board[row][col]) return false; } for (int y=0; y<3; y++) { for (int x=0; x<3; x++) { if ((3*(col/3)+x)==col && (3*(row/3)+y)==row) continue; if (board[3*(row/3)+y][3*(col/3)+x] == board[row][col]) return false; } } } } return true; } };