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 digit1-9
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.
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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;
}
};