Problem Statement
Determine if a 9x9 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 3x3 sub-boxes of the grid must contain the digits 1-9 without repetition.
Solution
Its a simple solution where we need to verify on two parts:
- Each row and column must have unique value (1-9).
- Each
3x3board inside the big9x9board for the unique value.
Check for each Row and Column
- We can iterate over matrix and can check a row and column in one iteration pass. Let me try to depict it in the form of some images:
- So in first iteration, we will cover single row and single column like this.
- After first iteration, complete matrix will be checked.
- We need to keep track of values for each row and col, for one iteration. So that, we can check if we got a same number or not.
- We can have an array of length-9, since we have numbers from 1-9. Index-0 will be kept unused.
Code Snippet for this
//char[][] board
for (int i=0; i<board[0].length; i++) {
boolean checkRow[] = new boolean[9];
boolean checkCol[] = new boolean[9];
for (int j=0; j<board.length; j++) {
if (board[i][j] != '.') {
//check row
if (checkRow[board[i][j] - '1']) {
return false;
}
else {
checkRow[board[i][j] - '1'] = true;
}
}
if (board[j][i] != '.') {
//check col
if (checkCol[board[j][i] - '1']) {
return false;
}
else {
checkCol[board[j][i] - '1'] = true;
}
}
}
}Check for each 3x3 matrix
- Similarly, while iterating over matrix. We need to check for each 3x3 matrix.
See the image below for more understanding:
Lets look at the code:
//char[][] board
for (int i=0; i<board[0].length; i+=3) {
for (int j=0; j<board.length; j+=3) {
boolean check3x3[] = new boolean[9];
for (int k=i; k<i+3; k++) {
for (int l=j; l<j+3; l++) {
if (board[k][l] == '.') continue;
if (check3x3[board[k][l] - '1']) {
return false;
}
else {
check3x3[board[k][l] - '1'] = true;
}
}
}
}
}Final Code
public boolean isValidSudoku(char[][] board) {
for (int i=0; i<board[0].length; i++) {
boolean checkRow[] = new boolean[9];
boolean checkCol[] = new boolean[9];
for (int j=0; j<board.length; j++) {
if (board[i][j] != '.') {
//check row
if (checkRow[board[i][j] - '1']) {
return false;
}
else {
checkRow[board[i][j] - '1'] = true;
}
}
if (board[j][i] != '.') {
//check col
if (checkCol[board[j][i] - '1']) {
return false;
}
else {
checkCol[board[j][i] - '1'] = true;
}
}
}
}
for (int i=0; i<board[0].length; i+=3) {
for (int j=0; j<board.length; j+=3) {
boolean check3x3[] = new boolean[9];
for (int k=i; k<i+3; k++) {
for (int l=j; l<j+3; l++) {
if (board[k][l] == '.') continue;
if (check3x3[board[k][l] - '1']) {
return false;
}
else {
check3x3[board[k][l] - '1'] = true;
}
}
}
}
}
return true;
}Complexity
The complexity is O(mxn)
We are iterating over whole matrix 2 times. If you are confused for last loop where you can see three nested loops. We are actually iterating over matrix only once.
Leet code submission result
Runtime: 1 ms, faster than 100.00% of Java online submissions for Valid Sudoku.
Memory Usage: 39.5 MB, less than 80.98% of Java online submissions for Valid Sudoku.













