Write a program to solve a Sudoku puzzle by filling the empty cells.
A sudoku solution must satisfy all of the following rules:
Each of the digits 1-9 must occur exactly once in each row.
Each of the digits 1-9 must occur exactly once in each column.
Each of the digits 1-9 must occur exactly once in each of the 9 3x3 sub-boxes of the grid.
The '.' character indicates empty cells.
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:** [["5","3","4","6","7","8","9","1","2"],["6","7","2","1","9","5","3","4","8"],["1","9","8","3","4","2","5","6","7"],["8","5","9","7","6","1","4","2","3"],["4","2","6","8","5","3","7","9","1"],["7","1","3","9","2","4","8","5","6"],["9","6","1","5","3","7","2","8","4"],["2","8","7","4","1","9","6","3","5"],["3","4","5","2","8","6","1","7","9"]]
**Explanation:** The input board is shown above and the only valid solution is shown below:
Constraints:
board.length == 9
board[i].length == 9
board[i][j] is a digit or '.'.
It is guaranteed that the input board has only one solution.
ac
class Solution {
boolean[][] row = new boolean[9][10];
boolean[][] col = new boolean[9][10];
boolean[][] grid = new boolean[9][10];
public void solveSudoku(char[][] board) {
for (int r = 0; r < board.length; r++) {
for (int c = 0; c < board[0].length; c++) {
if (board[r][c] == '.') continue;
int i = board[r][c] - '0';
row[r][i] = true;
col[c][i] = true;
grid[r / 3 * 3 + c / 3][i] = true;
}
}
helper(board, 0);
}
private boolean helper(char[][] board, int ith) {
if (ith >= 81) return true;
int r = ith / board[0].length;
int c = ith % board[0].length;
int g = r / 3 * 3 + c / 3;
if (board[r][c] != '.') {
return helper(board, ith+1);
}
for (int i = 1; i <= 9; i++) {
if (row[r][i] || col[c][i] || grid[g][i]) continue; // skip used element
board[r][c] = (char) ('0' + i);
row[r][i] = true;
col[c][i] = true;
grid[g][i] = true;
if(helper(board, ith + 1)) return true;
grid[g][i] = false;
col[c][i] = false;
row[r][i] = false;
board[r][c] = '.';
}
return false;
}
}
