# 0037. Sudoku Solver

<https://leetcode.com/problems/sudoku-solver>

## Description

Write a program to solve a Sudoku puzzle by filling the empty cells.

A sudoku solution must satisfy **all of the following rules**:

1. Each of the digits `1-9` must occur exactly once in each row.
2. Each of the digits `1-9` must occur exactly once in each column.
3. 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:**

![](https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Sudoku-by-L2G-20050714.svg/250px-Sudoku-by-L2G-20050714.svg.png)

```
**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:
![](https://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Sudoku-by-L2G-20050714_solution.svg/250px-Sudoku-by-L2G-20050714_solution.svg.png)
```

**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

```java
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;
    }
}
```


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