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Java-based LeetCode algorithm problem solutions, regularly updated

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37\. Sudoku Solver

Hard

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.