> For the complete documentation index, see [llms.txt](https://mayanktyagi3111.gitbook.io/interview-prep/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mayanktyagi3111.gitbook.io/interview-prep/recursion-and-backtracking/sudoku-solver.md).

# Sudoku Solver

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 the digits `1-9` must occur exactly once in each of the 9 `3x3` sub-boxes of the grid.

Empty cells are indicated by the character `'.'`.

\
A sudoku puzzle...

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

\
...and its solution numbers marked in red.

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

**Note:**

* The given board contain only digits `1-9` and the character `'.'`.
* You may assume that the given Sudoku puzzle will have a single unique solution.
* The given board size is always `9x9`.

```java
public class Solution {
    public void solveSudoku(char[][] board) {
        if (board == null || board.length == 0)
            return;
        solve(board);
    }

    public boolean solve(char[][] board) {
        for (int i = 0; i < board.length; i++)
            for (int j = 0; j < board[0].length; j++)
                if (board[i][j] == '.') {
                    for (char c = '1'; c <= '9'; c++) // Try 1 -> 9
                        if (isValid(board, i, j, c)) {
                            board[i][j] = c; // Put c for this cell
                            if (solve(board))
                                return true; // If it's the solution return true
                            else
                                board[i][j] = '.'; // Backtrack
                        }
                    return false;
                }
        return true;
    }

    private boolean isValid(char[][] board, int row, int col, char c) {
        for (int i = 0; i < 9; i++) {
            if (board[i][col] != '.' && board[i][col] == c)
                return false; // check row
            if (board[row][i] != '.' && board[row][i] == c)
                return false; // check column
            if (board[3 * (row / 3) + i / 3][3 * (col / 3) + i % 3] != '.'
                    && board[3 * (row / 3) + i / 3][3 * (col / 3) + i % 3] == c)
                return false; // check 3*3 block
        }
        return true;
    }
}
```