# Sudoku

## Sudoku

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`'.'`.

## Example

**Example 1:**

```
Input:

[
  ["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:
 true
```

**Example 2:**

```
Input:
[
  ["8","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:
 false

Explanation:
Same as Example 1, except with the 5 in the top left corner being modified to 8.
Since there are two 8's in the top left 3x3 sub-box, it is invalid.
```

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

![](https://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Sudoku-by-L2G-20050714_solution.svg/250px-Sudoku-by-L2G-20050714_solution.svg.png)\
...and its solution numbers marked in red.

**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`

## Note

Judge is Valid - set version: Time O(9\*9) space O(3\*9)

```
board[3*(i/3) + j/3][3*(i%3) + j%3]
i是0的时候，判断第一个九宫格，依次类推
```

```java
public boolean isValidSudoku(char[][] board) {
    for (int i = 0; i < 9; i++) {
        HashSet<Character> rows = new HashSet<>();
        HashSet<Character> cols = new HashSet<>();
        HashSet<Character> cell = new HashSet<>();
        for (int j = 0; j < 9; j++) {
            if (board[i][j] != '.' && !rows.add(board[i][j])) return false;
            if (board[j][i] != '.' && !cols.add(board[j][i])) return false;
            if (board[3*(i/3) + j/3][3*(i%3) + j%3] != '.' 
                && !cell.add(board[3*(i/3) + j/3][3*(i%3) + j%3])) 
                return false;                
        }
    }
    return true;
}
```

Judge is Valid - trick version 不推荐:

```java
public boolean isValidSudoku(char[][] board) {
    for (int i = 0; i < 9; i++) {
        for (int j = 0; j < 9; j++) {
            if (board[i][j] == '.') continue;
            if (!isValid(board, i, j)) return false;
        }
    }
    return true;
}

private static boolean isValid(char[][] board, int i, int j) {
    for (int row = 0; row < 9; row++) {
        if (row == i) continue;
        if (board[row][j] == board[i][j]) return false;
    }
    for (int col = 0; col < 9; col++) {
        if (col == j) continue;
        if (board[i][col] == board[i][j]) return false;
    }
    for (int row = (i/3)*3; row < (i/3)*3 + 3; row++) {
        for (int col = (j/3)*3; col < (j/3)*3 + 3; col++) {
            if (row == i && col == j) continue;
            if (board[i][j] == board[row][col]) return false;
        }
    }
    return true;
}
```

Solver:

暴力去添加1到9，如果合适（valid）就继续dfs，search函数是boolean，不行就改回去，都不行这一层就是false

## Code

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

    private static 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++) {
                        if (isValid(board, i, j, c)) {
                            board[i][j] = c;
                            if (solve(board)) return true;
                            else board[i][j] = '.';
                        }
                    }
                    return false;
                }
            }
        }
        return true;
    }

    private static boolean isValid(char[][] board, int row, int col, char c) {
        for (int i = 0; i < board.length; i++) {
            if (board[i][col] != '.' && board[i][col] == c) return false;
            if (board[row][i] != '.' && board[row][i] == c) return false;
            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; 
        }
        return true;
    }
}
```


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://luj.gitbook.io/code/dfs/3-search/sudoku.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.