【LeetCode】36. Valid Sudoku - Java实现

1. 题目描述：

Determine if a 9x9 Sudoku board is valid. Only the filled cells need to be validated according to the following rules:

1. Each row must contain the digits 1-9 without repetition.
2. Each column must contain the digits 1-9 without repetition.
3. Each of the 9 3x3 sub-boxes of the grid must contain the digits 1-9 without repetition.

A partially filled sudoku which is valid.

The Sudoku board could be partially filled, where empty cells are filled with the character '.'.

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.

Note:

A Sudoku board (partially filled) could be valid but is not necessarily solvable.
Only the filled cells need to be validated according to the mentioned rules.
The given board contain only digits 1-9 and the character '.'.
The given board size is always 9x9.

2. 思路分析：

题目的意思是检验该数独九宫格是否符合以下规则：

• 每一行的数字（1-9）是否不重复
• 每一列的数字（1-9）是否不重复
• 每一小格（九宫格）是否不重复

该数独九宫格必定要合法，但不一定可解。

不用解出这个九宫格，只需要判断当前存在的数是否符合条件即可，利用HashSet的特性：不可存在重复元素来解决。

将大的九宫格分为九个小宫格，行和列通过循环可以直接判断，每一小格（九宫格）是否不重复可以通过将i/3,j/3划分为同一个小宫格来判断是否重复。

• 5 in col 0可以被解读为第一列有数字5
• 6 in row 0可以解读为第一行有数字6
• 5 in sub box 0-0可以解读为第一个小宫格有数字5

3. Java代码：

源代码：见我GiHub主页

代码：

public boolean isValidSudoku(char[][] board) {
    Set<String> digitsSet = new HashSet<>();
    int rows = board.length;
    int cols = board[0].length;
    for (int i = 0; i < rows; i++) {
        for (int j = 0; j < cols; j++) {
            if (board[i][j] == '.') {
                continue;
            }
            char ch = board[i][j];
            String rowCheckKey = ch + " in row " + i;
            String colCheckKey = ch + " in col " + j;
            String subBoxCheckKey = ch + " in sub box " + i / 3 + "-" + j / 3;
            if (!digitsSet.add(rowCheckKey) || !digitsSet.add(colCheckKey) || !digitsSet.add(subBoxCheckKey)) {
                return false;
            }
        }
    }
    return true;
}