36. Valid Sudoku (M)

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本文介绍了一种算法，用于验证9x9数独板的有效性。通过检查每一行、每一列以及每个3x3子网格中的数字是否符合不重复的规则，确保数独的正确性。文章提供了两种实现方式，一种是直接实现，另一种是使用hash表进行优化。

Valid Sudoku (M)

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

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

在这里插入图片描述
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.

题意

判断一个数独中已经填入的数字是否有效。

思路

直接对每一个数字判断是否有效，可以直接实现，也可以借助hash实现。

代码实现 - 无hash

class Solution {
    public boolean isValidSudoku(char[][] board) {
        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                char c = board[i][j];
                if (c != '.' && !isValid(board, i, j, c)) {
                    return false;
                }
            }
        }

        return true;
    }
    
    private boolean isValid(char[][] board, int i, int j, char c) {
        for (int k = 0; k < 9; k++) {
            if (k != j && c == board[i][k] || k != i && c == board[k][j]) {
                return false;
            }
        }
		
        // x、y的初始值为对应九宫格左上顶点的坐标
        for (int x = 3 * (i / 3); x < 3 * (i / 3) + 3; x++) {
            for (int y = 3 * (j / 3); y < 3 * (j / 3) + 3; y++) {
                if (c == board[x][y] && x != i && y != j) {
                    return false;
                }
            }
        }

        return true;
    }
}

代码实现 - hash

class Solution {
    public boolean isValidSudoku(char[][] board) {
        List<Set<Character>> row = new ArrayList<>();
        List<Set<Character>> col = new ArrayList<>();
        List<Set<Character>> nine = new ArrayList<>();

        for (int i = 0; i < 9; i++) {
            row.add(new HashSet<>());
            col.add(new HashSet<>());
            nine.add(new HashSet<>());
        }

        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                char c = board[i][j];
                if (c != '.') {
                    if (!row.get(i).add(c)) {
                        return false;
                    }
                    if (!col.get(j).add(c)) {
                        return false;
                    }
                    // 九宫格序号的计算公式为 3 * (i / 3) + j / 3
                    if (!nine.get(3 * (i / 3) + j / 3).add(c)) {
                        return false;
                    }
                }
            }
        }

        return true;
    }
}