36.有效的数独

36.有效的数独

请你判断一个 9 x 9 的数独是否有效。只需要 根据以下规则 ，验证已经填入的数字是否有效即可。

1. 数字 1-9 在每一行只能出现一次。
2. 数字 1-9 在每一列只能出现一次。
3. 数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。（请参考示例图）

注意：

• 一个有效的数独（部分已被填充）不一定是可解的。
• 只需要根据以上规则，验证已经填入的数字是否有效即可。
• 空白格用 '.' 表示。

示例 1：

输入：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"]]
输出：true

示例 2：

输入：board = 
[["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"]]
输出：false
解释：除了第一行的第一个数字从 5 改为 8 以外，空格内其他数字均与 示例1 相同。 但由于位于左上角的 3x3 宫内有两个 8 存在, 因此这个数独是无效的。

提示：

• board.length == 9
• board[i].length == 9
• board[i][j] 是一位数字（1-9）或者 '.'

思路：

• 使用三个数组

  1. boolean[][] row = new boolean[9][10];
     //row数组中9表示0-8行，10表示该行数字值
     

  2. boolean[][] col = new boolean[9][10];
     //col数组中9表示0-9列，10表示该行数字值
     

  上面两个数组什么意思呢？画个图解释一下

  

  3. boolean[][] bucket = new boolean[9][10];
     //bucket数组表示将每一个以粗实线分隔的 3x3宫格为一个元素，如下图分成了九份
     

     

  遍历每一个位置，判断该位置数字在所在行row中是否出现过，或在所在列col中是否出现过，或者在3*3的小区域bucket中出现过，如果三者其一出现过，直接返回false。如果都没出现过，将该位置所在位置值都分别设置进row、col、bucket中，遍历下一个。

colpublic class Problem_0036_ValidSudoku {
	public boolean isValidSudoku(char[][] board) {
		boolean[][] row = new boolean[9][10];// 0-8指行 1-9是指出现的数字
		boolean[][] col = new boolean[9][10];
		boolean[][] bucket = new boolean[9][10];
		for (int i = 0; i < 9; i++) {
			for (int j = 0; j < 9; j++) {
				int bid = (i / 3) * 3 + (j / 3);
				if (board[i][j] != '.') {
					// '1' ~ '9'
					int num = board[i][j] - '0';
					if (row[i][num] || col[j][num] || bucket[bid][num]) {
						return false;
					}
					row[i][num] = true;
					col[j][num] = true;
					bucket[bid][num] = true;
				}

			}
		}
		return true;
	}
}