36. 有效的数独

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题目

判断一个 9x9 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。

数字 1-9 在每一行只能出现一次。
数字 1-9 在每一列只能出现一次。
数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。

示例1:

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输入:
[
  ["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：

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输入:
[
  ["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。。

说明：

  • 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。
  • 给定数独序列只包含数字 1-9 和字符 ‘.’ 。
  • 给定数独永远是 9x9 形式的。

解法

解法一：遍历

JAVA

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public boolean isValidSudoku(char[][] board) {
		if (board == null || board.length <= 1) {
			return false;
		}
		for (int i = 0; i < board.length; i++) {
			for (int j = 0; j < board[0].length; j++) {
				if (board[i][j] != '.') {
					if (!isValidHelp(board, board[i][j], i, j)) {
						return false;
					}
				}
			}
		}
		return true;
	}

	public boolean isValidHelp(char[][] board, char c, int row, int column) {

		if (board == null)
			return false;

		for (int i = 0; i < row; i++) {
			if (board[i][column] == c && i != row) {
				return false;
			}
		}
		for (int i = 0; i < column; i++) {
			if (board[row][i] == c && i != column) {
				return false;
			}
		}

		int n = row / 3;
		int m = column / 3;

		// 注意这里 *3 + 3 开始没注意我合并成 n*4 了 卡了很久
		for (int i = n * 3; i < n * 3 + 3; i++) {
			for (int j = m * 3; j < m * 3 + 3; j++) {
				if (board[i][j] == c) {
					// 判断是否是自己
					if (i != row && j != column) {
						return false;
					}
				}
			}
		}
		return true;
	}
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