36. 有效的数独¶

难度：中等

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。

上图是一个部分填充的有效的数独。

数独部分空格内已填入了数字，空白格用'.'表示。

示例 1：

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：

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。

Reference

题解¶

基本思路： 根据定义直接判断输入的数组是否满足数独的3个条件即可。

代码如下：

bool isValidSudoku(char** board, int boardSize, int* boardColSize){
    int i = 0, j = 0, positions1[boardSize], positions2[boardSize], k = 0;
    for (i = 0; i < boardSize; i++)
    {
        memset(positions1, 0, sizeof(int) * boardSize);
        memset(positions2, 0, sizeof(int) * boardSize);
        for (j = 0; j < boardSize; j++)
        {
            if (board[i][j] > '0' && positions1[board[i][j] - '1'])
                return false;
            if (board[j][i] > '0' && positions2[board[j][i] - '1'])
                return false;
            if (board[i][j] > '0')
                positions1[board[i][j] - '1'] = 1;
            if (board[j][i] > '0')
                positions2[board[j][i] - '1'] = 1;
        }
    }
    for (i = 0; i < 3; i++)
    {
        for (j = 0; j < 3; j++)
        {
            memset(positions1, 0, sizeof(int) * boardSize);
            for (k = 0; k < boardSize; k++)
            {
                if (board[i * 3 + k % 3][j * 3 + k / 3] > '0' && positions1[board[i * 3 + k % 3][j * 3 + k / 3] - '1'])
                    return false;
                if (board[i * 3 + k % 3][j * 3 + k / 3] > '0')
                    positions1[board[i * 3 + k % 3][j * 3 + k / 3] - '1'] = 1;
            }
        }
    }
    return true;
}

36. 有效的数独¶

题目¶

题解¶

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