LeetCode 36. 有效的数独

• 题目：36. 有效的数独判断一个 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。

• 思路1

public boolean isValidSudoku(char[][] board) {
        for (int i = 0; i < 9; i++) {
            //检查列
            if (!isParticallyValid(board, 0, 8, i, i)) {
                return false;
            }
            //检查行
            if (!isParticallyValid(board, i, i, 0, 8)) {
                return false;
            }
        }

        //检查块
        for (int i = 0; i < 3; i++) {
            for (int j = 0; j < 3; j++) {
                if (!isParticallyValid(board, i * 3, i * 3 + 2, j * 3, j * 3 + 2))
                    return false;
            }
        }
        return true;
    }

    //把要检查的值存入到set中，每次向set中添加值的时候，如果失败则证明该值已经存在
    private boolean isParticallyValid(char[][] board, int x1, int x2, int y1, int y2) {
        Set<Character> set = new HashSet<>();
        for (int i = x1; i <= x2; i++) {
            for (int j = y1; j <= y2; j++) {
                if (board[i][j] != '.' && !set.add(board[i][j]))
                    return false;
            }
        }
        return true;
    }

• 思路2

  //set中存放所有字符的3个属性：行、列、和块的位置；向set中添加属性的时候，添加失败则返回false；如果全部添加成功则返回true
    public boolean isValidSudoku(char[][] board) {
        Set<String> set = new HashSet<>();
        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                Character c = board[i][j];
                if (c != '.') {
                    if (!set.add(c + "in row" + i)
                            || !set.add(c + "in col" + j)
                            || !set.add(c + "in block" + i / 3 + "-" + j / 3))
                        return false;
                }
            }
        }
        return true;
    }