有效的数独

有效的数独 的题目是:

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。

image

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。

题目比较长，没有玩过数独的可能还要理解一下这个题目，其实就是判断横向的 9 个数组，竖向的 9 个数组和 9 个 3 * 3 的小方格里都没有重复的元素。有点绕的是遍历二维数组时怎么把每个元素存入对应的 3 * 3 的小方块里。对应子方块的 index 的计算方法为：

//horizonIndex 为遍历时横向 index，verticalIndex 为垂直 index
int cubeIndex = verticalIndex / 3 + (horizonIndex / 3) * 3;

然后还要利用Set 容器去重复的特性，Set.add(T item)会返回一个 boolean 值，为 true 就是容器里不存在同样的元素，false 就是存在，可以做为判断数独是否有效的简便方法。

其他没有什么好说的，放代码：

    public static boolean isValidSudoku(char[][] board) {
        List<Set<Character>> horizonList = new ArrayList<>(9);
        List<Set<Character>> verticalList = new ArrayList<>(9);
        List<Set<Character>> cubeList = new ArrayList<>(9);
        
        for (int i = 0; i < 9; i++) {
            horizonList.add(new HashSet<Character>());
            verticalList.add(new HashSet<Character>());
            cubeList.add(new HashSet<Character>());
        }

        for (int j = 0; j < 9; j++) {
            for (int k = 0; k < 9; k++) {
                char c = board[j][k];

                if(c == '.'){
                    continue;
                }

                if(!horizonList.get(j).add(c)){
                    return false;
                }

                if(!verticalList.get(k).add(c)){
                    return false;
                }

                int cubeIndex = k / 3 + (j / 3) * 3;
                Set<Character> set = cubeList.get(cubeIndex);

                if(!set.add(c)){
                    return false;
                }
            }
        }

        return true;