LeetCode No36. 有效的数独

题目

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。

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。（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

暴力模拟

数独的定义是行和列都是没有重复的数，那么可以在初始的时候就直接检查行和列是否满足条件，然后再每个小矩阵的起点(小矩阵左上角)，查看是否有重复的数即可。

哈希

暴力之后看了题解才想到的原来可以用哈希的思想，将每行，每列，每个小矩阵都哈希到一个数组中，如果出现有重复的数，则是不合格的。

AC代码

暴力模拟

点击查看代码

class Solution {
    char[][] board;

    private boolean initCheck() {
        for(int i=0; i<9; i++) {
            boolean[] rowOk = new boolean[10];
            boolean[] colOk = new boolean[10];
            for(int j=0; j<9; j++) {
                if(board[i][j]!='.') {
                    int numR = (int) (board[i][j] - '0');
                    if( rowOk[numR] ) {
                        return false;
                    }
                    rowOk[numR] = true;
                }
                if( board[j][i]!='.') {
                    int numC = (int) (board[j][i] - '0');
                    if( colOk[numC] ) {
                        return false;
                    }
                    colOk[numC] = true;
                }
            }
        }
        return true;
    }

    private boolean isLittleSudo(int row, int col) {
        // System.out.println("row = " + row + " col" + col);
        boolean[] arr = new boolean[10];
        int endR = row + 3;
        int endC = col + 3;
        // System.out.println("endR = " + endR + " endC" + endC);
        for(int i=row; i<endR; i++) {
            for(int j=col; j<endC; j++) {
                // if( row==0 && col==3 ) {
                    // System.out.print(board[i][j]);
                // } 
                if(board[i][j]=='.') {
                    continue;
                }
                int num = (int) (board[i][j] - '0');
                if( arr[num] ) {
                    return false;
                }
                arr[num] = true;
            }
            // System.out.println();
        }
        return true;
    }

    public boolean isValidSudoku(char[][] board) {
        this.board = board;
        boolean flag = initCheck();
        if( !flag ) {
            return false;
        }
        for(int i=0; i<9; i+=3) {
            for(int j=0; j<9; j+=3) {
                if( !isLittleSudo(i,j) ) {
                    return false;
                }
            }
        }
        return true;
    }
}

哈希

点击查看代码

class Solution {
    public boolean isValidSudoku(char[][] board) {
        boolean[][] rowOk = new boolean[10][10];
        boolean[][] colOk = new boolean[10][10];
        boolean[][][] littleSudo = new boolean[3][3][10];
        for(int i=0; i<9; i++) {
            for(int j=0; j<9; j++) {
                char ch = board[i][j];
                if( ch == '.' ) {
                    continue;
                }
                int num = (int)( board[i][j]-'0');
                if( rowOk[i][num] || colOk[j][num] || littleSudo[i/3][j/3][num] ) {
                    return false;
                }
                rowOk[i][num] = true;
                colOk[j][num] = true;
                littleSudo[i/3][j/3][num] = true;
            }
        }
        return true;
    }
}