leetcode--36--有效的数独

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。

题目来源：https://leetcode-cn.com/problems/valid-sudoku/

思路：
1、按行统计每行是否有重复的数字
2、按列统计每列是否有重复的数字
3、按小九宫格统计是否有重复的数字：这里有个小技巧，通过判断列所在的索引和3、6之间的关系来递增的获取小九宫格左上角位置的索引位置

C++代码

class Solution {
public:
    bool isValidSudoku(vector>& board) {
    
        int flag[10];

        // 按行进行排查，看每行是否有重复的数字
        for(int i=0; i<9; i++){
            memset(flag, 0, sizeof(int)*9);  // 重置 flag
            for(int j=0; j<9; j++){
                if (board[i][j]!='.'){
                    if (flag[board[i][j]-'1']){
                        return false;
                    }else{
                        flag[board[i][j]-'1'] = 1;
                    }
                }
            }
        }

        // 按列进行排查，看每列是否有重复的数字
        for(int i=0; i<9; i++){
            memset(flag, 0, sizeof(int)*9);   // 重置 flag
            for(int j=0; j<9; j++){
                if (board[j][i]!='.'){
                    if (flag[board[j][i]-'1']){
                        return false;
                    }else{
                        flag[board[j][i]-'1'] = 1;
                    }
                }
            }
        }   

        for(int col=0, row=0; row<9; ){
            memset(flag, 0, sizeof(int)*9);   // 重置 flag
            for(int i=0; i<3; i++){
                for(int j=0; j<3; j++){
                    if (board[col+i][row+j]!='.'){
                        if (flag[board[col+i][row+j]-'1']){
                            return false;
                        }else{
                            flag[board[col+i][row+j]-'1'] = 1;
                        }
                    }
                }
            }  

            if (col == 6){
                col = 0;
                row += 3;
            }else{
                col += 3;
            }
        }

        return true;

    }
};

Python版：

    class Solution(object):
        def isValidSudoku(self, board):
            """
            :type board: List[List[str]]
            :rtype: bool
            """
            ret = True

            for i in range(9):
                dt = {}
                for j in range(9):
                    if board[i][j] != '.':
                        if board[i][j] in dt:
                            return False
                        else:
                            dt[board[i][j]] = 1

            for i in range(9):
                dt = {}
                for j in range(9):
                    if board[j][i] != '.':
                        if board[j][i] in dt:
                            return False
                        else:
                            dt[board[j][i]] = 1
            col = 0
            row = 0
            while row<9:
                dt = {}
                for i in range(3):
                    for j in range(3):
                        if board[col+i][row+j] != '.':
                            if board[col+i][row+j] in dt:
                                return False
                            else:
                                dt[board[col+i][row+j]] = 1

                if col == 6:
                    col = 0
                    row += 3
                else:
                    col += 3

            return ret