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<vector<char>>& 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