LeetCode Medium: 36. Valid Sudoku

一、题目

Determine if a 9x9 Sudoku board is valid. Only the filled cells need to be validated according to the following rules:

Each row must contain the digits 1-9 without repetition.
Each column must contain the digits 1-9 without repetition.
Each of the 9 3x3 sub-boxes of the grid must contain the digits 1-9 without repetition.

A partially filled sudoku which is valid.

The Sudoku board could be partially filled, where empty cells are filled with the character '.'.

Example 1:

Input:
[
  ["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"]
]
Output: true

Example 2:

Input:
[
  ["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"]
]
Output: false
Explanation: Same as Example 1, except with the 5 in the top left corner being 
    modified to 8. Since there are two 8's in the top left 3x3 sub-box, it is invalid.

Note:

A Sudoku board (partially filled) could be valid but is not necessarily solvable.
Only the filled cells need to be validated according to the mentioned rules.
The given board contain only digits 1-9 and the character '.'.
The given board size is always 9x9.

题目大致意思就是，数独的规则，每行1~9不重复，每列1~9不能重复，3x3小方格1~9不重复。

二、思路

此题使用可以分别判断行列和小方格内的数字是否重复，可以利用哈希思想，其实就是python中的字典也是一样的，逐一遍历行列和小方格，遇到不同的值就存进去，若是存储的过程中遇到相同的就返回False。

行号规律

观察行号规律：

第0个九宫格：000111222; 第1个九宫格：000111222; 第2个九宫格：000111222;

第3个九宫格：333444555; 第4个九宫格：333444555; 第5个九宫格：333444555;

第6个九宫格：666777888; 第7个九宫格：666777888; 第8个九宫格：666777888;

可见对于每三个九宫格行号增3；对于单个九宫格，每三个格点行号增1。

因此第i个九宫格的第j个格点的行号可表示为i/3*3+j/3

三、代码

#coding:utf-8
'''
Solution0最原始暴力求解，但代码冗余
'''
class Solution0:
    def isValidSudoku(self, board):
        """
        :type board: List[List[str]]
        :rtype: bool
        """
        for row in range(9):
            if not self.isValidNine(board[row]):
                return False
            column = [c[row] for c in board]
            if not self.isValidNine(column):
                print('False')
                return False
        for i in [0,3,6]:
            for j in [0,3,6]:
                block = [board[s][t] for s in [i,i+1,i+2] for t in [j,j+1,j+2]]
                if not self.isValidNine(block):
                    print(False)
                    return False
        print('True')
        return True

    def isValidNine(self,row):
        """
        当前九个数字是否有效
        :param row:int
        :return:bool
        """
        map = {}
        for c in row:
            if c != '.':
                if c in map:
                    return False
                else:
                    map[c] = True #若字典map中没有c，则将c存至该map字典中，key为c，value为True
        return True

'''
Solution1精简代码，分别用三个矩阵来检查三个规则是否有重复数字
'''
class Solution1:
    def isValidSudoku(self, board):
        """
        :type board: List[List[str]]
        :rtype: bool
        """
        row = [[False for i in range(9)] for j in range(9)]
        col = [[False for i in range(9)] for j in range(9)]
        block = [[False for i in range(9)] for j in range(9)]
        for i in range(9):
            for j in range(9):
                if board[i][j] != '.':
                    num = int(board[i][j])-1  #这里其实使用了哈希思想，因为数字都是在0~9之间，所以索引减1，试想如果某个位置上的数字和其他位置的数字相同的话，其num值也是一样的，所以通过True或者False就可以辨别是否有重复
                    k = i//3*3 + j//3    #K表示第i个九宫格的第j个格点的行号
                    if row[i][num] or col[j][num] or block[k][num]:
                        print('False')
                        return False
                    row[i][num] = col[j][num] = block[k][num] = True
        print('True')
        return True

if __name__ == '__main__':
    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"]
]
    #ss =Solution0()
    ss = Solution1()
    ss.isValidSudoku(board)

　参考博客：https://www.cnblogs.com/ganganloveu/p/4170632.html https://blog.csdn.net/coder_orz/article/details/51596499

LeetCode Medium: 36. Valid Sudoku

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