[LeetCode]36. Valid Sudoku

Description

Determine if a Sudoku is valid, according to: Sudoku Puzzles - The Rules.

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

A partially filled sudoku which is valid.

Note:
A valid Sudoku board (partially filled) is not necessarily solvable. Only the filled cells need to be validated.

Discussion

判断一个给定的9*9矩阵是否满足数独的规则，只考虑已经填充的数字。

我们需要把每行进行一次判断，每列进行一次判断，每个九宫格进行一次判断。

第i行的第j个元素的坐标为board[i][j]
第i列的第j个元素的坐标为board[j][i]
第i个九宫格中第j个元素的坐标为board[i/3*3 + j/3][i%3*3 + j%3]

算法的时间复杂度为O(n^2)。

C++ Code

class Solution {public:    bool isValidSudoku(vector<vector<char>>& board) {        //下面遍历第i行／列／个九宫格中的第j个数。        for(int i = 0; i < 9; i++)        {            unordered_map<char, int> row_map;       //检查第i行            unordered_map<char, int> col_map;       //检查第i列            unordered_map<char, int> subgrid_map;   //检查第i个九宫格            for(int j = 0; j < 9; j++)            {                //第i行的第j个元素的坐标为board[i][j]                if(board[i][j] != '.')                {                    row_map[board[i][j]] ++;                    if(row_map[board[i][j]] > 1)                    {                        return false;                    }                }                //第i列的第j个元素的坐标为board[j][i]                if(board[j][i] != '.')                {                    col_map[board[j][i]] ++;                    if(col_map[board[j][i]] > 1)                    {                        return false;                    }                }                //第i个九宫格中第j个元素的坐标为board[i/3*3 + j/3][i%3*3 + j%3]                if(board[i/3*3 + j/3][i%3*3 + j%3] != '.')                {                    subgrid_map[board[i/3*3 + j/3][i%3*3 + j%3]] ++;                    if(subgrid_map[board[i/3*3 + j/3][i%3*3 + j%3]] > 1)                    {                        return false;                    }                }            }        }        return true;    }};