36. Valid Sudoku

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.

2015年6月8日

一单某一行中、某一列中或某一个小9宫格中有一个数字重复出现，则该解法为非法。

class Solution {public:    bool isValidSudoku(vector<vector<char>>& board) {        //for every row,creat a hash table for number 1~9(actually 0~8),        //1 denotes a number has been used,0 denotes a number has not been used        int rowHashTable[9][9]={0};                //the same as rowHashTable        int colHashTable[9][9]={0};                //the same as rowHashTable        int boxHashTable[9][9]={0};                for(int i = 0;i<board.size();++i)        {            for(int j = 0;j<board[0].size();++j)            {                //only  handle non . cells                if(board[i][j] != '.')                {                    int num = board[i][j] - '0' - 1;                    int boxNum = i / 3 * 3+j / 3;                    if(rowHashTable[i][num] || colHashTable[j][num] || boxHashTable[boxNum][num])                        return false;                    rowHashTable[i][num] = colHashTable[j][num] = boxHashTable[boxNum][num] = 1;                }            }                    }                return true;            }};

验证每一个9宫格中的数字是否合法是这个题的关键

class Solution {public:    bool isValidSudoku(vector<vector<char> > &board) {        if(isValidRow(board) && isValidCol(board) && isValidBox(board))            return true;        else            return false;            }        //通过计数，来判定某一个数是否合法    //不管是在行还是在列还是在9宫格中，每一个数字最多只能出现1次    bool isValidNum(int count[],char c)    {        if(c == '.')            return true;        else            return ++count[c-'1']<=1;    }    bool isValidRow(vector<vector<char> > &board)    {                for(int row = 0;row < 9;row++)        {            int count[9]={0};            for(int col = 0;col < 9;col++)                if(!isValidNum(count,board[row][col]))                    return false;        }        return true;    }        bool isValidCol(vector<vector<char> > &board)    {                for(int col = 0;col < 9;col++)        {            int count[9]={0};            for(int row = 0;row < 9;row++)                if(!isValidNum(count,board[row][col]))                    return false;        }        return true;    }        bool isValidBox(vector<vector<char> > &board)    {        //存储每个9宫格的中心坐标        int boxCenter[9][2]={{1,1},{1,4},{1,7},                             {4,1},{4,4},{4,7},                             {7,1},{7,4},{7,7}};        //九宫格中其他格子与中心的偏移量        int shift[9][2]={{-1,-1},{-1,0},{-1,1},                         {0,-1},{0,0},{0,1},                         {1,-1},{1,0},{1,1}};                for(int i = 0;i<9;i++)        {            int count[9]={0};            int boxCenterX = boxCenter[i][0];            int boxCenterY = boxCenter[i][1];            for(int j = 0;j<9;j++)            {                if(!isValidNum(count,board[boxCenterX+shift[j][0]][boxCenterY+shift[j][1]]))                    return false;            }        }                return true;                    }};