LeetCode 036 Valid Sudoku

题目要求：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.

分析：

本题是让写数独的check函数（isValidSudoku）~基本有三个步骤：

① 每一行都合法；

② 每一列都合法；

③ 每一块都合法（3 * 3）。

代码如下：

class Solution {
public:
    bool isValidSudoku(vector<vector<char> > &board) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        return 
            isValidRow(board) && isValidColumn(board) && isValidBox(board);
    }

private:    

    bool isValidRow(vector<vector<char> > &board) {
        int count[9];        
        for (int i = 0; i < 9; i++) {
            memset(count, 0, sizeof(int) * 9);
            for (int j = 0; j < 9; j++) {
                if (!add(count, board[i][j])) {
                    return false;
                }
            }
        }
        return true;
    }
    
    bool isValidColumn(vector<vector<char> > &board) {
        int count[9];        
        for (int i = 0; i < 9; i++) {
            memset(count, 0, sizeof(int) * 9);
            for (int j = 0; j < 9; j++) {
                if (!add(count, board[j][i])) {
                    return false;
                }
            }
        }
        return true;    
    }
    
    bool isValidBox(vector<vector<char> > &board) {
        int point[9][2] = {
            {1, 1}, {1, 4}, {1, 7}, {4, 1}, {4, 4}, {4, 7}, {7, 1}, {7, 4}, {7, 7}
        };
        int dir[8][2] = {
            {-1, 0}, {-1, 1}, {0, 1}, {1, 1}, {1, 0}, {1, -1}, {0, -1}, {-1, -1}
        };        
        int count[10];
        
        for (int i = 0, x, y; i < 9; i++) {
            memset(count, 0, sizeof(int) * 10);                            
            x = point[i][0];
            y = point[i][1];
            add(count, board[x][y]);                
            for (int j = 0; j < 8; j++) {
                if (!add(count, board[dir[j][0] + x][dir[j][1] + y])) {
                    return false;
                }
            }
        }
        return true;
    }
    
    bool add(int count[], char c) {
        if (c == '.') {
            return true;
        }
        
        //如果每个字符出现次数 <= 1，则正常+_+
        return (++count[c - '1']) <= 1;
    }
};

简化版本：

class Solution {
public:
    bool isValidSudoku(vector<vector<char> > &board) {
        // Note: The Solution object is instantiated only once.
        vector<vector<bool>> rows(9, vector<bool>(9,false));
        vector<vector<bool>> cols(9, vector<bool>(9,false));
        vector<vector<bool>> blocks(9, vector<bool>(9,false));

        for(int i = 0; i < 9; i++)
            for(int j = 0; j < 9; j++){
                if(board[i][j] == '.')continue;
                
                //rows, cols, blocks分别是9个布尔值
                //将每个点分别赋值为true
                //若未赋值的为true了，则有问题
                int num = board[i][j] - '1';
                if(rows[i][num] || cols[j][num] || blocks[i - i%3 + j/3][num])
                    return false;
                rows[i][num] = cols[j][num] = blocks[i - i%3 + j/3][num] = true;
            }
        return true;
    }

};