leetcode 36. 有效的数独

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。

1. 数字 1-9 在每一行只能出现一次。
2. 数字 1-9 在每一列只能出现一次。
3. 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。

解法一：非常巧妙！！！利用三个二维数组

class Solution {
public:
	bool isValidSudoku(vector<vector<char>>& board) {
        int row[9][9] = {0}, col[9][9] = {0}, box[9][9] = {0};
        for (int i = 0; i != board.size(); ++i){
            for (int j = 0; j != board[i].size(); ++j){
                if (board[i][j] != '.')
                {
                    int num = board[i][j] - '0' - 1, k = i / 3 * 3 + j / 3;
                    if (row[i][num] || col[j][num] || box[k][num])
                        return false;
                    row[i][num] = col[j][num] = box[k][num] = 1;
                }
            }
        }
	return true;
	}
};

解法二：利用自定义函数，很繁琐。。。

class Solution {
public:
    bool isvalid(vector<char> vec){//判断9个元素中是否有重复的
        for(int i = 0;i < vec.size()-1;++i){
            for(int j = i+1;j < vec.size();++j){
                if(vec[i]==vec[j] && vec[i]!='.') return false;
            }
        }
        return true;
    }
    vector<char> fun(int a,int b,vector<vector<char>> board){//将方格型的9个元素写到vector中
        vector<char> v(9);
        int k=0;
        for(int i=0;i<3;i++){
            for(int j=0;j<3;j++){
                v[k++]=board[a+i][b+j];
            }
        }
        return v;
    }
    bool isValidSudoku(vector<vector<char>>& board) {
        vector<char> v(9);
        for(int i=0;i<9;++i){//将竖着的9个元素写成vector，添加到board里
            for(int j=0;j<9;++j){
                v[j]=board[j][i];
            }
            board.push_back(v);
        }
        for(int i=0;i<7;i+=3){//将9个9宫格加入到board里
            for(int j=0;j<7;j+=3){
                board.push_back(fun(i,j,board));
            }
        }
        for(int n=0;n<board.size();++n){//判断所有的27个vector
            if(!isvalid(board[n])) return false;
        }
        return true;
    }
};