【初级算法】10.有效的数独

题目：

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。

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

解题思路：

本题初看起来比较怪异，实际只需要判断数据是否合规即可。数独9*9要求每一列的数据为1到9，每一行的数据为1到9.每一个3*3的block也为数字1到9.

因此只需要判断列，行，块是否合法即可。具体该数独有没有解不必关心。

代码：

class Solution {
public:
    bool isValidBlock(vector<vector<char>>& board,int x,int y){
        set<int> test;
        for(int i = x;i<x+3;++i){
            for(int j = y;j < y+3;++j){
                if(board[i][j] == '.'){
                    continue;
                }
                if(!(board[i][j] <= '9' && board[i][j] >= '1')){
                    return false;
                }
                if(board[i][j] <= '9' && board[i][j] >= '1'){
                    if(test.find(board[i][j]-'0')==test.end()){
                        test.insert(board[i][j]-'0');
                    }else{
                        return false;
                    }
                }
            }
        }
        
        return true;
    }
    
    bool isValidRow(vector<vector<char>>& board,int row){
        set<int> test;
        for(int i = 0;i < 9;++i){
           if(board[row][i] == '.'){
               continue;
           }
           if(!(board[row][i] >= '1' && board[row][i] <= '9')){
               return false;
           }
           if(test.find(board[row][i]-'0')==test.end()){
               test.insert(board[row][i]-'0');
           }else{
               return false;
           }
        }
        
        return true;
    }
    
    bool isValidColum(vector<vector<char>>& board,int colum){
        set<char> test;
        for(int i = 0;i<9;++i){
           if(board[i][colum] == '.'){
               continue;
           }
           if(!(board[i][colum] <= '9' && board[i][colum] >= '1')){
               return false;
           }
           if(test.find(board[i][colum]-'0')==test.end()){
               test.insert(board[i][colum]-'0');
           }else{
               return false;
           }
        }
        
        return true;
    }
    
    bool isValidSudoku(vector<vector<char>>& board) {
        
        /*check row & colum*/
        for(int i = 0; i < 9; ++i){
            if(!isValidRow(board,i)||!isValidColum(board,i)){
                cout<<i<<endl;
                return false;
            }
        }
                
        /*check block*/
        for(int i = 0;i < 9; i += 3){
            for(int j = 0;j < 9; j += 3){
                if(!isValidBlock(board,i,j)){
                    cout<<i<<j<<endl;
                    return false;
                }
            }
        }
        
        return true;
    }
};