【初級算法】10.有效的數獨

題目：

判斷一個 9x9 的數獨是否有效。只需要根據以下規則，驗證已經填入的數字是否有效即可。

數字 1-9 在每一行只能出現一次。
數字 1-9 在每一列只能出現一次。
數字 1-9 在每一個以粗實線分隔的 3x3 宮內只能出現一次。


上圖是一個部分填充的有效的數獨。

數獨部分空格內已填入了數字，空白格用 '.' 表示。

示例 1:

輸入:
[
  ["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"]
]
輸出: true
示例 2:

輸入:
[
  ["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"]
]
輸出: false
解釋: 除了第一行的第一個數字從 5 改為 8 以外，空格內其他數字均與 示例1 相同。
     但由於位於左上角的 3x3 宮內有兩個 8 存在, 因此這個數獨是無效的。
說明:

一個有效的數獨（部分已被填充）不一定是可解的。
只需要根據以上規則，驗證已經填入的數字是否有效即可。
給定數獨序列只包含數字 1-9 和字符 '.' 。
給定數獨永遠是 9x9 形式的。

解題思路：

本題初看起來比較怪異，實際只需要判斷數據是否合規即可。數獨9*9要求每一列的數據為1到9，每一行的數據為1到9.每一個3*3的block也為數字1到9.

因此只需要判斷列，行，塊是否合法即可。具體該數獨有沒有解不必關心。

代碼：

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;
    }
};