有效的數獨

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。

1. 數字 1-9 在每一行只能出現一次。
2. 數字 1-9 在每一列只能出現一次。
3. 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 和字元 '.' 。
• 給定數獨永遠是 9x9 形式的。

題解:

今天刷了好幾道題，就這題還有點意思，主要是優化，橫縱座標的有效性沒問題直接用map搞，3x3的方格的有效性我一開始是直接寫了個check函式，在函式裡用map進行驗證，後來看見別人的程式碼，覺得很巧妙，可以開一個三維陣列，假設驗證第i行第j個，那麼可以把它唯一標記為p[i/3][j/3]，可以驗證(0,0),(0,1)一直到(2,2)也就是第一個方格所有座標都符合這個唯一標記，而其他的座標不符合，那麼開一個三維陣列就可以標記整張圖的每個3x3的方格里的有效性。我修改之後的時間居然跑得和原來的一樣。。莫名其妙

我修改前的程式碼:

class Solution {
public:
    bool isValidSudoku(vector<vector<char>>& board) {
        for(int i=0;i<9;i++)
        {
            map<char,int>p;
            map<char,int>p1;
            for(int j=0;j<9;j++)
            {
                if(i%3==0&&j%3==0)
                {
                    if(!check(board,i,j))
                        return false;
                }
                if(board[i][j]!='.')
                {
                    if(p[board[i][j]])
                        return false;
                    p[board[i][j]]=1;
                }
                if(board[j][i]!='.')
                {
                    if(p1[board[j][i]])
                        return false;
                    p1[board[j][i]]=1;
                }
            }
        }
        return true;
    }
    bool check(vector<vector<char>>& board,int sx,int sy)
    {
        map<char,int>p;
        for(int i=sx;i<sx+3;i++)
        {
            for(int j=sy;j<sy+3;j++)
            {
                if(board[i][j]=='.')
                    continue;
                if(p[board[i][j]])
                    return false;
                p[board[i][j]]=1;
            }
        }
        return true;
    }
};

我修改後的程式碼:

class Solution {
public:
    bool isValidSudoku(vector<vector<char>>& board) {
        int p2[10][10][10];
        memset(p2,0,sizeof(p2));
        for(int i=0;i<9;i++)
        {
            map<char,int>p;
            map<char,int>p1;
            for(int j=0;j<9;j++)
            {
                if(board[i][j]!='.')
                {
                    if(p[board[i][j]])
                        return false;
                    p[board[i][j]]=1;
                    int t=board[i][j]-'0';
                    if(p2[i/3][j/3][t])
                        return false;
                    p2[i/3][j/3][t]=1;
                }
                if(board[j][i]!='.')
                {
                    if(p1[board[j][i]])
                        return false;
                    p1[board[j][i]]=1;
                }
            }
        }
        return true;
    }
};