leetcode 36. 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 改爲 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。

解法一：非常巧妙！！！利用三個二維數組

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：利用自定義函數，很繁瑣。。。

class Solution {
public:
    bool isvalid(vector<char> vec){//判斷9個元素中是否有重複的
        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){//將方格型的9個元素寫到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){//將豎着的9個元素寫成vector，添加到board裏
            for(int j=0;j<9;++j){
                v[j]=board[j][i];
            }
            board.push_back(v);
        }
        for(int i=0;i<7;i+=3){//將9個9宮格加入到board裏
            for(int j=0;j<7;j+=3){
                board.push_back(fun(i,j,board));
            }
        }
        for(int n=0;n<board.size();++n){//判斷所有的27個vector
            if(!isvalid(board[n])) return false;
        }
        return true;
    }
};