有效的数独 LeetCode(数组的巧妙运用)

布满荆棘的人生 2022-05-14 13:20 251阅读 0赞

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。

![250px-Sudoku-by-L2G-20050714.svg.png][]

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。

题解:

今天刷了好几道题，就这题还有点意思，主要是优化，横纵坐标的有效性没问题直接用map搞，3x3的方格的有效性我一开始是直接写了个check函数，在函数里用map进行验证，后来看见别人的代码，觉得很巧妙，可以开一个三维数组，假设验证第i行第j个，那么可以把它唯一标记为p\[i/3\]\[j/3\]，可以验证(0,0),(0,1)一直到(2,2)也就是第一个方格所有坐标都符合这个唯一标记，而其他的坐标不符合，那么开一个三维数组就可以标记整张图的每个3x3的方格里的有效性。我修改之后的时间居然跑得和原来的一样。。莫名其妙

我修改前的代码:

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;
        }
    };

我修改后的代码:

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;
        }
    };

[250px-Sudoku-by-L2G-20050714.svg.png]: https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Sudoku-by-L2G-20050714.svg/250px-Sudoku-by-L2G-20050714.svg.png