Leetcode-36.有效的数独

题目描述

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。

解法1：一次迭代

思路:

构建三个二维数组，row,col,box 表示，这一位位置的行，列，宫是否符合要求

注意：box下标可以用 row/3*3+col/3 求得

class Solution {
public:
    bool isValidSudoku(vector<vector<char>>& board) {
        int row[9][9];
        int col[9][9];
        int box[9][9];
        memset(row,0,sizeof(row));
        memset(col,0,sizeof(col));
        memset(box,0,sizeof(box));
        int i,j;
        int k;
        for(i=0;i<9;i++)
        {
            for(j=0;j<9;j++)
            {
                if(board[i][j]=='.')
                {
                    continue;
                }
                else
                {
                    k=board[i][j]-'0'-1;
                    if(row[i][k]!=0||col[j][k]!=0||box[i/3*3+j/3][k]!=0)
                        return false;
                    row[i][k]++;
                    col[j][k]++;
                    box[i/3*3+j/3][k]++;
                }
            }
        }
        return true;
    }
};