36. 有效的数独

1.题目

请你判断一个 9 x 9 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。（请参考示例图）

注意：

• 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。
  空白格用 ‘.’ 表示。

• board.length == 9

• board[i].length == 9

• board[i][j] 是一位数字（1-9）或者 ‘.’

2.示例

输入：board = 
[["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
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输入：board = 
[["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。

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3.答案

题目就是给了一个99的方格，方格的每个元素要么是0-9的数字要么是 ‘.’，需要判断每一行，每一列，每一个33方格里面的9个元素是否有重复的数字。

 bool isValidSudoku(vector<vector<char>>& board) {
        for(int i=0;i<9;i++){  //检查每一行的元素
            unordered_set<char> s;  //记录每一行的数字
            for(int j=0;j<9;j++){
                if(board[i][j]>='0'&&board[i][j]<='9'){
                    if(s.count(board[i][j])) return false; //行有重复元素
                    s.insert(board[i][j]);
                }
            }
        }

         for(int i=0;i<9;i++){  //检查每一列的元素
            unordered_set<char> s;
            for(int j=0;j<9;j++){
                if(board[j][i]>='0'&&board[j][i]<='9'){
                    if(s.count(board[j][i])) return false; //列有重复元素
                    s.insert(board[j][i]);
                }
            }
        }

        for(int i=0;i<9;i+=3){  //检查每一3*3的元素
            for(int j=0;j<9;j+=3){
                //(i,j)为左上角元素
                set<char> s;
                for(int k=i;k<i+3;k++){
                    for(int p=j;p<j+3;p++){
                    if(board[k][p]>='0'&&board[k][p]<='9'){ 
                    if(s.count(board[k][p])) return false; //列有重复元素
                    s.insert(board[k][p]);
                }
                    }
                }
                
            }
        }
        return true;
    }
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简单的使用三个数组保存每行，每列，每个方块内1-9数字的出现次数。

bool isValidSudoku(vector<vector<char>>& board) {
        int row[9][9];  //每一行的元素统计
        int col[9][9];  //每一列的元素统计
        int square[3][3][9]; //统计每个方块内的元素

        memset(row,0,sizeof(row));    
        memset(col,0,sizeof(col));
        memset(square,0,sizeof(square)); 
        for(int i=0;i<9;i++){
            for(int j=0;j<9;j++){
                if(board[i][j]!='.'){
                    int tmp=board[i][j]-'1';  //数字从1-9
                    row[i][tmp]++;  // 第i行tmp这个数字出现1次
                    col[j][tmp]++;  //第j行tmp这个数字出现1次
                    square[i/3][j/3][tmp]++;
                    if(row[i][tmp]>1||col[j][tmp]>1||square[i/3][j/3][tmp]>1) return false;
                }
            }
        }
    return true;
       
    }
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来源：力扣（LeetCode）
链接：https://leetcode.cn/problems/valid-sudoku