leetcode Valid Sudoku题解

题目描述：

Determine if a 9x9 Sudoku board is valid. Only the filled cells need to be validated according to the following rules:

1. Each row must contain the digits 1-9 without repetition.
2. Each column must contain the digits 1-9 without repetition.
3. Each of the 9 3x3 sub-boxes of the grid must contain the digits 1-9 without repetition.

A partially filled sudoku which is valid.

The Sudoku board could be partially filled, where empty cells are filled with the character '.'.

Example 1:

Input:
[
  ["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"]
]
Output: true

Example 2:

Input:
[
  ["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"]
]
Output: false
Explanation: Same as Example 1, except with the 5 in the top left corner being 
    modified to 8. Since there are two 8's in the top left 3x3 sub-box, it is invalid.

中文理解：

给定一个9*9的矩阵，矩阵的元素有1-9的数组和.组成，要求每一行的数字不能重复，每一列的数字不能重复，9*9的9个3*3的矩阵中1-9的数字也不能重复，如果满足条件返回true，否则返回false。

解题思路：

使用一个int[10]的数组来存储1-9的数字是否出现以及出现的次数，然后先横向遍历，判断每行是否满足条件，再纵向遍历，判断每列是否满足条件，再9个3*3小矩阵遍历，判断每个小矩阵是否满足条件，如果都满足则返回true，否则返回false。

代码（java）：

class Solution {
    public boolean isValidSudoku(char[][] board) {
        int []numbers=new int[10];
        for(int i=0;i<board.length;i++){
            numbers=new int[10];
            for(int j=0;j<board[0].length;j++){
                if(board[i][j]>'0' && board[i][j]<='9')
                    numbers[board[i][j]-'0']++;
            }
            if(!number(numbers))return false;
        }
        for(int i=0;i<board[0].length;i++){
            numbers=new int[10];
            for(int j=0;j<board.length;j++){
                if(board[j][i]>'0'&&board[j][i]<='9')
                    numbers[board[j][i]-'0']++;
            }
            if(!number(numbers))return false;
        }
        for(int i=0;i<board.length-2;i+=3){
            for(int j=0;j<board[0].length-2;j+=3){
                numbers=new int[10];
                for(int k=0;k<=2;k++){
                    for(int l=0;l<=2;l++){
                        if(board[i+k][j+l]>'0'&&board[i+k][j+l]<='9')
                            numbers[board[i+k][j+l]-'0']++;
                    }
                }
                if(!number(numbers))return false;
            }
        }
        return true;
        
    }
    public boolean number(int[]number){
        for(int val:number){
            if(val>1)return false;
        }
        return true;
    }
}