【leetcode刷题笔记】Valid Sudoku

Determine if a Sudoku is valid, according to: Sudoku Puzzles - The Rules.

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

A partially filled sudoku which is valid.

Note:
A valid Sudoku board (partially filled) is not necessarily solvable. Only the filled cells need to be validated.

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题解：根据题目的意思，每行每列和每一个3*3的九宫格里面1~9这9个数不能有重复的，那么就按行，列，和九宫格一一检查即可，要注意下标的计算和'.'符号的处理。

代码如下：

public class Solution {
    public boolean isValidSudoku(char[][] board) {
        int length = board.length;
        if(length == 0)
            return true;
        
        for(int i = 0;i < length;i++){
            boolean[] row_numbers = new boolean[10];
            boolean[] column_numbers = new boolean[10];
            for(int j = 0;j < length;j++){
                //check if rows are valid
                if(board[i][j]!= '.' ){
                    if(row_numbers[board[i][j] - '0'])
                        return false;
                    row_numbers[board[i][j]-'0'] = true;
                }
                
                //check if colums are valid
                if(board[j][i]!= '.'){
                    if(column_numbers[board[j][i]-'0'])
                        return false;
                    column_numbers[board[j][i]-'0'] = true;
                }
            }                
        }
        
        //check if every 3*3 grid is valid
        for(int i = 0;i < 3;i++){
            for(int j = 0;j < 3;j++){
                boolean[] numbers = new boolean[10];
                for(int row = 3*i;row < 3*i+3;row++){
                    for(int column = 3*j;column < 3*j+3;column++){
                        if(board[row][column] != '.'){
                            if(numbers[board[row][column]-'0'])
                                return false;
                            numbers[board[row][column]-'0'] = true;
                        }
                    }
                }
            }
        }
        
        return true;
    }
}

代码中行和列的检查在一次9*9的循环中解决了，可以省一点时间，最终耗时532ms。

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