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Problem:

Write a program to solve a Sudoku puzzle by filling the empty cells.

A sudoku solution must satisfy

all of the following rules

:

1. Each of the digits
   
1-9

   must occur exactly once in each row.
2. Each of the digits
   
1-9

   must occur exactly once in each column.
3. Each of the the digits
   
1-9

   must occur exactly once in each of the 9
   
3x3

   sub-boxes of the grid.

Empty cells are indicated by the character

'.'

.

A sudoku puzzle…

…and its solution numbers marked in red.

Note:

• The given board contain only digits
  
1-9

  and the character
  
'.'

  .
• You may assume that the given Sudoku puzzle will have a single unique solution.
• The given board size is always
  
9x9

  .

Analysis:

本题的思路是采用回溯的方法进行递归的寻找并填充符合题意的数字。使用三个二维数组用来标记行，列，方块中的数字使用情况，以此来防止出现重复的数字。此题的难点也就在于如何界定方块中的数字有没有被使用过。代码如下：

Code:

class Solution {
    boolean[][] row = new boolean[9][9];
    boolean[][] col = new boolean[9][9];
    boolean[][] box = new boolean[9][9];
    
    public void solveSudoku(char[][] board) {
        for(int i = 0; i < 9; i++) {
            for(int j = 0; j < 9; j++) {
                if(board[i][j] != '.') {
                    int p = board[i][j] - '1';
                    row[i][p] = true;
                    col[p][j] = true;
                    box[i/3 * 3 + j/3][p] = true;
                }
            }
        }    
        
        backtracking(board, 0, 0);
    }
    
    boolean backtracking(char[][] board, int i, int j) {
        if(i == board.length) return true;
        if(j == board.length) return backtracking(board, i + 1, 0);
        
        if(board[i][j] != '.') return backtracking(board, i, j + 1);
        
        int m = i/3 * 3 + j/3;
        for(int k = 0; k < 9; k++) {
            if(!row[i][k] && !col[k][j] && !box[m][k]) {
                row[i][k] = true;
                col[k][j] = true;
                box[m][k] = true;
                board[i][j] = (char)(k + '1');
                
                if(backtracking(board, i, j + 1))
                    return true;
                
                board[i][j] = '.';
                row[i][k] = false;
                col[k][j] = false;
                box[m][k] = false;
            }
        }
        return false;
    }
}