37. Sudoku Solver

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.

如果当前位置是空，则尝试1到9中所有的数字，如果对于1到9中的某些数字，当前是合法的，则继续尝试下一个位置（调用自身）。

 1 public class Solution {
 2     public void solveSudoku(char[][] board) {
 3         if(board == null || board.length == 0)
 4             return;
 5         solve(board);
 6     }
 7     
 8     public boolean solve(char[][] board){
 9         for(int i = 0; i < board.length; i++){
10             for(int j = 0; j < board[0].length; j++){
11                 if(board[i][j] == '.'){
12                     for(char c = '1'; c <= '9'; c++){//trial. Try 1 through 9
13                         if(isValid(board, i, j, c)){
14                             board[i][j] = c; //Put c for this cell
15                             
16                             if(solve(board))
17                                 return true; //If it's the solution return true
18                             else
19                                 board[i][j] = '.'; //Otherwise go back
20                         }
21                     }
22                     
23                     return false;
24                 }
25             }
26         }
27         return true;
28     }
29     
30     private boolean isValid(char[][] board, int row, int col, char c){
31         for(int i = 0; i < 9; i++) {
32             if(board[i][col] != '.' && board[i][col] == c) return false; //check row
33             if(board[row][i] != '.' && board[row][i] == c) return false; //check column
34         }
35         for(int i = 3*(row/3);i<3*(row/3+1);i++)
36             for(int j = 3*(col/3);j<3*(col/3+1);j++)
37             if(board[i][j] != '.' && board[i][j] == c) return false; //check 3*3 block
38         
39         return true;
40     }
41 }