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.
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.



// other’ s 


Try 1 through 9 for each cell. The time complexity should be 9 ^ m (m represents the number of blanks to be filled in), since each blank can have 9 choices. Details see comments inside code.

public class Solution {
    public void solveSudoku(char[][] board) {
        if(board == null || board.length == 0)
            return;
        solve(board);
    }
    
    public boolean solve(char[][] board){
        for(int i = 0; i < board.length; i++){
            for(int j = 0; j < board[0].length; j++){
                if(board[i][j] == '.'){
                    for(char c = '1'; c <= '9'; c++){//trial. Try 1 through 9
                        if(isValid(board, i, j, c)){
                            board[i][j] = c; //Put c for this cell
                            
                            if(solve(board))
                                return true; //If it's the solution return true
                            else
                                board[i][j] = '.'; //Otherwise go back
                        }
                    }
                    
                    return false;
                }
            }
        }
        return true;
    }
    
    private boolean isValid(char[][] board, int row, int col, char c){
        for(int i = 0; i < 9; i++) {
            if(board[i][col] != '.' && board[i][col] == c) return false; //check row
            if(board[row][i] != '.' && board[row][i] == c) return false; //check column
            if(board[3 * (row / 3) + i / 3][ 3 * (col / 3) + i % 3] != '.' && 
board[3 * (row / 3) + i / 3][3 * (col / 3) + i % 3] == c) return false; //check 3*3 block
        }
        return true;
    }
}

 two things: 

 

带返回值的dfs recursion

 

 if(board[3 * (row / 3) + i / 3][ 3 * (col / 3) + i % 3] != '.' && 

board[3 * (row / 3) + i / 3][3 * (col / 3) + i % 3] == c) return false;

 

 

Row : 3 * (row / 3) + i / 3

Col :  3 * (col / 3) + i % 3

 

 

x : 012/ 3 = 000 * 3 = 000       345/3 = 111  *3 = 333      678/3 = 222 * 3 = 666

y : 012/ 3 = 000 * 3 = 000       345/3 = 111 * 3 = 333         678/3 = 222 * 3 = 666

 

I =     0, 1 2 3 4 5 6 7 8 9

I/3 = 0  0 0 1  1  1 1 2 2 2

I%3= 0 1  2 0 1 2 0 1 2 0 

 

 

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.