37. Sudoku Solver

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

Empty cells are indicated by the character '.'.

You may assume that there will be only one unique solution.

A sudoku puzzle...

 

...and its solution numbers marked in red.

 

 

深度优先遍历解决问题，从（0，0）点开始遍历，每个点依次试1-9的数，合法或者已经有数则递归到下个位置，直到到达（9，0）点，说明所有点都解决了

 

 

public class Solution {
   public void solveSudoku(char[][] board) {
        solveSudoku_helper(board,0,0);
    }
    public boolean vaild(char[][] board, int x,int y,char val) {
        for (int i=0;i<9;i++){
            if (board[i][y]==val){
                return false;
            }
            if (board[x][i]==val){
                return false;
            }
        }
        for (int i=0;i<3;i++){
            for (int j=0;j<3;j++){
                if (board[x/3*3+i][y/3*3+j]==val)
                    return false;
            }
        }
        return true;
    }
    public boolean solveSudoku_helper(char[][] board,int x,int y) {
        if (x==9&&y==0)
            return true;

        if (board[x][y]=='.'){
            for (int i=1;i<=9;i++){
                if (vaild(board,x,y,(char)(i+'0'))){
                    board[x][y]=(char)(i+'0');
                    if(solveSudoku_helper(board,x+(y+1)/9,(y+1)%9)==true)
                        return true;
                    board[x][y]='.';
                }
            }
        }else {
            if(solveSudoku_helper(board,x+(y+1)/9,(y+1)%9)==true)
                return true;
        }
        return false;
    }
    
}