(Leetcode)37. Sudoku Solver

回溯法(Backtracking)求数独的解

回溯法 Backtracking

深度优先搜索 策略
遍历空间树，找到一个结点。如果符合解的要求，则继续向下探索；如果不符合解的要求，则退回其父节点。
比较形象来说可以用走迷宫做例子，大多人类一般就是使用回溯法，当走到一条死路，就往回退到前一个岔路，尝试另外一条，直到走出。

Problem

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.

Solution

Java Code

public class Solution {
    public void solveSudoku(char[][] board) {
        backtracking(board);


    }

    boolean backtracking(char[][] board){
        for(int i = 0; i < 9; i++){
            for(int j = 0; j < 9; j++){
                if(board[i][j] == '.'){
                    for(char c = '1'; c <= '9'; c++){//trial. Try 1 through 9 for each cell
                        if(isValid(board, i, j, c)){
                            board[i][j] = c; //Put c for this cell

                            if(backtracking(board))
                                return true; //If it's the solution return true
                            else
                                board[i][j] = '.'; //Otherwise go back
                        }
                    }
                    return false;
                }
            }
        }
        return true;
    }


    public boolean isValid(char board[][], int i, int j, char c){
        //row
        for(int m = 0; m < 9; m++){
            if( m!=i){
                if( c == board[m][j] ){
                    return false;
                }
            }
        }
        //column
        for(int n = 0; n < 9; n++){
            if( n!=j){
                if( c == board[i][n] ){
                    return false;
                }
            }
        }
        int k_row = i/3;
        int k_column = j/3;
        //sub-box
        for(int m = k_row*3; m < k_row*3+3; m++){
            for(int n = k_column*3; n < k_column*3+3; n++)
            if( m!=i && n!=j){
                if( c == board[m][n] ){
                    return false;
                }
            }
        }
        return true;
    }
    /**
     * @param args
     */
    public static void main(String[] args) {
        // TODO Auto-generated method stub

    }

}