leetcode-37 Sudoku Solver

问题描述：

Write a program to solve aSudoku 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.

 

问题分析：

解数独问题，问题类似八皇后问题，采用回溯算法BackTracking；即向[i,j]尝试放入数字data,若满足数独规则，则继续进行下一步；若不满足，则回溯到上一步，重新进行遍历。

 

代码：

public class Solution {
   public void solveSudoku(char[][] board) {
        // 判断输入board是否合法
        if(board == null || board.length == 0)
            return;
        solve(board);
   }
   
   // 回溯算法遍历解数独
   private boolean solve(char[][] board) {
        for (int i = 0; i < board.length; i++) {
            for (int j = 0; j < board[0].length; j++) {
                // 填充空格处
                if (board[i][j] == '.') {
                   for (char data = '1'; data <= '9'; data++) {
                        // 如果该data放入当前数组中合法
                        if (isValid(board, i, j,data)) {
                            board[i][j] = data;
                            // 判断填充后是否完成解数独
                            if (solve(board))
                                return true;
                            else // 否则，进行回溯，回到上一状态
                                board[i][j] = '.';
                        }
                    }
                    // 对应无解情况
                    return false;
                }
            }
        }
        return true;
   }
   
   // 判断新设定的数是否合法
   private boolean isValid(char[][] board, int i, int j, char data) {
        // 判断是否行有效
        for (int row = 0; row < board.length; row++) {
            if (board[row][j] == data)
                return false;
        }
        // 判断是否列有效
        for (int column = 0; column < board[0].length; column++) {
            if (board[i][column] == data)
                return false;
        }
        // 判断对角线元素是否有效
        for (int row = i / 3 * 3; row < i / 3 * 3 + 3;row++) {
            for (int column = j / 3 * 3; column < j / 3 * 3 +3; column++) {
                if (board[row][column] == data)
                    return false;
            }
        }
        return true;
   }
}