题目
编写一个程序，通过填充空格来解决数独问题。
数独的解法需 遵循如下规则：
- 数字 1-9 在每一行只能出现一次。
- 数字 1-9 在每一列只能出现一次。
- 数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。（请参考示例图）
数独部分空格内已填入了数字，空白格用 ‘.’ 表示。
示例：
输入：board = [["5","3",".",".","7",".",".",".","."],["6",".",".","1","9","5",".",".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".",".","3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6"],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],[".",".",".",".","8",".",".","7","9"]] 输出：[["5","3","4","6","7","8","9","1","2"],["6","7","2","1","9","5","3","4","8"],["1","9","8","3","4","2","5","6","7"],["8","5","9","7","6","1","4","2","3"],["4","2","6","8","5","3","7","9","1"],["7","1","3","9","2","4","8","5","6"],["9","6","1","5","3","7","2","8","4"],["2","8","7","4","1","9","6","3","5"],["3","4","5","2","8","6","1","7","9"]] 解释：输入的数独如上图所示，唯一有效的解决方案如下所示：
解题
方法一：回溯
由于每个数独的长、宽、值都可以用for循环可以遍历的，但是需要填的空格数却不知道，这时候就需要用到回溯，需要填的空格就是递归的次数。 (否则就要用使用 空格个 for循环，显然是不可能的。)
class Solution { public: bool backtracing(vector<vector<char>>& board){ for(int i=0;i<board.size();i++){ //遍历行 for(int j=0;j<board[0].size();j++){ //遍历列 if(board[i][j]!='.') continue; for(char k='1';k<='9';k++){ if(isValid(i,j,k,board)){ board[i][j]=k; if(backtracing(board)) return true; // 如果找到合适一组立刻返回 board[i][j]='.'; } } return false; // 9个数都试完了，都不行，那么就返回false } } return true; //遍历完没有返回false，说明找到了合适棋盘位置了 } bool isValid(int row,int col,char val,vector<vector<char>>& board){ for(int i=0;i<9;i++){ // 判断列里是否重复 if(board[i][col]==val) return false; } for(int j=0;j<9;j++){ // 判断行里是否重复 if(board[row][j]==val) return false; } int startRow=(row/3)*3; int startCol=(col/3)*3; for(int i=startRow;i<startRow+3;i++){ // 判断9方格里是否重复 for(int j=startCol;j<startCol+3;j++){ if(board[i][j]==val) return false; } } return true; } void solveSudoku(vector<vector<char>>& board){ backtracing(board); } };
java
class Solution { boolean dfs(char[][] board,int n){ for(int i=0;i<n;i++){ for(int j=0;j<n;j++){ if(board[i][j]!='.') continue; for(char k='1';k<='9';k++){ if(isValid(board,i,j,k)){ board[i][j]=k; if(dfs(board,n)) return true; board[i][j]='.'; } } return false; } } return true; } boolean isValid(char[][] board,int row,int col,int k){ for(int i=0;i<9;i++){ if(board[i][col]==k) return false; } for(int j=0;j<9;j++){ if(board[row][j]==k) return false; } int startRow=row/3*3; int startCol=col/3*3; for(int i=startRow;i<startRow+3;i++){ for(int j=startCol;j<startCol+3;j++){ if(board[i][j]==k) return false; } } return true; } public void solveSudoku(char[][] board) { int n=board.length; dfs(board,n); return; } }
