leetcode37. 解数独（C++|回溯）
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题目描述
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。
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：提示：
board.length == 9
board[i].length == 9
board[i][j] 是一位数字或者 '.'
题目数据 保证 输入数独仅有一个解
果果念
这道题目感觉挺难的，确实难哈。上一篇做了N皇后问题，也是回溯。回溯是不是都不简单啊，今天只做了两道题目。当然，这道题目也是看了别人的思路之后写出来的，但是没有比着别人抄。我是没有想到题解的话，复杂度也会这么高。这个是很难估量的，但是最大不会超过O(9^(9*9))，啊，算不出来了。我的代码跑了40-80ms，没有别人跑的快。
下面说下我的思路和遇到的坑吧
1.基本思路很好理解，暴力暴力暴力。对一个空闲的位置，要列举1-9，不行的话，再进行回溯，和八皇后问题很像哈。
2.递归一定要及时返回，否则不可收拾。为什么这样说呢？你想，题目中已经说了答案唯一，但是如果不是bool返回的话，那么就有可能找不到正确的值，因为他会一直递归一直递归，太长了。。。这个我之前没有想到，因为之前都是所有的解。就像八皇后问题。
总体说，这道题目是当时大二的时候学长宣传算法协会的时候，为了提高我们的兴趣进行介绍的一个题目，觉得挺有趣的，也一直没有机会去写，也算是画上了一个句号吧。
加油
代码
class Solution {
public:
void solveSudoku(vector>& board) {
rowSolve(0,0,board);
}
//正在求解第（rowIndex，cloumnIndex）处数字，0~8
//按照列优先，即先一列一列的来
bool rowSolve(int rowIndex,int cloumnIndex,vector>& board){
//找到可行解
if(rowIndex==9){
return true;
}
//查找下一行
if(cloumnIndex==9){
return rowSolve(rowIndex+1,0,board);
}
if(board[rowIndex][cloumnIndex]!='.'){
return rowSolve(rowIndex,cloumnIndex+1,board);
}else //if(board[rowIndex][cloumnIndex]=='.')
{
//满足行，列，九宫格，一次性放1个
for(int i=1;i<=9;i++){
if(judge(rowIndex,cloumnIndex,i,board)==true){
board[rowIndex][cloumnIndex]='0'+i;
if(rowSolve(rowIndex,cloumnIndex+1,board)==true){
return true;
}
board[rowIndex][cloumnIndex]='.';
}
}return false;
}
}
//0 2 0
bool judge(int r,int c,int num,vector>& board){
//检验第r行
for(int i=0;i<9;i++){
if(num==board[r][i]-'0'){
return false;
}
}
//检验第c列
for(int i=0;i<9;i++){
if(num==board[i][c]-'0'){
return false;
}
}
//九宫格的起点 0 3 6
int nineR,nineC;
nineR=(r/3)*3;
nineC=(c/3)*3;
cout<