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0037-解数独
https://leetcode.cn/problems/sudoku-solver
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：
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
思路
- 这一题是在 36 有效数独的基础上继续完善
- 每一个格子能够填充的数字，是可以从其他格子推算出来的。
- 回溯法探测能填的数字，如果一直可以填到底，则可以解出答案
- 设置好剪枝，防止超时
参考代码
csharp
public class Solution {
private char[][] result;
private void SetResult(char[][] board){
result = new char[board.Length][];
for(int i=0; i<result.Length; i++){
result[i] = new char[board[i].Length];
for(int j=0; j<board[i].Length; j++){
result[i][j] = board[i][j];
}
}
}
private bool IsValid(char[][] board, int row, int col, int num){
//探测横向
for(int j=0; j<board[0].Length; j++){
if(board[row][j] == (char)(num + '0')){
return false;
}
}
//探测纵向
for(int i=0; i<board.Length; i++){
if(board[i][col] == (char)(num + '0')){
return false;
}
}
//探测当前9宫格
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] == (char)(num + '0')){
return false;
}
}
}
return true;
}
private void dfs(char[][] board, int index){
if(index == board.Length * board[0].Length){
SetResult(board);
return;
}
int row = index / board[0].Length;
int col = index % board[0].Length;
if(board[row][col] == '.'){
for(int i=1;i<=9;i++){
//填入数字
if(IsValid(board,row,col,i)){
//Console.WriteLine("set i={0}",(char)(i + '0'));
board[row][col] = (char)(i + '0');
dfs(board,index+1);
board[row][col] = '.';
}
}
}
else{
dfs(board,index+1);
}
}
public void SolveSudoku(char[][] board) {
dfs(board,0);
for(int i=0;i<result.Length;i++){
for(int j=0;j<result[0].Length;j++){
board[i][j] = result[i][j];
}
}
}
}