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.



A sudoku puzzle...



...and its solution numbers marked in red.
求解数独。
根据规则，采用dfs求解即可。本题解法可以得出所有可能的解。

class Solution {

public void copyArray(char[][] des, char[][] source){
for (int i = 0; i < source.length; ++ i){
for (int j = 0; j < source[0].length; ++ j){
des[i][j] = source[i][j];
}
}
}

public boolean isValidFill(char[][] board, int row, int col, char c){
for (int i = 0; i < 9; ++ i){
if (board[row][i] != '.'&&board[row][i] == c){
return false;
}
if (board[i][col] != '.'&&board[i][col] == c){
return false;
}
if (board[3*(row/3) + i/3][3*(col/3) + i%3] != '.'&&board[3*(row/3) + i/3][3*(col/3) + i%3] == c){
return false;
}
}
return true;
}

public void dfs(char[][] tmp, char[][] board, int i){
if (i == 81){
copyArray(board, tmp);
return;
}
if (tmp[i/9][i%9] == '.'){
for (char c = '1'; c <= '9'; ++ c){
if (isValidFill(tmp, i/9, i%9, c)){
tmp[i/9][i%9] = c;
dfs(tmp, board, i + 1);
tmp[i/9][i%9] = '.';
}
}
}
else {
dfs(tmp, board, i + 1);
}
}

public void solveSudoku(char[][] board) {
char[][] tmp = new char[9][9];
copyArray(tmp, board);
dfs(tmp, board, 0);
}
}

由于题目已经假设只有一个解，所以也可以直接求解，只要在上面的结构上稍加限制即可。程序如下所示：

class Solution {
public boolean isValidFill(char[][] board, int row, int col, char c){
for (int i = 0; i < 9; ++ i){
if (board[row][i] != '.'&&board[row][i] == c){
return false;
}
if (board[i][col] != '.'&&board[i][col] == c){
return false;
}
if (board[3*(row/3) + i/3][3*(col/3) + i%3] != '.'&&board[3*(row/3) + i/3][3*(col/3) + i%3] == c){
return false;
}
}
return true;
}

public boolean dfs(char[][] board, int i){
if (i == 81){
return true;
}
if (board[i/9][i%9] == '.'){
for (char c = '1'; c <= '9'; ++ c){
if (isValidFill(board, i/9, i%9, c)){
board[i/9][i%9] = c;
if (dfs(board, i + 1)){
return true;
}
else {
board[i/9][i%9] = '.';
}
}
}
}
else {
return dfs(board, i + 1);
}
return false;
}

public void solveSudoku(char[][] board) {
dfs(board, 0);
}
}