Sudoku Solver
題意:給一個數獨,寫程式解開它
解題思路:
其實跟解n queen一樣,每放入一個合法的格,再往下一格寫,直到解完整個數獨,在這裡使用true false來判所是否這條路可行,若不可行,則不繼續往下走。
當當前元素為數字時,記得返回 helper(board, i, j + 1) 往下一個元素運算,否則上一層會認為是錯的則把board[i][j] 改回'.',等於白算了。
public class Solution {
public void solveSudoku(char[][] board) {
if (board == null || board.length != 9 || board[0].length != 9) {
return;
}
helper(board, 0, 0);
}
public boolean helper(char[][] board, int i, int j) {
// 已走到列的盡頭,繼續往下新的一列
if (j >= 9) {
return helper(board, i + 1, 0);
}
// 已完成整個填表動作
if (i == 9) {
return true;
}
// 當格子為'.'時才要去作填表動作
if (board[i][j] == '.') {
for (int k = 1; k <= 9; k++) {
board[i][j] = (char)(k + '0');
if (isValid(board, i, j)) {
if (helper(board, i, j + 1)) {
return true; // 找到對的答案要即時return,不能再變回'.'
}
}
board[i][j] = '.';
}
} else {
return helper(board,i, j + 1); // 記得作return動作,不return的話,上一層不知道你是對是錯,會把那格又改回'.'了。
}
return false;
}
private boolean isValid(char[][] board, int x, int y) {
// check column
for (int i = 0; i < 9; i++) {
if (i != x && board[i][y] == board[x][y]) {
return false;
}
}
// check row
for (int i = 0; i < 9; i++) {
if (i != y && board[x][i] == board[x][y]) {
return false;
}
}
// check block
for (int row = x / 3 * 3; row < x / 3 * 3 + 3; row++) {
for (int col = y / 3 * 3; col < y / 3 * 3 + 3; col++) {
if ((row != x || col != y) && board[row][col] == board[x][y]) {
return false;
}
}
}
return true;
}
}
updated 2015.11.18
public class Solution {
public void solveSudoku(char[][] board) {
if (board == null || board.length < 9) {
return;
}
helper(board, 0, 0);
}
private boolean helper(char[][] board, int x, int y) {
if (y >= 9) {
return helper(board, x + 1, 0);
}
if ( x == 9) {
return true;
}
if (board[x][y] == '.') {
for (int i = 1; i <= 9; i++) {
board[x][y] = (char) (i + '0');
if (isValid(board, x, y)) {
if (helper(board, x, y + 1)) {
return true; // 不能直接返回 false
}
}
board[x][y] = '.';
}
} else {
return helper(board, x, y + 1);
}
return false;
}
private boolean isValid(char[][] board, int x, int y) {
// check columns and rows
for (int i = 0; i < 9; i++) {
if (i != x && board[i][y] == board[x][y]) {
return false;
}
if (i != y && board[x][i] == board[x][y]) {
return false;
}
}
for (int i = x / 3 * 3; i < x / 3 * 3 + 3; i++) {
for (int j = y / 3 * 3; j < y / 3 * 3 + 3; j++) {
if ((i != x || j != y) && board[i][j] == board[x][y]) {
return false;
}
}
}
return true;
}
}