数独题如下，求出解答
数独
题目给定的数据是：
["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"]
‘.’代表空出的部分
题目给的方法是：
class Solution {
public void solveSudoku(char[][] board) {
}
本题可以用回溯法来解决。
第一步
首先解决辅助部分的函数
- 查看放入的数据是否有效
- 用list记录空格的位置，这样我们就不用每次遍历整个表来填空格，而是直接定位空格，这样就可以用少量空间换出时间。
实现
1
private boolean isValid(int row, int col, char c) {
for (int i = 0; i < 9; i++) {
if (board[i][col] != '.' && board[i][col] == c)
return false; // 检查行
if (board[row][i] != '.' && board[row][i] == c)
return false; // 检查列
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; // 检查3x3小方格
}
return true;
}
2 此处注意num=9*i+j的模式，可以反编译为i = num/9，j = num%9
记录空格的位置
public void CountEmptyCell() {
list = new ArrayList<>();
for (int i = 0; i < 9; i++) {
for (int j = 0; j < 9; j++)
if (board[i][j] == '.') {
list.add(9 * i + j);
}
}
}
dfs函数用回溯法
递归树
image.png
public boolean dfs(int cur) {
if (cur == list.size()) {
return true;
}
int decode = list.get(cur);
int row = decode / 9;
int col = decode % 9;
for (char i = '1'; i <= '9'; i++) {
if (isValid(row, col, i)) {
board[row][col] = i;
if (dfs(cur + 1))
return true;
else
board[row][col] = '.';//一定要记得状态回滚
}
}
return false;
}
注意此处的dfs方法我用的是boolean返回类型，就是能够让其找到了答案后不会继续的递归，而是及时的中断返回（由于正解只有一个，所以我们不必继续遍历把所有的解都找出来，如果不这样做，那么在查找下一个解的时候，会把状态给返回到默认的没有填写数字的状态，如果之后一直没有找到解，那么最后的答案就会是初始状态，这是因为没有找到解，就会把状态还原）
以下是没考虑的错误写法
image.png
public void dfs(int cur) { // 他也可以打印出结果，但是由于是全体枚举，即使找到了答案，还是会一直枚举之后的结果，看之后的结果是不是对的，但是这样的话就会冲掉我们的正确答案，因为只有一个解，其他的全是错误的！这样就会一直把我们填好的答案还原为'.'
if (cur == list.size()) {
for (int i = 0; i < 9; i++) {
for (int j = 0; j < 9; j++) {
System.out.print(board[i][j] + " ");
}
System.out.println();
}
return;
}
int decode = list.get(cur);
int row = decode / 9;
int col = decode % 9;
for (char i = '1'; i <= '9'; i++) {
if (isValid(row, col, i)) {
board[row][col] = i;
dfs(cur + 1);
board[row][col] = '.';
}
}
}
这样，输出结果在输出第一个解后，继续遍历，然后后面又找不到解了，整个函数就会把结果，也就是我们的board[][]还原为初始状态。
[图片上传中...(image.png-c68388-1547468691246-0)]
错误的输出结果为
package com.leetcode;
import java.io.File;
import java.io.FileNotFoundException;
import java.util.ArrayList;
import java.util.Scanner;
import javax.print.attribute.IntegerSyntax;
public class leet37 {
char[][] board;
ArrayList list;
public char[][] solveSudoku(char[][] board) {
this.board = board;
CountEmptyCell();
dfs(0);
return board;
}
/* public boolean dfs(int cur) {
if (cur == list.size()) {
return true;
}
int decode = list.get(cur);
int row = decode / 9;
int col = decode % 9;
for (char i = '1'; i <= '9'; i++) {
if (isValid(row, col, i)) {
board[row][col] = i;
if (dfs(cur + 1))
return true;
else
board[row][col] = '.';
}
}
return false;
}*/
public void dfs(int cur) {//他也可以打印出结果，但是由于是全体枚举，即使找到了答案，还是会一直枚举之后的结果，看之后的结果是不是对的，但是这样的话就会冲掉我们的正确答案， 因为只有一个解，其他的全是错误的！这样就会一直把我们填好的答案还原为'.'
if (cur == list.size()) {
for (int i =0; i < 9; i++) {
for (int j = 0; j < 9; j++) {
System.out.print(board[i][j]+" ");
}
System.out.println();
}
return;
}
int decode = list.get(cur);
int row = decode / 9;
int col = decode % 9;
for(char i = '1'; i <= '9'; i++) {
if (isValid(row, col, i)) {
board[row][col] =i;
dfs(cur + 1);
board[row][col] = '.';
}
}
}
public void CountEmptyCell() {
list = new ArrayList<>();
for (int i = 0; i < 9; i++) {
for (int j = 0; j < 9; j++)
if (board[i][j] == '.') {
list.add(9 * i + j);
}
}
}
private boolean isValid(int row, int col, char c) {
for (int i = 0; i < 9; i++) {
if (board[i][col] != '.' && board[i][col] == c)
return false; // check row
if (board[row][i] != '.' && board[row][i] == c)
return false; // check column
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; // check 3*3 block
}
return true;
}
public static void main(String[] args) throws FileNotFoundException {
leet37 test = new leet37();
File file = new File("C:\\Users\\yihon\\Desktop\\123.txt");
Scanner sc = new Scanner(file);
char[][] c = new char[9][9];
int i = 0;
while (sc.hasNextLine()) {
String in = sc.nextLine();
in = in.replace("[", "");
in = in.replace("]", "");
in = in.replaceAll("\"", "");
String[] t = in.split(",");
for (int j = 0; j < 9; j++)
c[i][j] = t[j].charAt(0);
i++;
}
for (i = 0; i < 9; i++) {
for (int j = 0; j < 9; j++) {
System.out.print(c[i][j] + " ");
}
System.out.println();
}
test.solveSudoku(c);
for (i = 0; i < 9; i++) {
for (int j = 0; j < 9; j++) {
System.out.print(c[i][j] + " ");
}
System.out.println();
}
}
}
输入
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：
这次输出是由于我在dfs函数没cur==list.size()的情况下输出的结果，然后继续遍历
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
main函数输出结果：（由于没有及时停止，继续遍历后没找到解，从而冲掉了原解）
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
然后以下是正确解法的源代码：（这里我把给定函数的void，换成了char[][]，主要是方便我本地输入测试用）
import java.io.File;
import java.io.FileNotFoundException;
import java.util.ArrayList;
import java.util.Scanner;
import javax.print.attribute.IntegerSyntax;
public class leet37 {
char[][] board;
ArrayList list;
public char[][] solveSudoku(char[][] board) {
this.board = board;
CountEmptyCell();
dfs(0);
return board;
}
public boolean dfs(int cur) {
if (cur == list.size()) {
return true;
}
int decode = list.get(cur);
int row = decode / 9;
int col = decode % 9;
for (char i = '1'; i <= '9'; i++) {
if (isValid(row, col, i)) {
board[row][col] = i;
if (dfs(cur + 1))
return true;
else
board[row][col] = '.';
}
}
return false;
}
/* public void dfs(int cur) {//他也可以打印出结果，但是由于是全体枚举，即使找到了答案，还是会一直枚举之后的结果，看之后的结果是不是对的，但是这样的话就会冲掉我们的正确答案， 因为只有一个解，其他的全是错误的！这样就会一直把我们填好的答案还原为'.'
if (cur == list.size()) {
for (int i =0; i < 9; i++) {
for (int j = 0; j < 9; j++) {
System.out.print(board[i][j]+" ");
}
System.out.println();
}
return;
}
int decode = list.get(cur);
int row = decode / 9;
int col = decode % 9;
for(char i = '1'; i <= '9'; i++) {
if (isValid(row, col, i)) {
board[row][col] =i;
dfs(cur + 1);
board[row][col] = '.';
}
}
}*/
public void CountEmptyCell() {
list = new ArrayList<>();
for (int i = 0; i < 9; i++) {
for (int j = 0; j < 9; j++)
if (board[i][j] == '.') {
list.add(9 * i + j);
}
}
}
private boolean isValid(int row, int col, char c) {
for (int i = 0; i < 9; i++) {
if (board[i][col] != '.' && board[i][col] == c)
return false; // check row
if (board[row][i] != '.' && board[row][i] == c)
return false; // check column
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; // check 3*3 block
}
return true;
}
public static void main(String[] args) throws FileNotFoundException {
leet37 test = new leet37();
File file = new File("C:\\Users\\yihon\\Desktop\\123.txt");
Scanner sc = new Scanner(file);
char[][] c = new char[9][9];
int i = 0;
while (sc.hasNextLine()) {
String in = sc.nextLine();
in = in.replace("[", "");
in = in.replace("]", "");
in = in.replaceAll("\"", "");
String[] t = in.split(",");
for (int j = 0; j < 9; j++)
c[i][j] = t[j].charAt(0);
i++;
}
for (i = 0; i < 9; i++) {
for (int j = 0; j < 9; j++) {
System.out.print(c[i][j] + " ");
}
System.out.println();
}
test.solveSudoku(c);
for (i = 0; i < 9; i++) {
for (int j = 0; j < 9; j++) {
System.out.print(c[i][j] + " ");
}
System.out.println();
}
}
}
运行结果
输入
["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