个人记录-LeetCode 36. Valid Sudoku

问题：

Determine if a Sudoku is valid, according to: Sudoku Puzzles - The Rules.

The Sudoku board could be partially filled, where empty cells are filled with the character ‘.’.

Note:

A valid Sudoku board (partially filled) is not necessarily solvable. Only the filled cells need to be validated.

代码示例：

1、分别检查每一行、每一列、每个独立的单元，判断是否满足有效数独问题的条件。

这个方法是最容易想到的，但需要重复扫描整个数据3次，比较费时。

public class Solution {
public boolean isValidSudoku(char[][] board) {
return isValid(board) && checkAllTheRow(board)
&& checkAllTheColumn(board) && checkAllUnits(board);
}

//检查输入数据是否正常
private boolean isValid(char[][] board) {
if (board == null) {
return false;
}

if (board.length != 9) {
return false;
}

for (int i = 0; i < 9; ++i) {
if (board[i].length != 9) {
return false;
}
}

return true;
}

//检查每一行是否正常，即1～9中的数字只出现一次
private boolean checkAllTheRow(char[][] board) {
TreeSet<Integer> count = new TreeSet<>();

for (int i = 0; i < 9; ++i) {
for (int j = 0; j < 9; ++j) {
if (board[i][j] != '.') {
int temp = board[i][j] - '0';
if (temp < 1 || temp > 9 || count.contains(temp)) {
return false;
}
count.add(temp);
}
}
count.clear();
}

return true;
}

//检查每一列是否正常
private boolean checkAllTheColumn(char[][] board) {
TreeSet<Integer> count = new TreeSet<>();

for (int j = 0; j < 9; ++j) {
for (int i = 0; i < 9; ++i) {
if (board[i][j] != '.') {
int temp = board[i][j] - '0';
if (temp < 1 || temp > 9 || count.contains(temp)) {
return false;
}
count.add(temp);
}
}
count.clear();
}

return true;
}

//依次检查每一个独立的单元是否正常
private boolean checkAllUnits(char[][] board) {
int rowBegin = 0;
int columnBegin = 0;
for (int i = 0; i < 3; ++i) {
for (int j = 0; j < 3; ++j) {
if (!checkUnit(board, rowBegin, columnBegin)) {
return false;
}
columnBegin += 3;
}
rowBegin += 3;
columnBegin = 0;
}

return true;
}

//检查一个独立的单元
private boolean checkUnit(char[][] board, int rowBegin, int columnBegin) {
TreeSet<Integer> count = new TreeSet<>();

for (int i = rowBegin; i < rowBegin + 3; ++i) {
for (int j = columnBegin; j < columnBegin + 3; ++j) {
if (board[i][j] != '.') {
int temp = board[i][j] - '0';
if (temp < 1 || temp > 9 || count.contains(temp)) {
return false;
}
count.add(temp);
}
}
}

return true;
}
}

2、建立映射关系

public class Solution {
public boolean isValidSudoku(char[][] board) {
return isValid(board) && check(board);
}

private boolean isValid(char[][] board) {
if (board == null) {
return false;
}

if (board.length != 9) {
return false;
}

for (int i = 0; i < 9; ++i) {
if (board[i].length != 9) {
return false;
}
}

return true;
}

private boolean check(char[][] board) {
//row存储每一行的信息，column存储每一列的信息，unit存储每个单元的信息
boolean row[][] = new boolean[9][9];
boolean column[][] = new boolean[9][9];
boolean unit[][] = new boolean[9][9];

for (int i = 0; i < 9; ++i) {
for(int j = 0; j < 9; ++j) {
if (board[i][j] == '.') {
continue;
}

int loc = board[i][j] - '1';
//这里就是每个单元的转换关系稍微复杂一点，稍微做一下计算即可理解
if (row[i][loc] || column[j][loc] || unit[(i/3) * 3 + j/3][loc]) {
return false;
}

row[i][loc] = true;
column[j][loc] = true;
unit[(i/3) * 3 + (j/3)][loc] = true;
}
}

return true;
}

}