0%

LeetCode 036 Valid Sudoku

发表于 更新于 分类于

Description

Determine if a 9x9 Sudoku board is valid. Only the filled cells need to be validated according to the following rules:

  1. Each row must contain the digits 1-9 without repetition.
  2. Each column must contain the digits 1-9 without repetition.
  3. Each of the 9 3x3 sub-boxes of the grid must contain the digits 1-9 without repetition.

pic

A partially filled sudoku which is valid.

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

Example 1:

1
2
3
4
5
6
7
8
9
10
11
12
13
Input:
[
  ["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"]
]
Output: true

Example 2:

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Input:
[
  ["8","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"]
]
Output: false
Explanation: Same as Example 1, except with the 5 in the top left corner being 
    modified to 8. Since there are two 8's in the top left 3x3 sub-box, it is invalid.

Note:

  • A Sudoku board (partially filled) could be valid but is not necessarily solvable.
  • Only the filled cells need to be validated according to the mentioned rules.
  • The given board contain only digits 1-9 and the character ‘.’.
  • The given board size is always 9x9.

Difficulty: Medium

Code:

1
2
3
4
5
class Solution {
    public boolean isValidSudoku(char[][] board) {
        
    }
}

题意

判断9x9的数独棋盘是否有效，要求满足以下条件：

  1. 每一行必须包含1-9，不能重复
  2. 每一列必须包含1-9，不能重复
  3. 每个3x3的格子必须包含1-9，不能重复

另外请注意

  1. 数独棋盘已经填充的部分要求有效但不要求能解出来
  2. 只有已经填充的格子才需要验证是否符合上述条件
  3. 棋盘只包含1-9和字符.
  4. 棋盘大小是9x9

Solution 1

准备三个set，分别记录各行、各列、各小方阵是否出现某个数字，下标需要转换。

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
class Solution {
    public boolean isValidSudoku(char[][] board) {
        for(int i=0;i<9;i++){
            Set<Character> row = new HashSet<Character>();
            Set<Character> column = new HashSet<Character>();
            Set<Character> block = new HashSet<Character>();
            for(int j=0;j<9;j++){
                if(board[i][j]!='.'&&!row.add(board[i][j])){
                    return false;
                }
                if(board[j][i]!='.'&&!column.add(board[j][i])){
                    return false;
                }
                int rowIndex = 3*(i/3);
                int colIndex = 3*(i%3);
                if(board[rowIndex+j/3][colIndex+j%3]!='.'&&!block.add(board[rowIndex+j/3][colIndex+j%3])){
                    return false;
                }
            }
        }
        return true;
    }
}

时间复杂度: O()。

空间复杂度: O()。

Solution 2

用一个set保存数字分别在行row、列column、块block中的值的字符串形式，若相同的数在同一行、同一列、同一块再次出现，则添加到set中会返回false，依次来判断是否有效。

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
class Solution {
    public boolean isValidSudoku(char[][] board) {
        Set<String> set = new HashSet<String>();
        for(int i=0;i<9;i++){
            for(int j=0;j<9;j++){
                char num = board[i][j];
                if(num=='.') continue;
                if(!set.add(num+" in row "+i)||
                   !set.add(num+" in column "+j)||
                   !set.add(num+" in block "+i/3+"-"+j/3)){
                    return false;
                }
            }
        }
        return true;
    }
}

时间复杂度: O()。

空间复杂度: O()。