Question

36. Valid Sudoku

中文文档

Description

Determine if a 9 x 9 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 nine 3 x 3 sub-boxes of the grid must contain the digits 1-9 without repetition.

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.

 

Example 1:

Input: board = 
[["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:

Input: board = 
[["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.

 

Constraints:

• board.length == 9
• board[i].length == 9
• board[i][j] is a digit 1-9 or '.'.

Solutions

Solution 1: Traversal once

The valid sudoku satisfies the following three conditions:

• The digits are not repeated in each row;
• The digits are not repeated in each column;
• The digits are not repeated in each $3 \times 3$ box.

Traverse the sudoku, for each digit, check whether the row, column and $3 \times 3$ box it is in have appeared the digit. If it is, return false. If the traversal is over, return true.

The time complexity is $O(C)$ and the space complexity is $O(C)$, where $C$ is the number of empty spaces in the sudoku. In this question, $C=81$.

class Solution:
  def isValidSudoku(self, board: List[List[str]]) -> bool:
    row = [[False] * 9 for _ in range(9)]
    col = [[False] * 9 for _ in range(9)]
    sub = [[False] * 9 for _ in range(9)]
    for i in range(9):
      for j in range(9):
        c = board[i][j]
        if c == '.':
          continue
        num = int(c) - 1
        k = i // 3 * 3 + j // 3
        if row[i][num] or col[j][num] or sub[k][num]:
          return False
        row[i][num] = True
        col[j][num] = True
        sub[k][num] = True
    return True

class Solution {
  public boolean isValidSudoku(char[][] board) {
    boolean[][] row = new boolean[9][9];
    boolean[][] col = new boolean[9][9];
    boolean[][] sub = new boolean[9][9];
    for (int i = 0; i < 9; ++i) {
      for (int j = 0; j < 9; ++j) {
        char c = board[i][j];
        if (c == '.') {
          continue;
        }
        int num = c - '0' - 1;
        int k = i / 3 * 3 + j / 3;
        if (row[i][num] || col[j][num] || sub[k][num]) {
          return false;
        }
        row[i][num] = true;
        col[j][num] = true;
        sub[k][num] = true;
      }
    }
    return true;
  }
}

class Solution {
public:
  bool isValidSudoku(vector<vector<char>>& board) {
    vector<vector<bool>> row(9, vector<bool>(9, false));
    vector<vector<bool>> col(9, vector<bool>(9, false));
    vector<vector<bool>> sub(9, vector<bool>(9, false));
    for (int i = 0; i < 9; ++i) {
      for (int j = 0; j < 9; ++j) {
        char c = board[i][j];
        if (c == '.') continue;
        int num = c - '0' - 1;
        int k = i / 3 * 3 + j / 3;
        if (row[i][num] || col[j][num] || sub[k][num]) {
          return false;
        }
        row[i][num] = true;
        col[j][num] = true;
        sub[k][num] = true;
      }
    }
    return true;
  }
};

func isValidSudoku(board [][]byte) bool {
  row, col, sub := [9][9]bool{}, [9][9]bool{}, [9][9]bool{}
  for i := 0; i < 9; i++ {
    for j := 0; j < 9; j++ {
      num := board[i][j] - byte('1')
      if num < 0 || num > 9 {
        continue
      }
      k := i/3*3 + j/3
      if row[i][num] || col[j][num] || sub[k][num] {
        return false
      }
      row[i][num] = true
      col[j][num] = true
      sub[k][num] = true
    }
  }
  return true
}

function isValidSudoku(board: string[][]): boolean {
  const row: boolean[][] = Array.from({ length: 9 }, () =>
    Array.from({ length: 9 }, () => false),
  );
  const col: boolean[][] = Array.from({ length: 9 }, () =>
    Array.from({ length: 9 }, () => false),
  );
  const sub: boolean[][] = Array.from({ length: 9 }, () =>
    Array.from({ length: 9 }, () => false),
  );
  for (let i = 0; i < 9; ++i) {
    for (let j = 0; j < 9; ++j) {
      const num = board[i][j].charCodeAt(0) - '1'.charCodeAt(0);
      if (num < 0 || num > 8) {
        continue;
      }
      const k = Math.floor(i / 3) * 3 + Math.floor(j / 3);
      if (row[i][num] || col[j][num] || sub[k][num]) {
        return false;
      }
      row[i][num] = true;
      col[j][num] = true;
      sub[k][num] = true;
    }
  }
  return true;
}

/**
 * @param {character[][]} board
 * @return {boolean}
 */
var isValidSudoku = function (board) {
  const row = [...Array(9)].map(() => Array(9).fill(false));
  const col = [...Array(9)].map(() => Array(9).fill(false));
  const sub = [...Array(9)].map(() => Array(9).fill(false));
  for (let i = 0; i < 9; ++i) {
    for (let j = 0; j < 9; ++j) {
      const num = board[i][j].charCodeAt() - '1'.charCodeAt();
      if (num < 0 || num > 8) {
        continue;
      }
      const k = Math.floor(i / 3) * 3 + Math.floor(j / 3);
      if (row[i][num] || col[j][num] || sub[k][num]) {
        return false;
      }
      row[i][num] = true;
      col[j][num] = true;
      sub[k][num] = true;
    }
  }
  return true;
};