GuilinDev

Lc0036

05 August 2008

36 Valid Sudoku

原体概述

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


A partially filled sudoku which is valid.

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

1
'.'
.

Example 1:

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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:

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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
    
    1-9
    
    and the character
    1
    
    '.'
    
    .
  • The given board size is always
    1
    
    9x9
    
    .

题意和分析

一个数独表里面已经填了一些数字,没填数字的cell用’.’表示,检查目前这个数独表是否有效。检查的方式是是行,列和3X3的小方块,对二维数组进行遍历,遍历每一行的时候,新建3个HashSet,来检查该行,该行/该列和该cube对应的set是否含有数字,注意,HashSet的add()方法是有返回值的。

代码

3个HashSets

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class Solution {
    public boolean isValidSudoku(char[][] board) {
        if (board == null || board.length == 0 || board[0].length == 0) {
            return false;
        }
        
        int m = board.length;
        int n = board[0].length;
        
        for (int i = 0; i < m; i++) {
            HashSet<Character> rows = new HashSet<>();
            HashSet<Character> cols = new HashSet<>();
            HashSet<Character> cube = new HashSet<>();
            
            for (int j = 0; j < n; j++) {
                
                char chRow = board[i][j];
                //判断current字符是否不在1~9范围之内
                if (chRow != '.' && (chRow < '1' || chRow > '9')) {
                    return false;
                }
                //check row
                if (chRow != '.' && !rows.add(chRow)) {
                    return false;
                }
                
                //check col
                char chCol = board[j][i];
                if (chCol != '.' && !cols.add(chCol)) {
                    return false;
                }
                
                // 得到cube中的坐標
                int cubeIndexX = 3 * (i / 3) + j / 3;
                int cubeIndexY = 3 * (i % 3) + j % 3;
                //check the cube
                if (board[cubeIndexX][cubeIndexY] != '.' && !cube.add(board[cubeIndexX][cubeIndexY])) {
                    return false;
                }
            }
        }
        return true;
    }
}

3个hashMaps

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class Solution {
  public boolean isValidSudoku(char[][] board) {
    // init data
    HashMap<Integer, Integer> [] rows = new HashMap[9];
    HashMap<Integer, Integer> [] columns = new HashMap[9];
    HashMap<Integer, Integer> [] boxes = new HashMap[9];
    for (int i = 0; i < 9; i++) {
      rows[i] = new HashMap<Integer, Integer>();
      columns[i] = new HashMap<Integer, Integer>();
      boxes[i] = new HashMap<Integer, Integer>();
    }

    // validate a board
    for (int i = 0; i < 9; i++) {
      for (int j = 0; j < 9; j++) {
        char num = board[i][j];
        if (num != '.') {
          int n = (int)num;
          int box_index = (i / 3 ) * 3 + j / 3;

          // keep the current cell value
          rows[i].put(n, rows[i].getOrDefault(n, 0) + 1);
          columns[j].put(n, columns[j].getOrDefault(n, 0) + 1);
          boxes[box_index].put(n, boxes[box_index].getOrDefault(n, 0) + 1);

          // check if this value has been already seen before
          if (rows[i].get(n) > 1 || columns[j].get(n) > 1 || boxes[box_index].get(n) > 1)
            return false;
        }
      }
    }

    return true;
  }
}