Valid Sudoku

Question: 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.

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

Example 1:

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:

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.

You may view the full question here.

Approach 1: Let’s try the simple approach of checking all the possibilities —

//Approach 1:
//Runtime: 3ms
//Memory usage: 45.3MB
class Solution {
    public boolean isValidSudoku(char[][] board) {
        return allRows(board) && allColumns(board) && subSets(board);
    }
    
    private boolean subSets(char[][] board){
        int[] iS = new int[]{0,3,6};
        int[] iE = new int[]{2,5,8};
        for(int i = 0; i<=2; i++){
            for(int j = 0; j<=2; j++){
                if(!check(board, iS[i], iE[i], iS[j], iE[j])){
                    return false;
                }
            }
        }
        return true;
    }
    
    private boolean allRows(char[][] board){
        int max = board.length - 1;
        for(int r = 0; r<=max; r++){
            if(!check(board, r, r, 0, max)){
                return false;
            }
        }
        return true;
    }
    
    private boolean allColumns(char[][] board){
        int max = board.length - 1;
        for(int c = 0; c<=max; c++){
            if(!check(board, 0, max, c, c)){
                return false;
            }
        }
        return true;
    }
    
    private boolean check(char[][] board, int rS, int rE, int cS, int cE){
        HashMap<Character, Integer> map = new HashMap();
        for(int r = rS; r<=rE; r++){
            for(int c =cS; c<=cE; c++){
                if(board[r][c]!='.'){
                    if(map.containsKey(board[r][c])){
                    return false;
                }
                map.put(board[r][c], 1);   
                }                
            }
        }
        return true;    
    }
}

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Cheers & Chao!