/*
36. Valid Sudoku
Medium - 63.6%

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
*/

import java.util.HashSet;
import java.util.Set;

class Solution {
    public boolean isValidSudoku(char[][] board) {
        // Use sets to track seen numbers in rows, columns, and boxes
        Set<Character>[] rows = new HashSet[9];
        Set<Character>[] cols = new HashSet[9];
        Set<Character>[] boxes = new HashSet[9];
        
        // Initialize sets
        for (int i = 0; i < 9; i++) {
            rows[i] = new HashSet<>();
            cols[i] = new HashSet<>();
            boxes[i] = new HashSet<>();
        }
        
        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                char num = board[i][j];
                if (num == '.') continue;
                
                // Calculate box index: (row/3)*3 + col/3
                int boxIndex = (i / 3) * 3 + j / 3;
                
                // Check if number already exists in row, column, or box
                if (rows[i].contains(num) || cols[j].contains(num) || boxes[boxIndex].contains(num)) {
                    return false;
                }
                
                // Add number to respective sets
                rows[i].add(num);
                cols[j].add(num);
                boxes[boxIndex].add(num);
            }
        }
        
        return true;
    }
}