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Valid Sudoku

Certification: Basic Level Accuracy: 50% Submissions: 2 Points: 10

Write a Java program to 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 digits 1-9 without repetition.
2. Each column must contain digits 1-9 without repetition.
3. Each of the nine 3x3 sub-boxes of the grid must contain 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 rules mentioned.
- The Sudoku board is represented as a 9x9 char array where '.' represents empty cells.

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
    •  
  • Explanation: 
       
    • Step 1: Create data structures to track digits in each row, column, and 3x3 sub-box.
      •  
    • Step 2: Iterate through each cell in the 9x9 Sudoku board.
      •  
    • Step 3: For each filled cell (non-'.'), check if the digit already exists in the current row.
      •  
    • Step 4: Check if the digit already exists in the current column.
      •  
    • Step 5: Check if the digit already exists in the current 3x3 sub-box.
      •  
    • Step 6: No duplicates are found in any row, column, or sub-box, so the board is valid.
      •  
    •
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: 
       
    • Step 1: Create data structures to track digits in each row, column, and 3x3 sub-box.
      •  
    • Step 2: Start iterating through the Sudoku board.
      •  
    • Step 3: Notice that the first cell of the first row contains '8'.
      •  
    • Step 4: Later, in the first cell of the fourth row, we find another '8'.
      •  
    • Step 5: Since the digit '8' appears twice in the first column, this violates rule #2.
      •  
    • Step 6: Return false as the board is invalid.
      •  
    •
Constraints
     
  • board.length == 9
    •  
  • board[i].length == 9
    •  
  • board[i][j] is a digit 1-9 or '.'
    •  
  • Time Complexity: O(1) - since the board size is fixed at 9x9
    •  
  • Space Complexity: O(1) - using fixed-size data structures
    •
NumberAccentureHCL Technologies
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Hint
Solution

Solution Hints

    
  
  • Use three separate sets of data structures to track digits in each row, column, and 3x3 sub-box
    • 
  
  • You can use boolean arrays or HashSets to track seen digits
    • 
  
  • For the 3x3 sub-boxes, you need to map each cell (i,j) to its corresponding sub-box index
    • 
  
  • Skip empty cells (represented by '.')
    • 
  
  • Return false as soon as you encounter a violation of any rule
    •

Steps to solve by this approach:

 Step 1: Create three 2D boolean arrays to track digits seen in each row, column, and 3x3 box.
 Step 2: Iterate through each cell in the 9x9 board.
 Step 3: Skip empty cells (represented by '.').
 Step 4: For filled cells, convert the digit to a 0-8 index for our boolean arrays.
 Step 5: Calculate the box index using the formula (i/3)*3 + j/3.
 Step 6: Check if the current digit has already been seen in the current row, column, or box.
 Step 7: If the digit has been seen, return false (invalid Sudoku); otherwise, mark the digit as seen and continue.

Submitted Code :