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How are empty cells represented on a Sudoku board?
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Empty cells are represented by a '.'.
Why are empty cells ignored during the validation process of a Sudoku board?
Empty cells are ignored because only filled cells need to be validated to check for duplicates. The placement of '1-9' in filled cells determines the board's validity.
What space complexity is involved in validating a Sudoku board?
The space complexity is O(9²) for storing the seen numbers in hash sets and hash maps.
What is the initial step in the algorithm for validating a Sudoku board?
The initial step is to traverse each row and ensure no duplicates using hash sets.
Explain how to determine which 3x3 sub-box a particular cell belongs to.
Derive the row and column index of the sub-box by integer division of the cell's row and column index by 3.
How does the use of hash maps improve the code readability and efficiency for Sudoku validation?
Hash maps simplify the tracking process by organizing seen numbers systematically, making the code cleaner and more efficient.
How do you handle edge cases like cell (8,8) while determining sub-box indexing?
Cell (8,8) will map to sub-box (2,2) using integer division (8//3 = 2).
What is the purpose of using a hash set for each row and each column during Sudoku validation?
The hash set ensures that each digit 1-9 appears only once in each row and column.
Why is it sufficient to use integer division by 3 for indexing sub-boxes?
Integer division by 3 clusters indices into groups of 3 (i.e., 0, 1, 2), allowing easy mapping of cells to their sub-boxes.
What approach should be used for effectively verifying the 3x3 sub-boxes on the Sudoku board?
Use hash sets for each sub-box keyed by row and column divided by 3; traverse the board to populate hash sets and check for duplicates.
Describe the verification process for rows and columns in the Sudoku board.
Traverse each row and column, add seen numbers to their respective hash sets, and check for duplicates.
What time complexity is involved in validating a Sudoku board?
The time complexity is O(N²) where N is 9 (i.e., O(9²)).
In what situation should the Sudoku validation procedure return false?
The procedure should return false if any duplicates are detected in rows, columns, or sub-boxes.
What are the three main rules that a 9x9 Sudoku board must follow to be considered valid?
1. Each row must contain digits 1-9 without repetition. 2. Each column must contain digits 1-9 without repetition. 3. Each 3x3 sub-box must contain digits 1-9 without repetition.
What data structure is primarily used to keep track of seen numbers for rows, columns, and sub-boxes during validation?
Hash sets are used to track seen numbers.
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