What is the optimal time complexity of solving Valid Sudoku?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Valid Sudoku?

The space complexity is O(n) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Valid Sudoku?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Valid Sudoku?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Valid Sudoku

Learn how to solve the 'Valid Sudoku' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

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.

Write a function isValidSudoku(board: List[List[str]]) -> bool.

Constraints

•board.length == 9
•board[i].length == 9
•board[i][j] is a digit 1-9 or '.'

Examples

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

No row, column, or 3x3 sub-box contains a duplicate digit.

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

The digit 8 appears twice in the first column (rows 0 and 3) and twice in the top-left 3x3 sub-box.

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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