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36. Valid Sudoku – Leetcode Solutions

Declan Clarke

Description:

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.

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

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: 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.

Solution in Python:

To determine if a 9×9 Sudoku board is valid, we need to check three main conditions:

  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 3×3 sub-boxes of the grid must contain the digits 1-9 without repetition.

We can achieve this by iterating through the board and using sets to keep track of the digits we’ve seen in each row, column, and sub-box. If we encounter a duplicate digit in any of these, the board is invalid.

Python
class Solution:
    def isValidSudoku(self, board: List[List[str]]) -> bool:
        # Initialize sets to keep track of seen numbers in rows, columns, and sub-boxes
        rows = [set() for _ in range(9)]
        cols = [set() for _ in range(9)]
        boxes = [set() for _ in range(9)]
        
        for i in range(9):
            for j in range(9):
                num = board[i][j]
                if num == '.':
                    continue
                
                # Calculate the index for the 3x3 sub-box
                box_index = (i // 3) * 3 + (j // 3)
                
                # Check if the number is already in the row, column or box
                if num in rows[i]:
                    return False
                if num in cols[j]:
                    return False
                if num in boxes[box_index]:
                    return False
                
                # Add the number to the respective sets
                rows[i].add(num)
                cols[j].add(num)
                boxes[box_index].add(num)
        
        # If no conflicts were found, the board is valid
        return True

Detailed Explanation:

  1. Initialize Sets:
    • We create three lists of sets: rows, cols, and boxes. Each list contains 9 sets (one for each row, column, and 3×3 sub-box).
  2. Iterate Through the Board:
    • We use nested loops to iterate over each cell in the 9×9 board.
  3. Skip Empty Cells:
    • If the cell contains ‘.’, we skip it because it does not need to be validated.
  4. Calculate Box Index:
    • We calculate the index for the 3×3 sub-box using the formula (i // 3) * 3 + (j // 3). This ensures that cells in the same 3×3 sub-box get the same index.
  5. Check for Duplicates:
    • We check if the number already exists in the corresponding row, column, or box set.
    • If it does, we return False immediately as the board is invalid.
  6. Add Number to Sets:
    • If the number is not a duplicate, we add it to the respective sets for the row, column, and box.
  7. Return True:
    • If we finish checking all cells without finding any duplicates, we return True, indicating the board is valid.

Solution in Javascript:

JavaScript
/**
 * @param {character[][]} board
 * @return {boolean}
 */
var isValidSudoku = function(board) {
    // Initialize sets to keep track of seen numbers in rows, columns, and sub-boxes
    const rows = Array.from({ length: 9 }, () => new Set());
    const cols = Array.from({ length: 9 }, () => new Set());
    const boxes = Array.from({ length: 9 }, () => new Set());

    // Iterate over each cell in the 9x9 board
    for (let i = 0; i < 9; i++) {
        for (let j = 0; j < 9; j++) {
            const num = board[i][j];
            // Skip empty cells
            if (num === '.') continue;

            // Calculate the index for the 3x3 sub-box
            const boxIndex = Math.floor(i / 3) * 3 + Math.floor(j / 3);

            // Check if the number is already in the row, column or box
            if (rows[i].has(num)) return false;
            if (cols[j].has(num)) return false;
            if (boxes[boxIndex].has(num)) return false;

            // Add the number to the respective sets
            rows[i].add(num);
            cols[j].add(num);
            boxes[boxIndex].add(num);
        }
    }

    // If no conflicts were found, the board is valid
    return true;
};

Solution in Java:

Java
class Solution {
    public boolean isValidSudoku(char[][] board) {
        // Initialize sets to keep track of seen numbers in rows, columns, and sub-boxes
        Set<Character>[] rows = new HashSet[9];
        Set<Character>[] cols = new HashSet[9];
        Set<Character>[] boxes = new HashSet[9];

        // Instantiate the sets
        for (int i = 0; i < 9; i++) {
            rows[i] = new HashSet<>();
            cols[i] = new HashSet<>();
            boxes[i] = new HashSet<>();
        }

        // Iterate over each cell in the 9x9 board
        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                char num = board[i][j];
                // Skip empty cells
                if (num == '.') continue;

                // Calculate the index for the 3x3 sub-box
                int boxIndex = (i / 3) * 3 + (j / 3);

                // Check if the number is already in the row, column or box
                if (rows[i].contains(num)) return false;
                if (cols[j].contains(num)) return false;
                if (boxes[boxIndex].contains(num)) return false;

                // Add the number to the respective sets
                rows[i].add(num);
                cols[j].add(num);
                boxes[boxIndex].add(num);
            }
        }

        // If no conflicts were found, the board is valid
        return true;
    }
}

Solution in C#:

C#
public class Solution {
    public bool IsValidSudoku(char[][] board) {
        // Initialize sets to keep track of seen numbers in rows, columns, and sub-boxes
        HashSet<char>[] rows = new HashSet<char>[9];
        HashSet<char>[] cols = new HashSet<char>[9];
        HashSet<char>[] boxes = new HashSet<char>[9];

        // Instantiate the sets
        for (int i = 0; i < 9; i++) {
            rows[i] = new HashSet<char>();
            cols[i] = new HashSet<char>();
            boxes[i] = new HashSet<char>();
        }

        // Iterate over each cell in the 9x9 board
        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                char num = board[i][j];
                // Skip empty cells
                if (num == '.') continue;

                // Calculate the index for the 3x3 sub-box
                int boxIndex = (i / 3) * 3 + (j / 3);

                // Check if the number is already in the row, column or box
                if (rows[i].Contains(num)) return false;
                if (cols[j].Contains(num)) return false;
                if (boxes[boxIndex].Contains(num)) return false;

                // Add the number to the respective sets
                rows[i].Add(num);
                cols[j].Add(num);
                boxes[boxIndex].Add(num);
            }
        }

        // If no conflicts were found, the board is valid
        return true;
    }
}

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