LeetCode //C - 36. Valid Sudoku

36. Valid Sudoku

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

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.

Constraints:

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

From: LeetCode
Link: 36. Valid Sudoku

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Solution:

Ideas：

• Iterate through each cell in the board.
• For each non-empty cell, check if its value violates the Sudoku rules.
• The Sudoku rules require that each number (1-9) must not repeat in the same row, the same column, or the same 3x3 box.
• We can use three 9x9 boolean matrices to track the existence of numbers in rows, columns, and boxes. The first matrix, rows, tracks numbers in each row, the second matrix, cols, tracks numbers in each column, and the third matrix, boxes, tracks numbers in each box.
• If we find a number that has already existed in the current row, column, or box, return false. If we successfully go through the board without finding any duplicates, return true.

Code:

bool isValidSudoku(char** board, int boardSize, int* boardColSize){
    bool rows[9][9] = {0};
    bool cols[9][9] = {0};
    bool boxes[9][9] = {0};

    for(int i = 0; i < 9; i++){
        for(int j = 0; j < 9; j++){
            if(board[i][j] != '.'){
                int num = board[i][j] - '1'; // subtract '1' to fit in 0-8 index
                int box_index = (i / 3) * 3 + j / 3; // map the box position to the box index
                
                // Check if this value has already been recorded in the current row, column, or box
                if(rows[i][num] || cols[j][num] || boxes[box_index][num]){
                    return false;
                }
                
                // Record the existence of the number in the current row, column, and box
                rows[i][num] = true;
                cols[j][num] = true;
                boxes[box_index][num] = true;
            }
        }
    }

    return true;
}