Recursion Backtracking Combinatorics
Intermediate Level

Implement the sudokuValidPlacementCount method that counts how many filled Sudoku cells are validly placed.

The input contains a Sudoku-style board and its size n.

Your task is to count how many filled positions are valid according to the placement rules. A filled value is valid when the same value does not appear again in its row, column, or related box area.

Empty cells are represented by . and are not treated as fixed duplicate values. The final count tells how many board positions pass the validity check.

Example 1
Input:
board (char[][]) = [[5,3,.],[6,.,.],[.,9,8]]
n (int) = 3
Return:
(int) 7
Example 2
Input:
board (char[][]) = [[1,2,3],[4,5,6],[7,8,9]]
n (int) = 3
Return:
(int) 9
Example 3
Input:
board (char[][]) = [[1,1,3],[4,5,6],[7,8,9]]
n (int) = 3
Return:
(int) 7

Check every filled cell against the rest of the board.

For each non-empty cell, compare its value with other cells in the same row and column. In a normal Sudoku board, you should also compare it with cells in the same sub-box. If another cell with the same value is found in any restricted area, that placement is not valid.

Count only the positions that pass the duplicate check.

Pseudocode:

function sudokuValidPlacementCount(board, n):
    count = 0
    for row from 0 to n - 1:
        for col from 0 to n - 1:
            if board[row][col] == '.':
                continue
            if isValidPlacement(row, col, board[row][col]):
                count++
    return count
function isValidPlacement(row, col, value):
    for each other column in the same row:
        if board[row][otherColumn] == value:
            return false
    for each other row in the same column:
        if board[otherRow][col] == value:
            return false
    check the related box area if required
    return true
Run your code to see the result.