Cells in a matrix

You are given an integer $N$ denoting an $N\times N$ matrix. Initially, each cell of the matrix is empty. You are given $K$ tasks. In each task, you are given a cell $(i,j)$ where cell $(i,j)$ represents the $i^{th}$ row and $j^{th}$ column of the given matrix.

You have to perform each task sequentially in the given order. Each task is described in cell $(i,j)$. For each task, you have to place $X$ in each cell of row $i$ and each cell column $j$. After you complete each task, you are required to print the number of empty cells in the matrix.

Example:

Input:  N=3, K=3, grid[][] = { { 1, 1 }, { 1, 3 }, { 3, 2 } };
Output: 4 2 0 

Approach

Java

public class CellsInMatrix {
    public static void main(String[] args) {
        int N = 3;
        int K = 3;

        boolean arr_row[] = new boolean[N];
        boolean arr_column[] = new boolean[N];
        int arr_row_remaining_blocks = N;
        int arr_column_remaining_blocks = N;
        int grid[][] = { { 1, 1 }, { 1, 3 }, { 3, 2 } };
        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < K; i++) {
            int row = grid[i][0] - 1;
            int column = grid[i][1] - 1;

            if (!arr_row[row]) {
                arr_row[row] = true;
                arr_row_remaining_blocks--;
            }

            if (!arr_column[column]) {
                arr_column[column] = true;
                arr_column_remaining_blocks--;
            }

            sb.append((long) arr_row_remaining_blocks * (long) arr_column_remaining_blocks + " ");
        }
        System.out.print(sb.toString());

    }
}