Number of Black Blocks
You are given two integers m and n representing the dimensions of a 0-indexed m x n grid.
You are also given a 0-indexed 2D integer matrix coordinates, where coordinates[i] = [x, y] indicates that the cell with coordinates [x, y] is colored black. All cells in the grid that do not appear in coordinates are white.
A block is defined as a 2 x 2 submatrix of the grid. More formally, a block with cell [x, y] as its top-left corner where 0 <= x < m - 1 and 0 <= y < n - 1 contains the coordinates [x, y], [x + 1, y], [x, y + 1], and [x + 1, y + 1].
Return a 0-indexed integer array arr of size 5 such that arr[i] is the number of blocks that contains exactly i black cells.
Example 1
Input
m = 3, n = 3, coordinates = [[0,0]]Output
[3,1,0,0,0]There is only 1 block with one black cell, and the other 3 blocks have zero black cells, so the result is [3,1,0,0,0].
Example 2
Input
m = 3, n = 3, coordinates = [[0,0],[1,1],[0,2]]Output
[0,2,2,0,0]There are 2 blocks with two black cells and 2 blocks with one black cell, so the result is [0,2,2,0,0].
Constraints
- 2 <= m <= 10^5
- 2 <= n <= 10^5
- 0 <= coordinates.length <= 10^4
- coordinates[i].length == 2
- 0 <= coordinates[i][0] < m
- 0 <= coordinates[i][1] < n
- It is guaranteed that coordinates contains pairwise distinct coordinates.