Checkerboard Resolution Python Codewars

Task

In this kata we will be counting the the black squares on a special checkerboard. It is special because it has a resolution which determines how the black and white squares are laid out.

The resolution refers to the dimensions of squares of a single colour. See below for an example with dimensions 11x6:

With resolution = 1:

Number of black squares = 33

And now with resolution = 2:

Number of black squares = 32

And one more example, resolution = 5:

Number of black squares = 31

_{^{Credit to awesomead for the pretty images!}}

As you may have noticed the top left square is always white, and we are counting the INDIVIDUAL black squares on the board.

Task

You are required to write a function that will take in three parameters:

• width -> The width of the board
• height -> The height of the board
• resolution -> The size of the coloured squares on the checkerboard (as shown above)

And returns the total count of all individual black squares.

Additional Info

• All inputs will be valid
• 0 <= width <= 10**32
• 0 <= height <= 10**32
• 1 <= resolution <= 10**32

Solution:

def count_checkerboard(width, height, resolution):
    p = resolution * 2
    sw = width // p * resolution + min(width % p, resolution)
    print(sw)
    sh = height // p * resolution + min(height % p, resolution)
    print(sh)
    return (width - sw) * sh + sw * (height - sh)

print(count_checkerboard(9, 5, 2))

Training on Checkerboard Resolution | Codewars

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