Instructions

Paint by number (also known as color by number) are black-and-white pictures meant for coloring. The different areas of the picture are annotated with different numbers, the numbers correspond to specific colors in a predefined color palette. The goal is to fill the areas with the right colors, revealing a beautiful colorful picture at the end. It's a relaxing activity for both kids and adults.

You have been tasked with writing a paint-by-number app in Elixir. You want your app to be able to import and export pictures in a custom data format. You have decided to use binary files to store your picture data.

Let's imagine you have a picture of a smiley, like the one shown below. The picture has a white background. The smiley has a black border and a yellow fill color.

This picture uses 3 colors. Let's say we assign indices to those colors:

• 0 (binary: 0b00) for white,
• 1 (binary: 0b01) for black,
• 2 (binary: 0b10) for yellow.

We can now use those color indices to represent the color of each pixel.

1. Calculate palette bit size

Implement the PaintByNumber.palette_bit_size/1 function. It should take the count of colors in the palette and return how many bits are necessary to represent that many color indices as binary numbers. Color indices always start at 0 and are continuous ascending integers.

For example, representing 13 different colors require 4 bits. 4 bits can store up to 16 color indices (2^4). 3 bits would not be enough because 3 bits can only store up to 8 color indices (2^3).

Note: there is no log2 function in the Elixir standard library. You will later learn how to use Erlang libraries from Elixir where you can find this function. Now, solve this task with recursion and the power operator ** instead.

2. Create an empty picture

Implement the PaintByNumber.empty_picture/0 function. It should return an empty bitstring.

3. Create a test picture

A predefined test picture will be used for manual testing of basic features of your app. The test picture consists of 4 pixels with 4 different colors.

Implement the PaintByNumber.test_picture/0 function. It should return a bitstring that consists of 4 segments. Each segment should have a bit size of 2. The segments should have values 0, 1, 2, and 3.

4. Prepend a pixel to a picture

Implement the PaintByNumber.prepend_pixel/3 function. It should take three arguments: a bitstring with the picture to which we're prepending, the count of colors in the palette, and the index of the color for the new pixel. It should return a bitstring with a picture with the new pixel added to the beginning.

5. Get the first pixel from a picture

Implement the PaintByNumber.get_first_pixel/2 function. It should take two arguments: a bitstring with the picture from which we're reading, and the count of colors in the palette. It should return the color index of the first pixel in the given picture. When given an empty picture, it should return nil.

6. Drop the first pixel from a picture

Implement the PaintByNumber.drop_first_pixel/2 function. It should take two arguments: a bitstring with the picture from which we're removing a pixel, and the count of colors in the palette. It should return the picture without the first pixel. When given an empty picture, it should return an empty picture.

7. Concatenate two pictures

Implement the PaintByNumber.concat_pictures/2 function. It should take two arguments, two bitstrings. It should return a bitstring that is the result of prepending the first argument to the second argument.