1. Define the categorizedColors object: The algorithm starts by defining an object categorizedColors with properties for primary, secondary, tertiary, background, text, and accent colors. Initially, all these properties are set to null.

2. Sort the input colors by perceived brightness: The input array colors is sorted in ascending order of perceived brightness using the formula (r * 299 + g * 587 + b * 114) / 1000, where r, g, and b are the red, green, and blue values of the color, respectively. This formula approximates how humans perceive the brightness of a color.

3. Assign the background color: The darkest color from the sorted array (sortedColors[0]) is assigned to categorizedColors.background.

4. Find the most visually distinct colors: The findBestCombination function is used to assign the primary, secondary, and tertiary colors. It does this by iterating over the remaining colors (excluding the background color) and calculating the color distance between each remaining color and the already assigned colors in categorizedColors. The color with the maximum distance is selected as the best color for the current category (primary, secondary, or tertiary). This ensures that the selected colors are visually distinct from each other.

5. Assign the text color: The findContrastingColor function is used to assign the text color. It takes the background color and an array of remaining colors as input. It iterates over the remaining colors and finds the color with the maximum contrast (brightness difference) from the background color, ensuring that it's not equal to any of the primary, secondary, or tertiary colors.

6. Assign the accent color: The accent color is assigned as the lightest remaining color from the input array. This is done by creating an array accentColors that contains all the remaining colors that haven't been assigned to any other category (primary, secondary, tertiary, background, or text), and then assigning the last color in the accentColors array (which will be the lightest color due to the sorting) to categorizedColors.accent.

The core functionality of the algorithm is achieved through the following helper functions:

• calculateColorDistance: This function calculates the maximum color distance between a given color and the already assigned colors in categorizedColors. It does this by iterating over the assigned colors and calculating the Euclidean distance between the given color and each assigned color in the RGB color space. The maximum distance is returned.

• getColorDistance: This function calculates the Euclidean distance between two colors in the RGB color space using the formula sqrt((r1 - r2)^2 + (g1 - g2)^2 + (b1 - b2)^2), where r1, g1, b1 and r2, g2, b2 are the red, green, and blue values of the two colors, respectively.

• findContrastingColor: This function takes a base color and an array of sorted colors as input. It iterates over the sorted colors and finds the color with the maximum contrast (brightness difference) from the base color. The contrast is calculated as the absolute difference between the perceived brightness of the base color and the sorted color. The color with the maximum contrast is returned, ensuring that it's not equal to the base color.

By following these steps and using the helper functions, the algorithm assigns visually distinct colors to the primary, secondary, and tertiary properties, finds a contrasting color for the text property, and assigns the lightest remaining color as the accent color. The background color is set to the darkest color from the input array. The algorithm ensures that all assigned colors are present in the input array, and it satisfies the business cases of having the text color distinct from primary, secondary, and tertiary, and the accent color being the lightest remaining color.