I need a clear, well-commented algorithm that automatically assigns colors to every cube in a fixed 5 × 5 grid so that no two cubes sharing a face end up with the same color. Because I’m letting the engine pick from an unrestricted, truly random pool of colors, your job is to focus solely on adjacency conflict-checking and minimal color reuse, not on matching a predefined palette. Here’s what I expect from you: • A concise explanation of the logic you choose (graph-coloring, backtracking, greedy, etc.) and why it suits a 25-cube layout. • Either language-agnostic pseudocode or working code in the language of your choice that I can drop straight into the rendering layer of the game. • A brief complexity analysis covering time and space so I know how it will scale if I later move to larger grids. Acceptance will be based on clean, readable code (or pseudocode), correctness when tested across multiple randomized runs, and an explanation that demonstrates you’ve considered edge cases such as minimal color sets and performance under rapid re-draws.