One-hot encoding a categorical column

The problem, from first principles

A column of city names, "NYC", "LA", "NYC", "Chicago", can't be fed directly into linear (this curriculum's very first question) or any matrix-multiply-based model, there's no meaningful numeric distance between "NYC" and "LA" the way there is between the number 3 and 5. Assigning NYC=0, LA=1, Chicago=2 doesn't fix this, it silently implies Chicago is "twice as far" from NYC as LA is, a completely fabricated numeric relationship that doesn't exist in the underlying category.

One-hot encoding sidesteps the problem entirely: instead of one arbitrary number per category, use one dedicated 0/1 column per possible category. No category is numerically "closer" to any other, every pairwise distance between two different categories is identical, exactly the "no fabricated relationship" property a categorical variable actually has.

From theory to code

Theory turns a length-n categorical column into an (n, k) binary matrix (k = number of distinct categories), one column per category, a single 1 per row marking that row's category. Implement the category-discovery step first, then the encoding itself, built to accept an explicit category list (not just always deriving one fresh) for the reason Theory's PyTorch section explains.

Implement get_unique_categories(column) and one_hot_encode(column, categories=None) against that reasoning. The signatures and docstrings are already in the editor.

Constraints

• get_unique_categories returns categories in a fixed, sorted order (so encoding is reproducible).
• one_hot_encode's output shape is (len(column), len(categories)).
• Every row of the output sums to exactly 1 (exactly one category per row).
• If categories is passed explicitly, use it as-is, don't recompute from column.

Hints

Open one at a time. Each gives away a little more than the last.