Set & Function

The problem, from first principles

ML papers write things like f: ℝⁿ → ℝᵐ, x ∈ ℝⁿ, A ⊆ B, and argmax_i f(i) constantly, without ever pausing to define them — they're assumed background, the same way for and if are assumed background in code. This question makes the two most operationally useful pieces concrete: ⊆ (subset), which shows up in "is this a valid choice from the allowed set," and argmax, which shows up everywhere a model has to pick the single best option out of many (classification's predicted class, a search algorithm's best move, a language model's next token under greedy decoding).

From theory to code

Implement is_subset(a, b), checking whether every element of set a is also in set b, then argmax(values), returning the index of the largest value. The signatures and docstrings are already in the editor.

Constraints

a and b are Python set objects for is_subset.
values is a non-empty list or tuple of numbers for argmax.
If more than one value is tied for the maximum, return the first such index (matching NumPy's np.argmax convention).

Hints

Hint 1

is_subset(a, b) is one line using Python's own set operations — no explicit loop needed, though writing the loop version once is worth doing mentally to see what the operator is actually checking.

Hint 2

For argmax, track both the best value seen so far and its index as you scan once through values; only update when you find something strictly greater, which is exactly what keeps the first tied index instead of the last.

The problem, from first principles

From theory to code

Constraints

Hints

Keywords