Product (∏)
The problem, from first principles
01-summation-notation's Σ accumulates by adding. ∏ (capital pi) is the exact same accumulation pattern, just multiplying instead — and it shows up wherever probabilities of independent events combine (the likelihood of a whole dataset is a product of per-example probabilities) or wherever a count is built up multiplicatively (a factorial, covered next, is itself a ∏).
From theory to code
Implement product(f, lo, hi), computing ∏_{i=lo}^{hi} f(i) — call f once per integer i from lo to hi inclusive, and multiply the results together. The signature and docstring are already in the editor.
Constraints
loandhiare integers;himay be less thanlo, in which case the product is empty (the standard mathematical convention: an empty product is1, not0— multiplying by nothing should leave a value unchanged, exactly like adding nothing leaves a sum unchanged at0).ftakes a single integer and returns a number (int or float).
Hints
Hint 1
Structurally identical to 01-summation-notation's loop — only the accumulator's starting value (1 instead of 0) and the combining operation (*= instead of +=) differ.
Hint 2
Starting the accumulator at 1 is exactly what makes the empty-range case correctly return 1 with no special-cased branch, the same way starting at 0 did for summation's empty case.
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