No Cent Left Behind

Algorithm

Medium

rounding

decimal

allocation

No Cent Left Behind

Finance rejected a posting this morning because it did not balance: an invoice-level charge of 0.99 was spread over six lines, each line got its proportional share rounded to the cent — and the six line amounts added up to 1.02. Three phantom cents, invented by rounding. Business Central faces this exact problem every time it distributes VAT or an invoice discount across lines, and it always closes the books to the cent.

Your job is that allocation algorithm in miniature: split a total across lines in proportion to their weights so that the rounded line amounts add up to exactly the total, with no line drifting more than a cent from its fair share.

Requirements

Create a codeunit named "Penny Allocator" with one public procedure:

procedure Allocate(TotalAmount: Decimal; Weights: List of [Decimal]): List of [Decimal]

What you may rely on — the tests never violate this:

TotalAmount is always an exact multiple of 0.01. It can be positive or negative — credit memos allocate too.
Weights contains at least one entry, every weight is >= 0, and at least one weight is > 0. Weights are not necessarily whole numbers and do not sum to anything special.

What the returned list must guarantee — all four are graded:

Exactly one amount per weight, in the same order: the amount at position i belongs to the weight at position i.
Every amount is an exact multiple of 0.01.
The amounts sum to exactly TotalAmount — not a cent more, not a cent less.
Every amount differs from its line's exact share — TotalAmount × Weight ÷ (sum of all Weights) — by strictly less than 0.01.

Guarantee 4 has teeth: a line with weight 0 must get exactly 0.00, a line whose exact share is already a whole number of cents must get exactly that share, and dumping the whole rounding difference on a single line fails the moment the drift exceeds one cent. More than one classic strategy satisfies all four guarantees — any of them passes.

What the tests check

The tests call Allocate and verify all four guarantees on fixed cases — a single line, weights that divide evenly, the classic three-way split of 100.00, 0.03 across two equal lines, 0.99 across six equal lines where every exact share ends in half a cent, a zero-weight line, and a negative credit-memo total — plus one invoice with a randomized total and weights, so hardcoding the examples fails. Sum comparisons are exact, and the per-line drift check is strict (< 0.01).

Learn More

Hint 1

Round each line's exact share on its own and add the results up: three equal lines of 100.00 hand out 99.99, and six lines whose shares all end in half a cent hand out 1.02 for a 0.99 invoice. The residual is not a rare edge case — it appears whenever the shares don't divide evenly.

Hint 2

Fixing the books by parking the whole difference on one line breaks guarantee 4: across many lines the drift can grow to several cents, and that line ends up more than a cent away from its fair share. The correction has to be spread over the lines.

Hint 3

Two classic strategies satisfy all four guarantees. Largest remainder: round every share down, then hand one extra cent each to the lines with the biggest discarded fractions until the total balances. Running total (BC's own VAT-rounding trick): walk the lines keeping the exact cumulative share, and give each line the rounded cumulative share minus everything you have already handed out.

ALBusiness Central 28.4

Press Compile to check your code compiles — Submit runs the tests.

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