How should I practice Allocate Workers for a Production Ratio?

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Problem · Array

Allocate Workers for a Production Ratio

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Problem statement

A factory must produce two products in a fixed quantity ratio. You are given positive integers total, firstRatio, secondRatio, firstRate, and secondRate.

The factory must produce exactly total items.
The first and second product quantities must have ratio firstRatio : secondRatio.
One first-product worker produces firstRate items per day.
One second-product worker produces secondRate items per day.

The ratio divides total exactly, and each product quantity is divisible by its corresponding per-worker rate. Return a two-element integer array containing the required first-product worker count followed by the required second-product worker count.

Function

allocateWorkers(total: int, firstRatio: int, secondRatio: int, firstRate: int, secondRate: int) → int[]

Examples

Example 1

total = 2160firstRatio = 2secondRatio = 1firstRate = 18secondRate = 24return = [80,30]

The ratio has three total parts, so the product quantities are 2160 * 2 / 3 = 1440 and 2160 * 1 / 3 = 720. The required worker counts are 1440 / 18 = 80 and 720 / 24 = 30.

Example 2

total = 1000firstRatio = 3secondRatio = 2firstRate = 20secondRate = 25return = [30,16]

The product quantities are 600 and 400. Dividing by the corresponding daily rates gives 30 and 16 workers.

Example 3

total = 630firstRatio = 1secondRatio = 2firstRate = 7secondRate = 14return = [30,30]

The two product quantities are 210 and 420. Although the quantities differ, the rates make both worker counts equal to 30.

Constraints

1 <= total, firstRatio, secondRatio, firstRate, secondRate <= 10^9.
firstRatio + secondRatio <= 2 * 10^9.
total * firstRatio and total * secondRatio fit in a signed 64-bit integer.
total * firstRatio and total * secondRatio are each divisible by firstRatio + secondRatio.
Each resulting product quantity is divisible by its corresponding per-worker rate.