How should I practice Count Power Products in Range?

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Problem · Math

Count Power Products in Range

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Problem statement

Given two integers low and high, count how many integers in the inclusive range [low, high] can be written in the form 3^x * 5^y, where x and y are non-negative integers.

Each valid value should be counted once, even if there is only one way to generate it. The value 1 is valid because 1 = 3⁰ * 5⁰.

Function

countPowerProductsInRange(low: long, high: long) → int

Complete the function countPowerProductsInRange in the editor below.

countPowerProductsInRange has the following parameters:

long low: the lower bound of the range
long high: the upper bound of the range

Returns

int: the number of integers in [low, high] that can be expressed as 3^x * 5^y.

Examples

Example 1

low = 1high = 15return = 5

The valid numbers in the range are 1, 3, 5, 9, 15. Therefore, the answer is 5.

Example 2

low = 16high = 100return = 5

The valid numbers in the range are 25, 27, 45, 75, 81. Therefore, the answer is 5.

Constraints

The source thread did not provide explicit numeric bounds.

x and y are non-negative integers.
Only values within the inclusive range [low, high] should be counted.
Implementations should avoid overflow when generating powers of 3 and 5.