How should I practice Count Divisible Power Sums?

Start by reading the full statement, solve the visible examples, then compare the pattern against related GoodScore onsite interview problems in FastPrep.

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Count Divisible Power Sums

GoodScore● MediumFULLTIMEONSITE INTERVIEW

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Problem statement

For every exponent triple (x, y, z) with 0 <= x <= maxExponent2, 0 <= y <= maxExponent3, and 0 <= z <= maxExponent5, form 2^x + 3^y + 5^z.

Return the number of exponent triples whose formed number is divisible by divisor.

Different exponent triples are counted separately, even if they produce the same numeric sum.

Implement countDivisiblePowerSums with integer parameters maxExponent2, maxExponent3, maxExponent5, and divisor. Return the number of valid triples as a long.

Function

countDivisiblePowerSums(maxExponent2: int, maxExponent3: int, maxExponent5: int, divisor: int) → long

Examples

Example 1

maxExponent2 = 0maxExponent3 = 0maxExponent5 = 0divisor = 3return = 1

The only triple is (0, 0, 0), producing 1 + 1 + 1 = 3, which is divisible by 3.

Example 2

maxExponent2 = 1maxExponent3 = 1maxExponent5 = 0divisor = 2return = 2

The triples (1, 0, 0) and (1, 1, 0) produce 4 and 6. The other two sums are odd.

Example 3

maxExponent2 = 2maxExponent3 = 2maxExponent5 = 2divisor = 5return = 7

Seven of the 27 exponent triples have a power sum congruent to 0 modulo 5.

Constraints

0 <= maxExponent2, maxExponent3, maxExponent5 <= 2000
1 <= divisor <= 2000
The answer fits in a signed 64-bit integer.