Code RoomDivisor count function
MediumPrep Room Coding #1407

Divisor count function

CodingAlgorithms & data structuresMid–Senior~20 min

Return the number of positive divisors of n (the divisor-count function tau(n)), for n up to about 10^12. Counting by looping to n is far too slow; instead factorize n by trial division up to sqrt(n), and use that if n = product of p_i^e_i, then tau(n) = product of (e_i + 1). Return 0 for n <= 0.

Implement
count_divisors(n: int) → int
Examples
in[12]out6
What a strong answer looks like

State your approach and its time/space complexity out loud before you optimize. Handle the edge cases (empty input, duplicates, overflow), and say why you chose this over the brute force. Green tests are the floor, not the grade.

0:00 of about 20 min
InputExpectedGot
[12]6not run yetsample