## F5 Networks Interview Question for Software Engineer / Developers

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Country: United States
Interview Type: Phone Interview

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``````public int numberOfFactors(int n) {
int totalFactors = 0;
int i = 1;
while (i <= n) {
if (n % i == 0) {
totalFactors++;
}
i++;
}
return totalFactors;
}``````

Is the total number of factors of N to be returned, or return the actual factors as well?

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0
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``````-- Filter all factors of n
factorsOfN n = length \$ filter ((==0). mod n) [1..n]

-- filter all factors of n from 1..sqrt of n - 1 for squares
factorsOfN' n = (cSqrt - trSq) - 1 + 2*length (filter ((==0) . mod n) [2.. trSq])
where
trSq = truncate \$ sqrt \$ fI n
cSqrt = ceiling \$ sqrt \$ fI n``````

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0
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O(sqrt(n)) algorithm:

``````factors = 0
for i in range(int(ceil(sqrt(n)))):
if n % i == 0 and sqrt(n) != i:
factors += 2
elif n % i == 0:
factors += 1``````

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0
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Based on Anonymous's O(sqrt(n)) algorithm. Not entirely sure about the ceil(sqrt(n) + 0.0001) part though.

``````from math import *

def num_factors(n):
factors = 2
for i in range(2, int(ceil(sqrt(n) + 0.0001))):
if n % i == 0:
factors += 1 if i*i == n else 2
return factors

print num_factors(12)``````

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0.0001 is added to ensure sqrt(n) is included in the iteration. The for..range in Python is exclusive at the closing bound.

This is the most efficient solution btw.

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public int numberOfFactors(int n) {
int totalNumOfFacts = 0;
for(int i=1;i<=n/2;i++) {
if(n%i == 0)
totalNumOfFacts++;
}
return ++totalNumOfFacts;
}

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This solution has the best case scenario complexity of O(log(sqrt(n)). The worst case scenario takes O(sqrt(n)) time. The idea is to find prime factors and their numbers. Then we just need to calculate the numbers each prime factor occurs in the input number.

``````private int FactorsNumber(int n)
{
var m = n;
var res = 1;
for (int d = 2; d <= Math.Sqrt(m); d++)
{
var k = 1;
while (m % d == 0)
{
m /= d;
k++;
}
if (k > 1) res *= k;
}
if (m > 1) res *= 2;
return res - 1;
}``````

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