# HackerRank 'Identify Smith Numbers' Solution

Martin Kysel · June 23, 2015

##### Short Problem Definition:

A Smith number is a composite number, the sum of whose digits is the sum of the digits of its prime factors obtained as a result of prime factorization (excluding 1). The first few such numbers are 4, 22, 27, 58, 85, 94, and 121.

Identify Smith Numbers

##### Complexity:

time complexity is `O(sqrt(N))`

space complexity is `O(sqrt(N))`

##### Execution:

There are many ways how to compute the prime composition of a number. I selected one with two optimization steps, there are many more. If there were many numbers to check I would use the Sieve of Eratosthenes to pre-compute the primes. The rest of the solution is straight forward. Do not forget that prime factors can also contain multiple digits.

##### Solution:
``````
#!/usr/bin/py
def factors(n):
f, fs = 3, []
while n % 2 == 0:
fs.append(2)
n /= 2
while f * f <= n:
while n % f == 0:
fs.append(f)
n /= f
f += 2
if n > 1: fs.append(n)
return fs

def getIntLetterCount(n):
return sum([int(l) for l in list(str(n))])

def isSmithNumber(n):
return sum([getIntLetterCount(f) for f in factors(n)]) == getIntLetterCount(n)

if __name__ == '__main__':
n = input()

if isSmithNumber(n):
print 1
else:
print 0
``````