Short Problem Definition:
You will be given two arrays of integers and asked to determine all integers that satisfy the following two conditions:
- The elements of the first array are all factors of the integer being considered
- The integer being considered is a factor of all elements of the second array
Link
Complexity:
time complexity is O(A\* (N+M))
space complexity is O(1)
Execution:
This challenge could also be solved using the Greatest Common Divisor. Given that the range of values is only [1,100], it is safe to assume that the naive solution will terminate within the time limit.
Solution:
#!/bin/python
import sys
def isValid(a, b, candidate):
for a_ele in a:
if candidate % a_ele != 0:
return False
for b_ele in b:
if b_ele % candidate != 0:
return False
return True
n,m = raw_input().strip().split(' ')
n,m = [int(n),int(m)]
a = map(int,raw_input().strip().split(' '))
b = map(int,raw_input().strip().split(' '))
cnt = 0
for candidate in xrange(max(a), min(b)+1):
if isValid(a, b, candidate):
cnt += 1
print cnt