HackerRank ‘Sherlock and GCD’ Solution

Short Problem Definition:

Sherlock is stuck while solving a problem: Given an array A={a1,a2,..aN}, he wants to know if there exists a subset, B={ai1,ai2,…aik} where 1≤i1<i2<…<ik≤N…

Link

Sherlock and GCD

Complexity:

time complexity is O(N);

space complexity is O(1)

Execution:

A subset has no common divisor if the GCD equals 1. There is an interesting fact that leads to my solution: If any subset has GCD 1, any bigger set containing this set will also have GCD 1. Therefore GCD(a,b,c,d) = GCD(GCD(GCD(a,b),c),d). This is easily generated by python reduce.

Beware: The problem statement allows n==1.

Solution:

#!/usr/bin/py
def gcd(a, b):
    if a % b == 0:
        return b
    else:
        return gcd(b, a % b)

def multiple_gcd(numbers):
    return reduce(lambda x,y: gcd(x,y), numbers)

if __name__ == '__main__':
    t = input()
    for _ in xrange(t):
        n = input()
        values = map(int, raw_input().split())
        if len(values) < 2:
            print "NO"
            continue
        if (multiple_gcd(values) == 1):
            print "YES"
        else:
            print "NO"