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
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:
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#!/usr/bin/pydef 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" |
