Question

JAVA What is the running time required for repeatedly splitting a problem into two equally sized halves, assuming no additional work needs to be done?

		O(1)
		O(log10N)
		O(log2N)
		O(log2N)
		O(N)
		O(N log N)
		O(N2)
		O(N3)
		O(Nk)
		O(2N)
		O(N!)

Answer 1

Recursive formula for repeatedly splitting a problem into two equally sized halves, assuming no additional work needs to be done
T(n) = T(n/2) + 1
     = T(n/4) + 1 + 1
     = T(n/8) + 1 + 1 + 1
     ......
     ......
     ......
     = T(n/n) + 1 + .... + 1 + 1 + 1 [log(n) +1 terms]
     = 1 + 1 + .... + 1 + 1 + 1 [log(n) +1 terms]
     = log2(n)
     = O(log2n)

O(log2N)