Question

Given a unsorted sequence of a[1,…,n] of integers, give an O(nlogn) runtime algorithm to check there are two indices i and j such that a[i] =2*a[j]. The algorithm should return i=0 and j=2 on input 4,12,8,10 and false on input 4,3,1,11.

I think we have to sort the array anyways which is O(nlogn). I’m not sure what to do after that.

Answer 1

You’re right that the first step is sorting the array.

Once the array is sorted, you can find out whether a given element is inside the array in O(log n) time. So if for every of the n elements, you check for the inclusion of another element in O(log n) time, you end up with a runtime of O(n log n).

Does that help you?