How can we find second maximum from array efficiently?

Question

Is it possible to find the second maximum number from an array of integers by traversing the array only once?

As an example, I have a array of five integers from whi

Answer 1

The upper bound should have be n+log2⁡n−2, but it bigger than O(n) in case of random selection algorithm, but in worst case it much smaller. The solution might be

1. build a tree like to find the MAX element with n - 1 comparisons

   max(N) / \ max(N/2) max(N/2)

2. remove the MAX and find the MAX again log2n - 1 comparison

PS. It uses additional memory, but it faster than random selection algorithm in worst case.